LMFDB - Embedded newform 931.2.v.a.422.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [931,2,Mod(177,931)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(931, base_ring=CyclotomicField(18))

chi = DirichletCharacter(H, H._module([6, 14]))

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

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

chi := DirichletCharacter("931.177");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 931 = 7^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	931.v (of order $9$, degree $6$, not 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:	$7.43407242818$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\Q(\zeta_{18})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{3} + 1 $ x^6 - x^3 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			422.1
Root			$-0.173648 - 0.984808i$ of defining polynomial
Character	$\chi$	$=$	931.422
Dual form			931.2.v.a.214.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.673648 - 0.565258i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-0.0812519 + 0.460802i) q^{6} +(1.41875 + 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +O(q^{10})$	\(q+(0.673648 - 0.565258i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-0.0812519 + 0.460802i) q^{6} +(1.41875 + 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.70574 + 2.95442i) q^{11} +(-0.326352 - 0.565258i) q^{12} +(0.918748 - 5.21048i) q^{13} +(-1.03209 - 0.866025i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(-0.286989 - 1.62760i) q^{17} +(1.19459 + 2.06910i) q^{18} +(-4.34002 + 0.405223i) q^{19} -3.10607 q^{20} +(0.520945 + 2.95442i) q^{22} +(-1.65270 + 0.601535i) q^{23} +(-1.41875 - 0.516382i) q^{24} +(-1.32635 + 0.482753i) q^{25} +(-2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(3.25877 - 1.18610i) q^{29} -1.18479 q^{30} -1.94356 q^{31} +(-5.29813 + 1.92836i) q^{32} +(-0.315207 - 1.78763i) q^{33} +(-1.11334 - 0.934204i) q^{34} +(-3.13176 - 1.13987i) q^{36} +(0.418748 - 0.725293i) q^{37} +(-2.69459 + 2.72621i) q^{38} +(1.40760 + 2.43804i) q^{39} +(-5.50387 + 4.61830i) q^{40} +(0.779715 + 4.42198i) q^{41} +(3.67752 - 3.08580i) q^{43} +(-3.20574 - 2.68993i) q^{44} -6.87939 q^{45} +(-0.773318 + 1.33943i) q^{46} +(-0.124485 + 0.705990i) q^{47} +(-0.0209445 + 0.00762319i) q^{48} +(-0.620615 + 1.07494i) q^{50} +(0.673648 + 0.565258i) q^{51} +(6.09879 + 2.21978i) q^{52} +(-1.06031 + 6.01330i) q^{53} +(-2.51367 - 0.914901i) q^{54} +(-8.11721 - 2.95442i) q^{55} +(1.63041 - 1.64955i) q^{57} +(1.52481 - 2.64106i) q^{58} +(1.86824 + 10.5953i) q^{59} +(1.26604 - 1.06234i) q^{60} +(4.12449 - 1.50119i) q^{61} +(-1.30928 + 1.09861i) q^{62} +(-2.52094 + 4.36640i) q^{64} +13.3969 q^{65} +(-1.22281 - 1.02606i) q^{66} +(10.8871 + 9.13538i) q^{67} +2.02734 q^{68} +(0.467911 - 0.810446i) q^{69} +(-10.5398 + 8.84397i) q^{71} +(-7.24422 + 2.63668i) q^{72} +(5.75877 - 4.83218i) q^{73} +(-0.127889 - 0.725293i) q^{74} +(0.375515 - 0.650411i) q^{75} +(0.434945 - 5.32926i) q^{76} +(2.32635 + 0.846723i) q^{78} +(6.54323 + 2.38154i) q^{79} +(-0.0184183 + 0.104455i) q^{80} +(-6.13816 - 2.23411i) q^{81} +(3.02481 + 2.53812i) q^{82} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(0.733078 - 4.15749i) q^{86} +(-0.922618 + 1.59802i) q^{87} -9.68004 q^{88} +(1.74897 + 1.46756i) q^{89} +(-4.63429 + 3.88863i) q^{90} +(-0.374638 - 2.12467i) q^{92} +(0.792204 - 0.664738i) q^{93} +(0.315207 + 0.545955i) q^{94} +(-2.91875 - 10.6442i) q^{95} +(1.50000 - 2.59808i) q^{96} +(-1.71301 - 0.623485i) q^{97} +(-7.10014 - 5.95772i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9	$ 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9} - 3 q^{12} + 3 q^{13} + 3 q^{15} + 9 q^{16} + 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} - 12 q^{23} - 6 q^{24} - 9 q^{25} - 15 q^{26} - 6 q^{27} - 3 q^{29} + 18 q^{31} - 18 q^{32} - 9 q^{33} - 24 q^{36} - 12 q^{38} + 12 q^{39} - 9 q^{40} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 30 q^{45} - 18 q^{46} + 12 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{54} - 18 q^{55} + 24 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} + 24 q^{65} - 18 q^{66} + 6 q^{67} - 30 q^{68} + 12 q^{69} - 6 q^{71} + 15 q^{72} + 12 q^{73} - 30 q^{74} + 15 q^{75} - 36 q^{76} + 15 q^{78} + 24 q^{79} - 12 q^{80} - 3 q^{81} - 9 q^{82} - 48 q^{86} + 21 q^{87} - 18 q^{88} - 15 q^{89} - 18 q^{90} + 42 q^{92} - 36 q^{93} + 9 q^{94} - 15 q^{95} + 9 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9 - 3 * q^12 + 3 * q^13 + 3 * q^15 + 9 * q^16 + 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 - 12 * q^23 - 6 * q^24 - 9 * q^25 - 15 * q^26 - 6 * q^27 - 3 * q^29 + 18 * q^31 - 18 * q^32 - 9 * q^33 - 24 * q^36 - 12 * q^38 + 12 * q^39 - 9 * q^40 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 30 * q^45 - 18 * q^46 + 12 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^54 - 18 * q^55 + 24 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 + 24 * q^65 - 18 * q^66 + 6 * q^67 - 30 * q^68 + 12 * q^69 - 6 * q^71 + 15 * q^72 + 12 * q^73 - 30 * q^74 + 15 * q^75 - 36 * q^76 + 15 * q^78 + 24 * q^79 - 12 * q^80 - 3 * q^81 - 9 * q^82 - 48 * q^86 + 21 * q^87 - 18 * q^88 - 15 * q^89 - 18 * q^90 + 42 * q^92 - 36 * q^93 + 9 * q^94 - 15 * q^95 + 9 * q^96 - 18 * q^97 + 9 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/931\mathbb{Z}\right)^\times$.

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{1}{9}\right)$

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 $

$2$	0.673648	−	0.565258i	0.476341	−	0.399698i	−0.372760	−	0.927928i	$-0.621589\pi$
$2$	0.673648	−	0.565258i	0.476341	−	0.399698i	0.849101	+	0.528230i	$0.177144\pi$
$3$	−0.407604	+	0.342020i	−0.235330	+	0.197465i	−0.752825	−	0.658221i	$-0.771309\pi$
$3$	−0.407604	+	0.342020i	−0.235330	+	0.197465i	0.517495	+	0.855686i	$0.326865\pi$
$4$	−0.213011	+	1.20805i	−0.106506	+	0.604023i
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	0.910069	+	0.414457i	$0.136028\pi$
$5$	0.439693	+	2.49362i	0.196637	+	1.11518i	−0.713432	+	0.700724i	$0.752860\pi$
$6$	−0.0812519	+	0.460802i	−0.0331710	+	0.188122i
$7$		0			0
$7$		0			0
$8$	1.41875	+	2.45734i	0.501603	+	0.868802i
$9$	−0.471782	+	2.67561i	−0.157261	+	0.891869i
$10$	1.70574	+	1.43128i	0.539401	+	0.452612i
$11$	−1.70574	+	2.95442i	−0.514299	+	0.890792i	0.485563	+	0.874202i	$0.338615\pi$
$11$	−1.70574	+	2.95442i	−0.514299	+	0.890792i	−0.999862	+	0.0165906i	$0.994719\pi$
$12$	−0.326352	−	0.565258i	−0.0942097	−	0.163176i
$13$	0.918748	−	5.21048i	0.254815	−	1.44513i	−0.541733	−	0.840551i	$-0.682231\pi$
$13$	0.918748	−	5.21048i	0.254815	−	1.44513i	0.796547	−	0.604576i	$-0.206657\pi$
$14$		0			0
$15$	−1.03209	−	0.866025i	−0.266484	−	0.223607i
$16$	0.0393628	+	0.0143269i	0.00984071	+	0.00358173i
$17$	−0.286989	−	1.62760i	−0.0696051	−	0.394750i	−0.999629	−	0.0272501i	$-0.991325\pi$
$17$	−0.286989	−	1.62760i	−0.0696051	−	0.394750i	0.930024	−	0.367500i	$-0.119786\pi$
$18$	1.19459	+	2.06910i	0.281568	+	0.487690i
$19$	−4.34002	+	0.405223i	−0.995669	+	0.0929645i
$19$	−4.34002	+	0.405223i	−0.995669	+	0.0929645i
$20$	−3.10607			−0.694538
$21$		0			0
$22$	0.520945	+	2.95442i	0.111066	+	0.629885i
$23$	−1.65270	+	0.601535i	−0.344613	+	0.125429i	−0.508527	−	0.861046i	$-0.669810\pi$
$23$	−1.65270	+	0.601535i	−0.344613	+	0.125429i	0.163915	+	0.986474i	$0.447588\pi$
$24$	−1.41875	−	0.516382i	−0.289601	−	0.105406i
$25$	−1.32635	+	0.482753i	−0.265270	+	0.0965505i
$26$	−2.32635	−	4.02936i	−0.456235	−	0.790222i
$27$	−1.52094	−	2.63435i	−0.292706	−	0.506982i
$28$		0			0
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	−0.0212363	−	0.999774i	$-0.506760\pi$
$29$	3.25877	−	1.18610i	0.605138	−	0.220252i	0.626375	+	0.779522i	$0.284538\pi$
$30$	−1.18479			−0.216313
$31$	−1.94356			−0.349074			−0.174537	−	0.984651i	$-0.555843\pi$
$31$	−1.94356			−0.349074			−0.174537	+	0.984651i	$0.555843\pi$
$32$	−5.29813	+	1.92836i	−0.936587	+	0.340890i
$33$	−0.315207	−	1.78763i	−0.0548706	−	0.311187i
$34$	−1.11334	−	0.934204i	−0.190936	−	0.160215i
$35$		0			0
$36$	−3.13176	−	1.13987i	−0.521960	−	0.189978i
$37$	0.418748	−	0.725293i	0.0688418	−	0.119237i	−0.829550	−	0.558433i	$-0.811403\pi$
$37$	0.418748	−	0.725293i	0.0688418	−	0.119237i	0.898392	+	0.439195i	$0.144736\pi$
$38$	−2.69459	+	2.72621i	−0.437121	+	0.442250i
$39$	1.40760	+	2.43804i	0.225397	+	0.390399i
$40$	−5.50387	+	4.61830i	−0.870238	+	0.730217i
$41$	0.779715	+	4.42198i	0.121771	+	0.690598i	0.983173	+	0.182675i	$0.0584755\pi$
$41$	0.779715	+	4.42198i	0.121771	+	0.690598i	−0.861402	+	0.507923i	$0.830413\pi$
$42$		0			0
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	−0.317768	−	0.948169i	$-0.602933\pi$
$43$	3.67752	−	3.08580i	0.560816	−	0.470581i	0.878584	+	0.477588i	$0.158489\pi$
$44$	−3.20574	−	2.68993i	−0.483283	−	0.405523i
$45$	−6.87939			−1.02552
$46$	−0.773318	+	1.33943i	−0.114020	+	0.197488i
$47$	−0.124485	+	0.705990i	−0.0181580	+	0.102979i	−0.992540	−	0.121921i	$-0.961095\pi$
$47$	−0.124485	+	0.705990i	−0.0181580	+	0.102979i	0.974382	+	0.224900i	$0.0722056\pi$
$48$	−0.0209445	+	0.00762319i	−0.00302308	+	0.00110031i
$49$		0			0
$50$	−0.620615	+	1.07494i	−0.0877682	+	0.152019i
$51$	0.673648	+	0.565258i	0.0943296	+	0.0791519i
$52$	6.09879	+	2.21978i	0.845750	+	0.307828i
$53$	−1.06031	+	6.01330i	−0.145644	+	0.825991i	0.821203	+	0.570636i	$0.193303\pi$
$53$	−1.06031	+	6.01330i	−0.145644	+	0.825991i	−0.966847	+	0.255354i	$0.917808\pi$
$54$	−2.51367	−	0.914901i	−0.342067	−	0.124502i
$55$	−8.11721	−	2.95442i	−1.09452	−	0.398374i
$56$		0			0
$57$	1.63041	−	1.64955i	0.215954	−	0.218488i
$58$	1.52481	−	2.64106i	0.200218	−	0.346788i
$59$	1.86824	+	10.5953i	0.243224	+	1.37939i	0.824581	+	0.565744i	$0.191411\pi$
$59$	1.86824	+	10.5953i	0.243224	+	1.37939i	−0.581356	+	0.813649i	$0.697478\pi$
$60$	1.26604	−	1.06234i	0.163446	−	0.137147i
$61$	4.12449	−	1.50119i	0.528086	−	0.192208i	−0.0641974	−	0.997937i	$-0.520449\pi$
$61$	4.12449	−	1.50119i	0.528086	−	0.192208i	0.592284	+	0.805730i	$0.298227\pi$
$62$	−1.30928	+	1.09861i	−0.166278	+	0.139524i
$63$		0			0
$64$	−2.52094	+	4.36640i	−0.315118	+	0.545801i
$65$	13.3969			1.66168
$66$	−1.22281	−	1.02606i	−0.150518	−	0.126299i
$67$	10.8871	+	9.13538i	1.33007	+	1.11606i	0.984060	+	0.177835i	$0.0569094\pi$
$67$	10.8871	+	9.13538i	1.33007	+	1.11606i	0.346014	+	0.938229i	$0.387535\pi$
$68$	2.02734			0.245851
$69$	0.467911	−	0.810446i	0.0563299	−	0.0975662i
$70$		0			0
$71$	−10.5398	+	8.84397i	−1.25085	+	1.04959i	−0.254252	+	0.967138i	$0.581829\pi$
$71$	−10.5398	+	8.84397i	−1.25085	+	1.04959i	−0.996595	+	0.0824479i	$0.973726\pi$
$72$	−7.24422	+	2.63668i	−0.853740	+	0.310736i
$73$	5.75877	−	4.83218i	0.674013	−	0.565564i	−0.240237	−	0.970714i	$-0.577225\pi$
$73$	5.75877	−	4.83218i	0.674013	−	0.565564i	0.914250	+	0.405150i	$0.132781\pi$
$74$	−0.127889	−	0.725293i	−0.0148668	−	0.0843136i
$75$	0.375515	−	0.650411i	0.0433607	−	0.0751030i
$76$	0.434945	−	5.32926i	0.0498916	−	0.611308i
$77$		0			0
$78$	2.32635	+	0.846723i	0.263407	+	0.0958725i
$79$	6.54323	+	2.38154i	0.736171	+	0.267944i	0.682775	−	0.730629i	$-0.260773\pi$
$79$	6.54323	+	2.38154i	0.736171	+	0.267944i	0.0533965	+	0.998573i	$0.482995\pi$
$80$	−0.0184183	+	0.104455i	−0.00205923	+	0.0116785i
$81$	−6.13816	−	2.23411i	−0.682017	−	0.248234i
$82$	3.02481	+	2.53812i	0.334035	+	0.280289i
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	−0.788807	−	0.614641i	$-0.789301\pi$
$83$	1.25624	−	2.17588i	0.137891	−	0.238834i	0.926698	+	0.375807i	$0.122634\pi$
$84$		0			0
$85$	3.93242	−	1.43128i	0.426531	−	0.155244i
$86$	0.733078	−	4.15749i	0.0790499	−	0.448314i
$87$	−0.922618	+	1.59802i	−0.0989151	+	0.171326i
$88$	−9.68004			−1.03190
$89$	1.74897	+	1.46756i	0.185390	+	0.155561i	0.730760	−	0.682635i	$-0.239166\pi$
$89$	1.74897	+	1.46756i	0.185390	+	0.155561i	−0.545369	+	0.838196i	$0.683611\pi$
$90$	−4.63429	+	3.88863i	−0.488497	+	0.409897i
$91$		0			0
$92$	−0.374638	−	2.12467i	−0.0390587	−	0.221513i
$93$	0.792204	−	0.664738i	0.0821477	−	0.0689301i
$94$	0.315207	+	0.545955i	0.0325112	+	0.0563110i
$95$	−2.91875	−	10.6442i	−0.299457	−	1.09207i
$96$	1.50000	−	2.59808i	0.153093	−	0.265165i
$97$	−1.71301	−	0.623485i	−0.173930	−	0.0633053i	0.253587	−	0.967312i	$-0.418389\pi$
$97$	−1.71301	−	0.623485i	−0.173930	−	0.0633053i	−0.427517	+	0.904007i	$0.640612\pi$
$98$		0			0
$99$	−7.10014	−	5.95772i	−0.713591	−	0.598774i
$100$	−0.300660	−	1.70513i	−0.0300660	−	0.170513i
$101$	−7.44356	+	2.70924i	−0.740662	+	0.269579i	−0.684671	−	0.728852i	$-0.740054\pi$
$101$	−7.44356	+	2.70924i	−0.740662	+	0.269579i	−0.0559912	+	0.998431i	$0.517832\pi$
$102$	0.773318			0.0765699
$103$	0.0145479			0.00143345			0.000716725	−	1.00000i	$-0.499772\pi$
$103$	0.0145479			0.00143345			0.000716725		1.00000i	$0.499772\pi$
$104$	14.1074	−	5.13468i	1.38335	−	0.503497i
$105$		0			0
$106$	2.68479	+	4.65020i	0.260770	+	0.451667i
$107$	1.77719	+	3.07818i	0.171807	+	0.297579i	0.939052	−	0.343776i	$-0.111706\pi$
$107$	1.77719	+	3.07818i	0.171807	+	0.297579i	−0.767244	+	0.641355i	$0.778373\pi$
$108$	3.50640	−	1.27622i	0.337403	−	0.122805i
$109$	−6.92514	−	2.52055i	−0.663309	−	0.241425i	−0.0116444	−	0.999932i	$-0.503707\pi$
$109$	−6.92514	−	2.52055i	−0.663309	−	0.241425i	−0.651664	+	0.758508i	$0.725929\pi$
$110$	−7.13816	+	2.59808i	−0.680596	+	0.247717i
$111$	0.0773815	+	0.438852i	0.00734473	+	0.0416540i
$112$		0			0
$113$	7.37733			0.694000			0.347000	−	0.937865i	$-0.387200\pi$
$113$	7.37733			0.694000			0.347000	+	0.937865i	$0.387200\pi$
$114$	0.165907	−	2.03282i	0.0155387	−	0.190391i
$115$	−2.22668	−	3.85673i	−0.207639	−	0.359642i
$116$	0.738703	+	4.18939i	0.0685869	+	0.388976i
$117$	13.5077	+	4.91642i	1.24879	+	0.454523i
$118$	7.24763	+	6.08148i	0.667198	+	0.559846i
$119$		0			0
$120$	0.663848	−	3.76487i	0.0606008	−	0.343684i
$121$	−0.319078	−	0.552659i	−0.0290071	−	0.0502417i
$122$	1.92989	−	3.34267i	0.174724	−	0.302631i
$123$	−1.83022	−	1.53574i	−0.165026	−	0.138473i
$124$	0.414000	−	2.34791i	0.0371783	−	0.210849i
$125$	4.54323	+	7.86911i	0.406359	+	0.703835i
$126$		0			0
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	−0.985576	−	0.169233i	$-0.945871\pi$
$127$	−0.0175410	+	0.0994798i	−0.00155651	+	0.00882740i	0.984020	+	0.178060i	$0.0569822\pi$
$128$	−1.18820	−	6.73859i	−0.105023	−	0.595613i
$129$	−0.443563	+	2.51557i	−0.0390535	+	0.221484i
$130$	9.02481	−	7.57272i	0.791529	−	0.664171i
$131$	2.32635	−	1.95204i	0.203254	−	0.170551i	−0.535479	−	0.844549i	$-0.679869\pi$
$131$	2.32635	−	1.95204i	0.203254	−	0.170551i	0.738733	+	0.673998i	$0.235424\pi$
$132$	2.22668			0.193808
$133$		0			0
$134$	12.4979			1.07966
$135$	5.90033	−	4.95096i	0.507820	−	0.426111i
$136$	3.59240	−	3.01438i	0.308045	−	0.258481i
$137$	3.39306	−	19.2430i	0.289888	−	1.64404i	−0.397394	−	0.917648i	$-0.630085\pi$
$137$	3.39306	−	19.2430i	0.289888	−	1.64404i	0.687282	−	0.726390i	$-0.258803\pi$
$138$	−0.142903	−	0.810446i	−0.0121648	−	0.0689897i
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	0.632485	+	0.774573i	$0.282035\pi$
$139$	−2.67365	+	15.1630i	−0.226776	+	1.28611i	−0.859261	+	0.511537i	$0.829076\pi$
$140$		0			0
$141$	−0.190722	−	0.330341i	−0.0160617	−	0.0278197i
$142$	−2.10101	+	11.9154i	−0.176313	+	0.999922i
$143$	13.8268	+	11.6021i	1.15626	+	0.970215i
$144$	−0.0569038	+	0.0985603i	−0.00474198	+	0.00821336i
$145$	4.39053	+	7.60462i	0.364614	+	0.631529i
$146$	1.14796	−	6.51038i	0.0950055	−	0.538803i
$147$		0			0
$148$	0.786989	+	0.660362i	0.0646901	+	0.0542814i
$149$	3.53936	+	1.28822i	0.289956	+	0.105535i	0.482903	−	0.875674i	$-0.339582\pi$
$149$	3.53936	+	1.28822i	0.289956	+	0.105535i	−0.192947	+	0.981209i	$0.561805\pi$
$150$	−0.114685	−	0.650411i	−0.00936399	−	0.0531058i
$151$	7.29813	+	12.6407i	0.593914	+	1.02869i	0.993699	+	0.112080i	$0.0357513\pi$
$151$	7.29813	+	12.6407i	0.593914	+	1.02869i	−0.399786	+	0.916609i	$0.630915\pi$
$152$	−7.15317	−	10.0900i	−0.580199	−	0.818409i
$153$	4.49020			0.363011
$154$		0			0
$155$	−0.854570	−	4.84651i	−0.0686407	−	0.389281i
$156$	−3.24510	+	1.18112i	−0.259816	+	0.0945653i
$157$	−9.74897	−	3.54834i	−0.778053	−	0.283188i	−0.0776922	−	0.996977i	$-0.524755\pi$
$157$	−9.74897	−	3.54834i	−0.778053	−	0.283188i	−0.700360	+	0.713789i	$0.746977\pi$
$158$	5.75402	−	2.09429i	0.457765	−	0.166613i
$159$	−1.62449	−	2.81369i	−0.128830	−	0.223140i
$160$	−7.13816	−	12.3636i	−0.564321	−	0.977432i
$161$		0			0
$162$	−5.39780	+	1.96464i	−0.424091	+	0.154357i
$163$	−2.02229			−0.158398			−0.0791989	−	0.996859i	$-0.525236\pi$
$163$	−2.02229			−0.158398			−0.0791989	+	0.996859i	$0.525236\pi$
$164$	−5.50805			−0.430106
$165$	4.31908	−	1.57202i	0.336240	−	0.122381i
$166$	−0.383666	−	2.17588i	−0.0297783	−	0.168881i
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.969720	+	0.244218i	$0.0785312\pi$
$167$	17.8157	+	14.9491i	1.37862	+	1.15680i	0.408898	+	0.912580i	$0.365913\pi$
$168$		0			0
$169$	−14.0890	−	5.12797i	−1.08377	−	0.394460i
$170$	1.84002	−	3.18701i	0.141123	−	0.244433i
$171$	0.963326	−	11.8034i	0.0736673	−	0.902626i
$172$	2.94444	+	5.09992i	0.224511	+	0.388865i
$173$	−0.686852	+	0.576337i	−0.0522204	+	0.0438181i	−0.668524	−	0.743690i	$-0.733074\pi$
$173$	−0.686852	+	0.576337i	−0.0522204	+	0.0438181i	0.616304	+	0.787508i	$0.288629\pi$
$174$	0.281774	+	1.59802i	0.0213613	+	0.121146i
$175$		0			0
$176$	−0.109470	+	0.0918566i	−0.00825164	+	0.00692395i
$177$	−4.38532	−	3.67972i	−0.329620	−	0.276584i
$178$	2.00774			0.150487
$179$	10.6591	−	18.4621i	0.796699	−	1.37992i	−0.125056	−	0.992150i	$-0.539911\pi$
$179$	10.6591	−	18.4621i	0.796699	−	1.37992i	0.921755	−	0.387773i	$-0.126755\pi$
$180$	1.46538	−	8.31061i	0.109223	−	0.619436i
$181$	−15.1284	+	5.50627i	−1.12448	+	0.409278i	−0.836286	−	0.548294i	$-0.815278\pi$
$181$	−15.1284	+	5.50627i	−1.12448	+	0.409278i	−0.288196	+	0.957571i	$0.593055\pi$
$182$		0			0
$183$	−1.16772	+	2.02255i	−0.0863202	+	0.149511i
$184$	−3.82295	−	3.20783i	−0.281831	−	0.236485i
$185$	1.99273	+	0.725293i	0.146508	+	0.0533246i
$186$	0.157918	−	0.895599i	0.0115791	−	0.0656685i
$187$	5.29813	+	1.92836i	0.387438	+	0.141016i
$188$	−0.826352	−	0.300767i	−0.0602679	−	0.0219357i
$189$		0			0
$190$	−7.98293	−	5.52060i	−0.579142	−	0.400506i
$191$	−9.47431	+	16.4100i	−0.685537	+	1.18738i	0.287731	+	0.957711i	$0.407099\pi$
$191$	−9.47431	+	16.4100i	−0.685537	+	1.18738i	−0.973268	+	0.229673i	$0.926234\pi$
$192$	−0.465852	−	2.64198i	−0.0336200	−	0.190668i
$193$	9.88326	−	8.29304i	0.711412	−	0.596946i	−0.213583	−	0.976925i	$-0.568513\pi$
$193$	9.88326	−	8.29304i	0.711412	−	0.596946i	0.924995	+	0.379979i	$0.124069\pi$
$194$	−1.50640	+	0.548284i	−0.108153	+	0.0393645i
$195$	−5.46064	+	4.58202i	−0.391044	+	0.328125i
$196$		0			0
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	−0.0743108	−	0.997235i	$-0.523676\pi$
$197$	11.6001	−	20.0920i	0.826476	−	1.43150i	0.900786	−	0.434263i	$-0.142991\pi$
$198$	−8.15064			−0.579241
$199$	−7.06418	−	5.92755i	−0.500766	−	0.420193i	0.357100	−	0.934066i	$-0.383766\pi$
$199$	−7.06418	−	5.92755i	−0.500766	−	0.420193i	−0.857866	+	0.513873i	$0.828210\pi$
$200$	−3.06805	−	2.57440i	−0.216944	−	0.182037i
$201$	−7.56212			−0.533391
$202$	−3.48293	+	6.03260i	−0.245058	+	0.424453i
$203$		0			0
$204$	−0.826352	+	0.693392i	−0.0578562	+	0.0485471i
$205$	−10.6839	+	3.88863i	−0.746197	+	0.271593i
$206$	0.00980018	−	0.00822333i	0.000682811	−	0.000572946i
$207$	−0.829755	−	4.70578i	−0.0576720	−	0.327074i
$208$	0.110815	−	0.191936i	0.00768361	−	0.0133084i
$209$	6.20574	−	13.5135i	0.429260	−	0.934746i
$210$		0			0
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.177478	−	0.984125i	$-0.556794\pi$
$211$	−13.7417	−	5.00157i	−0.946017	−	0.344322i	−0.768539	+	0.639803i	$0.779016\pi$
$212$	−7.03849	−	2.56180i	−0.483405	−	0.175945i
$213$	1.27126	−	7.20967i	0.0871052	−	0.493998i
$214$	2.93717	+	1.06904i	0.200781	+	0.0730781i
$215$	9.31180	+	7.81353i	0.635060	+	0.532878i
$216$	4.31567	−	7.47497i	0.293644	−	0.508607i
$217$		0			0
$218$	−6.08987	+	2.21653i	−0.412458	+	0.150122i
$219$	−0.694593	+	3.93923i	−0.0469362	+	0.266189i
$220$	5.29813	−	9.17664i	0.357200	−	0.618689i
$221$	−8.74422			−0.588200
$222$	0.300193	+	0.251892i	0.0201476	+	0.0169059i
$223$	2.30928	−	1.93771i	0.154641	−	0.129759i	−0.562185	−	0.827012i	$-0.690039\pi$
$223$	2.30928	−	1.93771i	0.154641	−	0.129759i	0.716825	+	0.697253i	$0.245595\pi$
$224$		0			0
$225$	−0.665907	−	3.77655i	−0.0443938	−	0.251770i
$226$	4.96972	−	4.17009i	0.330581	−	0.277390i
$227$	−6.86097	−	11.8835i	−0.455378	−	0.788738i	0.543332	−	0.839518i	$-0.317163\pi$
$227$	−6.86097	−	11.8835i	−0.455378	−	0.788738i	−0.998710	+	0.0507798i	$0.983829\pi$
$228$	1.64543	+	2.32099i	0.108971	+	0.153711i
$229$	4.70708	−	8.15290i	0.311053	−	0.538759i	−0.667538	−	0.744576i	$-0.732652\pi$
$229$	4.70708	−	8.15290i	0.311053	−	0.538759i	0.978591	+	0.205817i	$0.0659851\pi$
$230$	−3.68004	−	1.33943i	−0.242655	−	0.0883192i
$231$		0			0
$232$	7.53802	+	6.32515i	0.494895	+	0.415266i
$233$	−4.19981	−	23.8183i	−0.275139	−	1.56039i	−0.738521	−	0.674230i	$-0.764476\pi$
$233$	−4.19981	−	23.8183i	−0.275139	−	1.56039i	0.463383	−	0.886158i	$-0.346635\pi$
$234$	11.8785	−	4.32342i	0.776522	−	0.282631i
$235$	−1.81521			−0.118411
$236$	−13.1976			−0.859090
$237$	−3.48158	+	1.26719i	−0.226153	+	0.0823130i
$238$		0			0
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	0.945665	+	0.325143i	$0.105413\pi$
$239$	11.6630	+	20.2009i	0.754415	+	1.30668i	−0.191250	+	0.981541i	$0.561254\pi$
$240$	−0.0282185	−	0.0488759i	−0.00182150	−	0.00315492i
$241$	0.279715	−	0.101808i	0.0180180	−	0.00655803i	−0.332995	−	0.942928i	$-0.608059\pi$
$241$	0.279715	−	0.101808i	0.0180180	−	0.00655803i	0.351013	+	0.936370i	$0.385837\pi$
$242$	−0.527341	−	0.191936i	−0.0338988	−	0.0123381i
$243$	11.8414	−	4.30990i	0.759624	−	0.276481i
$244$	0.934945	+	5.30234i	0.0598537	+	0.339447i
$245$		0			0
$246$	−2.10101			−0.133956
$247$	−1.87598	+	22.9859i	−0.119366	+	1.46256i
$248$	−2.75743	−	4.77600i	−0.175097	−	0.303276i
$249$	0.232145	+	1.31656i	0.0147116	+	0.0834334i
$250$	7.50862	+	2.73291i	0.474887	+	0.172845i
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	0.944050	−	0.329802i	$-0.106982\pi$
$251$	12.4081	+	10.4116i	0.783190	+	0.657175i	−0.160859	+	0.986977i	$0.551427\pi$
$252$		0			0
$253$	1.04189	−	5.90885i	0.0655030	−	0.371486i
$254$	0.0444153	+	0.0769295i	0.00278686	+	0.00482699i
$255$	−1.11334	+	1.92836i	−0.0697201	+	0.120759i
$256$	−12.3341	−	10.3495i	−0.770881	−	0.646846i
$257$	−2.66637	+	15.1218i	−0.166324	+	0.943269i	0.781365	+	0.624074i	$0.214524\pi$
$257$	−2.66637	+	15.1218i	−0.166324	+	0.943269i	−0.947689	+	0.319195i	$0.896587\pi$
$258$	1.12314	+	1.94534i	0.0699237	+	0.121111i
$259$		0			0
$260$	−2.85369	+	16.1841i	−0.176979	+	1.00370i
$261$	1.63610	+	9.27876i	0.101272	+	0.574341i
$262$	0.463736	−	2.62998i	0.0286497	−	0.162481i
$263$	7.38713	−	6.19853i	0.455510	−	0.382218i	−0.385966	−	0.922513i	$-0.626132\pi$
$263$	7.38713	−	6.19853i	0.455510	−	0.382218i	0.841476	+	0.540295i	$0.181687\pi$
$264$	3.94562	−	3.31077i	0.242836	−	0.203764i
$265$	−15.4611			−0.949768
$266$		0			0
$267$	−1.21482			−0.0743459
$268$	−13.3550	+	11.2062i	−0.815789	+	0.684528i
$269$	14.0025	−	11.7495i	0.853749	−	0.716381i	−0.106863	−	0.994274i	$-0.534081\pi$
$269$	14.0025	−	11.7495i	0.853749	−	0.716381i	0.960612	+	0.277893i	$0.0896361\pi$
$270$	1.17617	−	6.67042i	0.0715797	−	0.405949i
$271$	−3.29308	−	18.6760i	−0.200040	−	1.13449i	−0.905056	−	0.425293i	$-0.860171\pi$
$271$	−3.29308	−	18.6760i	−0.200040	−	1.13449i	0.705015	−	0.709192i	$-0.250940\pi$
$272$	0.0120217	−	0.0681784i	0.000728923	−	0.00413393i
$273$		0			0
$274$	−8.59152	−	14.8809i	−0.519033	−	0.898991i
$275$	0.836152	−	4.74205i	0.0504219	−	0.285957i
$276$	0.879385	+	0.737892i	0.0529328	+	0.0444159i
$277$	−6.88191	+	11.9198i	−0.413494	+	0.716193i	−0.995269	−	0.0971571i	$-0.969025\pi$
$277$	−6.88191	+	11.9198i	−0.413494	+	0.716193i	0.581775	+	0.813350i	$0.302358\pi$
$278$	6.76991	+	11.7258i	0.406033	+	0.703269i
$279$	0.916937	−	5.20021i	0.0548956	−	0.311328i
$280$		0			0
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	0.891175	−	0.453661i	$-0.149882\pi$
$281$	10.0437	+	8.42767i	0.599157	+	0.502752i	−0.292018	+	0.956413i	$0.594327\pi$
$282$	−0.315207	−	0.114726i	−0.0187703	−	0.00683184i
$283$	3.01754	+	17.1133i	0.179374	+	1.01728i	0.932973	+	0.359947i	$0.117205\pi$
$283$	3.01754	+	17.1133i	0.179374	+	1.01728i	−0.753599	+	0.657335i	$0.771684\pi$
$284$	−8.43882	−	14.6165i	−0.500752	−	0.867327i
$285$	4.83022	+	3.34034i	0.286118	+	0.197865i
$286$	15.8726			0.938565
$287$		0			0
$288$	−2.65998	−	15.0855i	−0.156741	−	0.888921i
$289$	13.4081	−	4.88014i	0.788710	−	0.287067i
$290$	7.25624	+	2.64106i	0.426101	+	0.155088i
$291$	0.911474	−	0.331749i	0.0534316	−	0.0194475i
$292$	4.61081	+	7.98617i	0.269828	+	0.467355i
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	0.998734	−	0.0503091i	$-0.0160206\pi$
$293$	7.80200	+	13.5135i	0.455798	+	0.789465i	−0.542936	+	0.839774i	$0.682687\pi$
$294$		0			0
$295$	−25.5993	+	9.31737i	−1.49045	+	0.542478i
$296$	2.37639			0.138125
$297$	10.3773			0.602154
$298$	3.11246	−	1.13284i	0.180300	−	0.0656239i
$299$	1.61587	+	9.16404i	0.0934480	+	0.529970i
$300$	0.705737	+	0.592184i	0.0407457	+	0.0341897i
$301$		0			0
$302$	12.0617	+	4.39008i	0.694070	+	0.252621i
$303$	2.10741	−	3.65014i	0.121068	−	0.209695i
$304$	−0.176641	−	0.0462284i	−0.0101311	−	0.00265138i
$305$	5.55690	+	9.62484i	0.318187	+	0.551117i
$306$	3.02481	−	2.53812i	0.172917	−	0.145095i
$307$	−3.73695	−	21.1933i	−0.213279	−	1.20956i	−0.883868	−	0.467736i	$-0.845070\pi$
$307$	−3.73695	−	21.1933i	−0.213279	−	1.20956i	0.670589	−	0.741829i	$-0.266041\pi$
$308$		0			0
$309$	−0.00592979	+	0.00497568i	−0.000337334	+	0.000283057i
$310$	−3.31521	−	2.78179i	−0.188291	−	0.157995i
$311$	−14.4953			−0.821950			−0.410975	−	0.911647i	$-0.634812\pi$
$311$	−14.4953			−0.821950			−0.410975	+	0.911647i	$0.634812\pi$
$312$	−3.99407	+	6.91793i	−0.226120	+	0.391651i
$313$	−3.38935	+	19.2219i	−0.191577	+	1.08649i	0.725632	+	0.688083i	$0.241547\pi$
$313$	−3.38935	+	19.2219i	−0.191577	+	1.08649i	−0.917209	+	0.398406i	$0.869564\pi$
$314$	−8.57310	+	3.12035i	−0.483808	+	0.176092i
$315$		0			0
$316$	−4.27079	+	7.39723i	−0.240251	+	0.416127i
$317$	21.7153	+	18.2213i	1.21965	+	1.02341i	0.998843	+	0.0480926i	$0.0153143\pi$
$317$	21.7153	+	18.2213i	1.21965	+	1.02341i	0.220809	+	0.975317i	$0.429130\pi$
$318$	−2.68479	−	0.977185i	−0.150556	−	0.0547978i
$319$	−2.05438	+	11.6510i	−0.115023	+	0.652328i
$320$	−11.9966	−	4.36640i	−0.670630	−	0.244089i
$321$	−1.77719	−	0.646844i	−0.0991930	−	0.0361033i
$322$		0			0
$323$	1.90508	+	6.94751i	0.106001	+	0.386570i
$324$	4.00640	−	6.93928i	0.222578	−	0.385516i
$325$	1.29679	+	7.35446i	0.0719329	+	0.407952i
$326$	−1.36231	+	1.14311i	−0.0754514	+	0.0633113i
$327$	3.68479	−	1.34115i	0.203769	−	0.0741660i
$328$	−9.76011	+	8.18971i	−0.538912	+	0.452201i
$329$		0			0
$330$	2.02094	−	3.50038i	0.111249	−	0.192690i
$331$	−1.71007			−0.0939942			−0.0469971	−	0.998895i	$-0.514965\pi$
$331$	−1.71007			−0.0939942			−0.0469971	+	0.998895i	$0.514965\pi$
$332$	2.36097	+	1.98109i	0.129575	+	0.108726i
$333$	1.74304	+	1.46258i	0.0955180	+	0.0801491i
$334$	20.4516			1.11906
$335$	−17.9932	+	31.1651i	−0.983073	+	1.70273i
$336$		0			0
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.0672796	−	0.997734i	$-0.478568\pi$
$337$	19.4873	−	16.3518i	1.06154	−	0.890737i	0.994259	+	0.106997i	$0.0341236\pi$
$338$	−12.3897	+	4.50946i	−0.673908	+	0.245283i
$339$	−3.00703	+	2.52319i	−0.163319	+	0.137041i
$340$	0.891407	+	5.05542i	0.0483433	+	0.274169i
$341$	3.31521	−	5.74211i	0.179529	−	0.310953i
$342$	−6.02300	−	8.49584i	−0.325687	−	0.459403i
$343$		0			0
$344$	12.8004	+	4.65895i	0.690149	+	0.251194i
$345$	2.22668	+	0.810446i	0.119881	+	0.0436329i
$346$	−0.136917	+	0.776497i	−0.00736072	+	0.0417447i
$347$	−7.23783	−	2.63435i	−0.388547	−	0.141419i	0.140358	−	0.990101i	$-0.455175\pi$
$347$	−7.23783	−	2.63435i	−0.388547	−	0.141419i	−0.528904	+	0.848681i	$0.677397\pi$
$348$	−1.73396	−	1.45496i	−0.0929498	−	0.0779941i
$349$	11.3785	−	19.7082i	0.609078	−	1.05495i	−0.382315	−	0.924032i	$-0.624873\pi$
$349$	11.3785	−	19.7082i	0.609078	−	1.05495i	0.991393	−	0.130921i	$-0.0417935\pi$
$350$		0			0
$351$	−15.1236	+	5.50454i	−0.807238	+	0.293811i
$352$	3.34002	−	18.9422i	0.178024	−	1.00962i
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	−0.977171	−	0.212454i	$-0.931854\pi$
$353$	−5.72281	+	9.91220i	−0.304595	+	0.527573i	0.672576	+	0.740028i	$0.265188\pi$
$354$	−5.03415			−0.267562
$355$	−26.6878	−	22.3937i	−1.41644	−	1.18853i
$356$	−2.14543	+	1.80023i	−0.113708	+	0.0954120i
$357$		0			0
$358$	−3.25537	−	18.4621i	−0.172051	−	0.975752i
$359$	7.95471	−	6.67479i	0.419833	−	0.352282i	−0.408266	−	0.912863i	$-0.633867\pi$
$359$	7.95471	−	6.67479i	0.419833	−	0.352282i	0.828100	+	0.560581i	$0.189422\pi$
$360$	−9.76011	−	16.9050i	−0.514403	−	0.890972i
$361$	18.6716	−	3.51735i	0.982715	−	0.185124i
$362$	−7.07873	+	12.2607i	−0.372050	+	0.644409i
$363$	0.319078	+	0.116135i	0.0167472	+	0.00609550i
$364$		0			0
$365$	14.5817	+	12.2355i	0.763242	+	0.640436i
$366$	0.356630	+	2.02255i	0.0186413	+	0.105720i
$367$	−30.5710	+	11.1269i	−1.59580	+	0.580822i	−0.978561	−	0.205957i	$-0.933969\pi$
$367$	−30.5710	+	11.1269i	−1.59580	+	0.580822i	−0.617234	+	0.786779i	$0.711747\pi$
$368$	−0.0736733			−0.00384048
$369$	−12.1993			−0.635072
$370$	1.75237	−	0.637812i	0.0911016	−	0.0331583i
$371$		0			0
$372$	0.634285	+	1.09861i	0.0328862	+	0.0569605i
$373$	−15.2429	−	26.4014i	−0.789246	−	1.36701i	−0.926429	−	0.376469i	$-0.877138\pi$
$373$	−15.2429	−	26.4014i	−0.789246	−	1.36701i	0.137183	−	0.990546i	$-0.456195\pi$
$374$	4.65910	−	1.69577i	0.240916	−	0.0876864i
$375$	−4.54323	−	1.65360i	−0.234612	−	0.0853916i
$376$	−1.91147	+	0.695720i	−0.0985768	+	0.0358790i
$377$	−3.18614	−	18.0695i	−0.164094	−	0.930626i
$378$		0			0
$379$	17.8598			0.917396			0.458698	−	0.888592i	$-0.348316\pi$
$379$	17.8598			0.917396			0.458698	+	0.888592i	$0.348316\pi$
$380$	13.4804	−	1.25865i	0.691530	−	0.0645674i
$381$	−0.0268743	−	0.0465477i	−0.00137681	−	0.00238471i
$382$	2.89352	+	16.4100i	0.148045	+	0.839608i
$383$	−22.0415	−	8.02244i	−1.12627	−	0.409928i	−0.289331	−	0.957229i	$-0.593433\pi$
$383$	−22.0415	−	8.02244i	−1.12627	−	0.409928i	−0.836936	+	0.547301i	$0.815655\pi$
$384$	2.78905	+	2.34029i	0.142328	+	0.119427i
$385$		0			0
$386$	1.97013	−	11.1732i	0.100277	−	0.568700i
$387$	6.52141	+	11.2954i	0.331502	+	0.574178i
$388$	1.11809	−	1.93659i	0.0567623	−	0.0983153i
$389$	2.99479	+	2.51292i	0.151842	+	0.127410i	0.715544	−	0.698568i	$-0.246179\pi$
$389$	2.99479	+	2.51292i	0.151842	+	0.127410i	−0.563702	+	0.825978i	$0.690623\pi$
$390$	−1.08853	+	6.17334i	−0.0551197	+	0.312599i
$391$	1.45336	+	2.51730i	0.0734997	+	0.127305i
$392$		0			0
$393$	−0.280592	+	1.59132i	−0.0141540	+	0.0802714i
$394$	−3.54277	−	20.0920i	−0.178482	−	1.01222i
$395$	−3.06165	+	17.3635i	−0.154048	+	0.873652i
$396$	8.70961	−	7.30823i	0.437674	−	0.367252i
$397$	−6.86303	+	5.75876i	−0.344445	+	0.289024i	−0.798555	−	0.601922i	$-0.794402\pi$
$397$	−6.86303	+	5.75876i	−0.344445	+	0.289024i	0.454110	+	0.890946i	$0.349957\pi$
$398$	−8.10936			−0.406486
$399$		0			0
$400$	−0.0591253			−0.00295627
$401$	−1.55303	+	1.30315i	−0.0775548	+	0.0650762i	−0.680741	−	0.732524i	$-0.738342\pi$
$401$	−1.55303	+	1.30315i	−0.0775548	+	0.0650762i	0.603186	+	0.797600i	$0.293898\pi$
$402$	−5.09421	+	4.27455i	−0.254076	+	0.213195i
$403$	−1.78564	+	10.1269i	−0.0889493	+	0.504457i
$404$	−1.68732	−	9.56926i	−0.0839472	−	0.476088i
$405$	2.87211	−	16.2886i	0.142716	−	0.809385i
$406$		0			0
$407$	1.42855	+	2.47432i	0.0708105	+	0.122647i
$408$	−0.433296	+	2.45734i	−0.0214513	+	0.121657i
$409$	24.6728	+	20.7029i	1.21999	+	1.02369i	0.998825	+	0.0484567i	$0.0154303\pi$
$409$	24.6728	+	20.7029i	1.21999	+	1.02369i	0.221165	+	0.975236i	$0.429014\pi$
$410$	−4.99912	+	8.65873i	−0.246889	+	0.427624i
$411$	5.19846	+	9.00400i	0.256421	+	0.444135i
$412$	−0.00309887	+	0.0175745i	−0.000152670	+	0.000865836i
$413$		0			0
$414$	−3.21894	−	2.70101i	−0.158202	−	0.132747i
$415$	5.97818	+	2.17588i	0.293457	+	0.106810i
$416$	5.18004	+	29.3775i	0.253973	+	1.44035i
$417$	−4.09627	−	7.09494i	−0.200595	−	0.347441i
$418$	−3.45811	−	12.6112i	−0.169142	−	0.616832i
$419$	23.2499			1.13583			0.567916	−	0.823086i	$-0.307750\pi$
$419$	23.2499			1.13583			0.567916	+	0.823086i	$0.307750\pi$
$420$		0			0
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	0.999862	−	0.0166178i	$-0.00528986\pi$
$421$	1.12061	+	6.35532i	0.0546154	+	0.309739i	−0.945246	+	0.326357i	$0.894179\pi$
$422$	−12.0842	+	4.39831i	−0.588252	+	0.214106i
$423$	−1.83022	−	0.666146i	−0.0889884	−	0.0323891i
$424$	−16.2811	+	5.92582i	−0.790678	+	0.287783i
$425$	1.16637	+	2.02022i	0.0565775	+	0.0979950i
$426$	−3.21894	−	5.57537i	−0.155958	−	0.270128i
$427$		0			0
$428$	−4.09714	+	1.49124i	−0.198043	+	0.0720817i
$429$	−9.60401			−0.463686
$430$	10.6895			0.515495
$431$	13.1532	−	4.78736i	0.633566	−	0.230599i	−0.00521671	−	0.999986i	$-0.501661\pi$
$431$	13.1532	−	4.78736i	0.633566	−	0.230599i	0.638783	+	0.769387i	$0.279438\pi$
$432$	−0.0221266	−	0.125486i	−0.00106457	−	0.00603745i
$433$	21.9800	+	18.4434i	1.05629	+	0.886333i	0.993741	−	0.111709i	$-0.0356323\pi$
$433$	21.9800	+	18.4434i	1.05629	+	0.886333i	0.0625499	+	0.998042i	$0.480077\pi$
$434$		0			0
$435$	−4.39053	−	1.59802i	−0.210510	−	0.0766193i
$436$	4.52007	−	7.82899i	0.216472	−	0.374940i
$437$	6.92902	−	3.28039i	0.331460	−	0.156922i
$438$	1.75877	+	3.04628i	0.0840373	+	0.145557i
$439$	10.2208	−	8.57623i	0.487810	−	0.409321i	−0.365431	−	0.930839i	$-0.619078\pi$
$439$	10.2208	−	8.57623i	0.487810	−	0.409321i	0.853241	+	0.521517i	$0.174634\pi$
$440$	−4.25624	−	24.1384i	−0.202908	−	1.15075i
$441$		0			0
$442$	−5.89053	+	4.94274i	−0.280184	+	0.235102i
$443$	25.9559	+	21.7796i	1.23320	+	1.03478i	0.998024	+	0.0628264i	$0.0200114\pi$
$443$	25.9559	+	21.7796i	1.23320	+	1.03478i	0.235177	+	0.971953i	$0.424433\pi$
$444$	−0.546637			−0.0259422
$445$	−2.89053	+	5.00654i	−0.137024	+	0.237333i
$446$	0.460332	−	2.61068i	0.0217974	−	0.123619i
$447$	−1.88326	+	0.685449i	−0.0890749	+	0.0324206i
$448$		0			0
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	−0.998022	−	0.0628725i	$-0.979974\pi$
$449$	−9.42009	+	16.3161i	−0.444562	+	0.770003i	0.553460	+	0.832876i	$0.313307\pi$
$450$	−2.58331	−	2.16766i	−0.121778	−	0.102184i
$451$	−14.3944	−	5.23913i	−0.677806	−	0.246701i
$452$	−1.57145	+	8.91215i	−0.0739149	+	0.419192i
$453$	−7.29813	−	2.65630i	−0.342896	−	0.124804i
$454$	−11.3391	−	4.12711i	−0.532172	−	0.193695i
$455$		0			0
$456$	6.36665	+	1.66620i	0.298146	+	0.0780270i
$457$	−7.13950	+	12.3660i	−0.333972	+	0.578456i	−0.983287	−	0.182064i	$-0.941722\pi$
$457$	−7.13950	+	12.3660i	−0.333972	+	0.578456i	0.649315	+	0.760520i	$0.275056\pi$
$458$	−1.43758	−	8.15290i	−0.0671736	−	0.380960i
$459$	−3.85117	+	3.23151i	−0.179757	+	0.150834i
$460$	5.13341	−	1.86841i	0.239346	−	0.0871150i
$461$	10.6695	−	8.95280i	0.496930	−	0.416973i	−0.359572	−	0.933117i	$-0.617077\pi$
$461$	10.6695	−	8.95280i	0.496930	−	0.416973i	0.856502	+	0.516144i	$0.172633\pi$
$462$		0			0
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	−0.844816	−	0.535056i	$-0.820290\pi$
$463$	0.881445	−	1.52671i	0.0409642	−	0.0709521i	0.885781	+	0.464104i	$0.153624\pi$
$464$	0.145268			0.00674388
$465$	2.00593	+	1.68317i	0.0930228	+	0.0780554i
$466$	−16.2927	−	13.6712i	−0.754743	−	0.633305i
$467$	−22.0419			−1.01998			−0.509988	−	0.860181i	$-0.670350\pi$
$467$	−22.0419			−1.01998			−0.509988	+	0.860181i	$0.670350\pi$
$468$	−8.81655	+	15.2707i	−0.407545	+	0.705889i
$469$		0			0
$470$	−1.22281	+	1.02606i	−0.0564041	+	0.0473286i
$471$	5.18732	−	1.88803i	0.239019	−	0.0869958i
$472$	−23.3858	+	19.6230i	−1.07642	+	0.903222i
$473$	2.84389	+	16.1285i	0.130762	+	0.741590i
$474$	−1.62907	+	2.82163i	−0.0748257	+	0.129602i
$475$	5.56077	−	2.63263i	0.255146	−	0.120793i
$476$		0			0
$477$	−15.5890	−	5.67393i	−0.713771	−	0.259791i
$478$	19.2754	+	7.01568i	0.881638	+	0.320890i
$479$	4.42056	−	25.0702i	0.201981	−	1.14549i	−0.700140	−	0.714005i	$-0.746879\pi$
$479$	4.42056	−	25.0702i	0.201981	−	1.14549i	0.902121	−	0.431483i	$-0.142010\pi$
$480$	7.13816	+	2.59808i	0.325811	+	0.118585i
$481$	−3.39440	−	2.84824i	−0.154771	−	0.129869i
$482$	0.130882	−	0.226694i	0.00596150	−	0.0103256i
$483$		0			0
$484$	0.735604	−	0.267738i	0.0334366	−	0.0121699i
$485$	0.801537	−	4.54574i	0.0363959	−	0.206411i
$486$	5.54071	−	9.59679i	0.251332	−	0.435319i
$487$	−22.5107			−1.02006			−0.510029	−	0.860157i	$-0.670365\pi$
$487$	−22.5107			−1.02006			−0.510029	+	0.860157i	$0.670365\pi$
$488$	9.54054	+	8.00547i	0.431880	+	0.362390i
$489$	0.824292	−	0.691663i	0.0372758	−	0.0312781i
$490$		0			0
$491$	2.71482	+	15.3965i	0.122518	+	0.694835i	0.982751	+	0.184934i	$0.0592071\pi$
$491$	2.71482	+	15.3965i	0.122518	+	0.694835i	−0.860233	+	0.509902i	$0.829682\pi$
$492$	2.24510	−	1.88386i	0.101217	−	0.0849311i
$493$	−2.86571	−	4.96356i	−0.129065	−	0.223548i
$494$	11.7292	+	16.5448i	0.527722	+	0.744387i
$495$	11.7344	−	20.3246i	0.527423	−	0.913524i
$496$	−0.0765042	−	0.0278452i	−0.00343514	−	0.00125029i
$497$		0			0
$498$	0.900578	+	0.755675i	0.0403559	+	0.0338626i
$499$	−4.96926	−	28.1820i	−0.222454	−	1.26160i	−0.867492	−	0.497451i	$-0.834269\pi$
$499$	−4.96926	−	28.1820i	−0.222454	−	1.26160i	0.645038	−	0.764151i	$-0.276842\pi$
$500$	−10.4740	+	3.81223i	−0.468412	+	0.170488i
$501$	−12.3746			−0.552858
$502$	14.2439			0.635737
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.808428	−	0.588595i	$-0.799681\pi$
$503$	−23.5351	+	8.56607i	−1.04938	+	0.381942i	−0.240950	+	0.970538i	$0.577459\pi$
$504$		0			0
$505$	−10.0287	−	17.3702i	−0.446271	−	0.772963i
$506$	−2.63816	−	4.56942i	−0.117280	−	0.203135i
$507$	7.49660	−	2.72854i	0.332936	−	0.121179i
$508$	−0.116440	−	0.0423806i	−0.00516617	−	0.00188033i
$509$	31.4996	−	11.4649i	1.39619	−	0.508173i	0.469148	−	0.883119i	$-0.344561\pi$
$509$	31.4996	−	11.4649i	1.39619	−	0.508173i	0.927047	+	0.374946i	$0.122339\pi$
$510$	0.340022	+	1.92836i	0.0150564	+	0.0853893i
$511$		0			0
$512$	−0.473897			−0.0209435
$513$	7.66843	+	10.8168i	0.338570	+	0.477575i
$514$	6.75150	+	11.6939i	0.297796	+	0.515797i
$515$	0.00639661	+	0.0362770i	0.000281868	+	0.00159856i
$516$	−2.94444	−	1.07169i	−0.129622	−	0.0471785i
$517$	−1.87346	−	1.57202i	−0.0823945	−	0.0691372i
$518$		0			0
$519$	0.0828445	−	0.469834i	0.00363647	−	0.0206234i
$520$	19.0069	+	32.9209i	0.833506	+	1.44367i
$521$	−13.7392	+	23.7969i	−0.601924	+	1.04256i	0.390606	+	0.920558i	$0.372266\pi$
$521$	−13.7392	+	23.7969i	−0.601924	+	1.04256i	−0.992530	+	0.122005i	$0.961068\pi$
$522$	6.34705	+	5.32581i	0.277803	+	0.233104i
$523$	1.79854	−	10.2000i	0.0786448	−	0.446017i	−0.919903	−	0.392146i	$-0.871733\pi$
$523$	1.79854	−	10.2000i	0.0786448	−	0.446017i	0.998548	−	0.0538712i	$-0.0171560\pi$
$524$	1.86262	+	3.22615i	0.0813687	+	0.140935i
$525$		0			0
$526$	1.47255	−	8.35126i	0.0642064	−	0.364132i
$527$	0.557781	+	3.16333i	0.0242973	+	0.137797i
$528$	0.0132037	−	0.0748822i	0.000574619	−	0.00325883i
$529$	−15.2494	+	12.7958i	−0.663019	+	0.556339i
$530$	−10.4153	+	8.73951i	−0.452414	+	0.379620i
$531$	−29.2303			−1.26849
$532$		0			0
$533$	23.7570			1.02903
$534$	−0.818363	+	0.686688i	−0.0354140	+	0.0297159i
$535$	−6.89440	+	5.78509i	−0.298071	+	0.250111i
$536$	−7.00269	+	39.7142i	−0.302470	+	1.71539i
$537$	1.96972	+	11.1708i	0.0849998	+	0.482058i
$538$	2.79127	−	15.8301i	0.120340	−	0.682483i
$539$		0			0
$540$	4.72416	+	8.18248i	0.203295	+	0.352118i
$541$	0.438348	−	2.48600i	0.0188461	−	0.106881i	−0.973934	−	0.226833i	$-0.927163\pi$
$541$	0.438348	−	2.48600i	0.0188461	−	0.106881i	0.992780	+	0.119952i	$0.0382739\pi$
$542$	−12.7751	−	10.7196i	−0.548739	−	0.460447i
$543$	4.28312	−	7.41858i	0.183806	−	0.318362i
$544$	4.65910	+	8.06980i	0.199757	+	0.345990i
$545$	3.24035	−	18.3770i	0.138801	−	0.787182i
$546$		0			0
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	0.759768	−	0.650194i	$-0.225312\pi$
$547$	5.87939	+	4.93339i	0.251384	+	0.210937i	−0.508384	+	0.861131i	$0.669757\pi$
$548$	22.5236	+	8.19793i	0.962162	+	0.350198i
$549$	2.07074	+	11.7437i	0.0883769	+	0.501210i
$550$	−2.11721	−	3.66712i	−0.0902782	−	0.156366i
$551$	−13.6625	+	6.46821i	−0.582042	+	0.275555i
$552$	2.65539			0.113021
$553$		0			0
$554$	2.10179	+	11.9198i	0.0892963	+	0.506425i
$555$	−1.06031	+	0.385920i	−0.0450075	+	0.0163814i
$556$	−17.7481	−	6.45978i	−0.752687	−	0.273956i
$557$	−3.05943	+	1.11354i	−0.129632	+	0.0471823i	−0.406022	−	0.913863i	$-0.633084\pi$
$557$	−3.05943	+	1.11354i	−0.129632	+	0.0471823i	0.276389	+	0.961046i	$0.410862\pi$
$558$	−2.32177	−	4.02142i	−0.0982882	−	0.170240i
$559$	−12.6998	−	21.9967i	−0.537145	−	0.930362i
$560$		0			0
$561$	−2.81908	+	1.02606i	−0.119022	+	0.0433203i
$562$	11.5297			0.486352
$563$	−5.25908			−0.221644			−0.110822	−	0.993840i	$-0.535348\pi$
$563$	−5.25908			−0.221644			−0.110822	+	0.993840i	$0.535348\pi$
$564$	0.439693	−	0.160035i	0.0185144	−	0.00673869i
$565$	3.24376	+	18.3963i	0.136466	+	0.773936i
$566$	11.7062	+	9.82267i	0.492048	+	0.412878i
$567$		0			0
$568$	−36.6860	−	13.3526i	−1.53931	−	0.560264i
$569$	14.9782	−	25.9430i	0.627918	−	1.08759i	−0.360051	−	0.932933i	$-0.617241\pi$
$569$	14.9782	−	25.9430i	0.627918	−	1.08759i	0.987969	−	0.154653i	$-0.0494260\pi$
$570$	5.14203	−	0.480105i	0.215376	−	0.0201094i
$571$	8.35504	+	14.4713i	0.349647	+	0.605607i	0.986187	−	0.165637i	$-0.0529680\pi$
$571$	8.35504	+	14.4713i	0.349647	+	0.605607i	−0.636539	+	0.771244i	$0.719635\pi$
$572$	−16.9611	+	14.2321i	−0.709179	+	0.595072i
$573$	−1.75078	−	9.92917i	−0.0731399	−	0.414797i
$574$		0			0
$575$	1.90167	−	1.59569i	0.0793053	−	0.0665450i
$576$	−10.4934	−	8.80504i	−0.437227	−	0.366877i
$577$	13.6800			0.569508			0.284754	−	0.958601i	$-0.408088\pi$
$577$	13.6800			0.569508			0.284754	+	0.958601i	$0.408088\pi$
$578$	6.27379	−	10.8665i	0.260955	−	0.451987i
$579$	−1.19207	+	6.76055i	−0.0495406	+	0.280959i
$580$	−10.1220	+	3.68409i	−0.420291	+	0.152974i
$581$		0			0
$582$	0.426489	−	0.738700i	0.0176785	−	0.0306201i
$583$	−15.9572	−	13.3897i	−0.660881	−	0.554545i
$584$	20.0446	+	7.29563i	0.829451	+	0.301895i
$585$	−6.32042	+	35.8449i	−0.261317	+	1.48200i
$586$	12.8944	+	4.69318i	0.532663	+	0.193873i
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.169164	−	0.985588i	$-0.554107\pi$
$587$	−22.5872	−	8.22108i	−0.932275	−	0.339320i	−0.763111	+	0.646268i	$0.776329\pi$
$588$		0			0
$589$	8.43511	−	0.787576i	0.347563	−	0.0324515i
$590$	−11.9782	+	20.7468i	−0.493134	+	0.854133i
$591$	2.14362	+	12.1571i	0.0881767	+	0.500075i
$592$	0.0268743	−	0.0225502i	0.00110453	−	0.000926809i
$593$	−3.98545	+	1.45059i	−0.163663	+	0.0595684i	−0.422552	−	0.906339i	$-0.638866\pi$
$593$	−3.98545	+	1.45059i	−0.163663	+	0.0595684i	0.258889	+	0.965907i	$0.416643\pi$
$594$	6.99067	−	5.86587i	0.286831	−	0.240679i
$595$		0			0
$596$	−2.31016	+	4.00131i	−0.0946276	+	0.163900i
$597$	4.90673			0.200819
$598$	6.26857	+	5.25996i	0.256341	+	0.215096i
$599$	−20.1270	−	16.8886i	−0.822367	−	0.690048i	0.131158	−	0.991362i	$-0.458131\pi$
$599$	−20.1270	−	16.8886i	−0.822367	−	0.690048i	−0.953525	+	0.301313i	$0.902575\pi$
$600$	2.13104			0.0869995
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	0.00899659	+	0.999960i	$0.497136\pi$
$601$	−21.1197	+	36.5805i	−0.861492	+	1.49215i	−0.870489	+	0.492188i	$0.836197\pi$
$602$		0			0
$603$	−29.5790	+	24.8198i	−1.20455	+	1.01074i
$604$	−16.8252	+	6.12386i	−0.684606	+	0.249176i
$605$	1.23783	−	1.03866i	0.0503248	−	0.0422275i
$606$	−0.643619	−	3.65014i	−0.0261452	−	0.148277i
$607$	−11.0484	+	19.1365i	−0.448443	+	0.776725i	−0.998285	−	0.0585431i	$-0.981355\pi$
$607$	−11.0484	+	19.1365i	−0.448443	+	0.776725i	0.549842	+	0.835269i	$0.314688\pi$
$608$	22.2126	−	10.5161i	0.900840	−	0.426483i
$609$		0			0
$610$	9.18392	+	3.34267i	0.371846	+	0.135341i
$611$	3.56418	+	1.29725i	0.144191	+	0.0524813i
$612$	−0.956462	+	5.42437i	−0.0386627	+	0.219267i
$613$	−6.74422	−	2.45470i	−0.272397	−	0.0991442i	0.202210	−	0.979342i	$-0.435188\pi$
$613$	−6.74422	−	2.45470i	−0.272397	−	0.0991442i	−0.474607	+	0.880198i	$0.657410\pi$
$614$	−14.4971	−	12.1645i	−0.585054	−	0.490918i
$615$	3.02481	−	5.23913i	0.121972	−	0.211262i
$616$		0			0
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.895995	−	0.444065i	$-0.146464\pi$
$617$	46.3953	−	16.8865i	1.86781	−	0.679826i	0.971811	−	0.235761i	$-0.0757583\pi$
$618$	−0.00118205	+	0.00670372i	−4.75489e−5	+	0.000269663i
$619$	13.2490	−	22.9479i	0.532521	−	0.922354i	−0.466758	−	0.884385i	$-0.654578\pi$
$619$	13.2490	−	22.9479i	0.532521	−	0.922354i	0.999279	−	0.0379684i	$-0.0120886\pi$
$620$	6.03684			0.242445
$621$	4.09833	+	3.43890i	0.164460	+	0.137998i
$622$	−9.76470	+	8.19356i	−0.391529	+	0.328532i
$623$		0			0
$624$	0.0204777	+	0.116135i	0.000819764	+	0.00464911i
$625$	−23.0312	+	19.3255i	−0.921248	+	0.773019i
$626$	8.58213	+	14.8647i	0.343011	+	0.594112i
$627$	2.09240	+	7.63063i	0.0835623	+	0.304738i
$628$	6.36319	−	11.0214i	0.253919	−	0.439800i
$629$	−1.30066	−	0.473401i	−0.0518607	−	0.0188757i
$630$		0			0
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.989138	−	0.146988i	$-0.0469579\pi$
$631$	25.5253	+	21.4183i	1.01615	+	0.852647i	0.0270071	+	0.999635i	$0.491402\pi$
$632$	3.43093	+	19.4578i	0.136475	+	0.773989i
$633$	7.31180	−	2.66128i	0.290618	−	0.105776i
$634$	24.9282			0.990025
$635$	−0.255777			−0.0101502
$636$	3.74510	−	1.36310i	0.148503	−	0.0540506i
$637$		0			0
$638$	5.20187	+	9.00990i	0.205944	+	0.356705i
$639$	−18.6905	−	32.3729i	−0.739384	−	1.28065i
$640$	16.2811	−	5.92582i	0.643565	−	0.234239i
$641$	0.127889	+	0.0465477i	0.00505130	+	0.00183852i	0.344545	−	0.938770i	$-0.388033\pi$
$641$	0.127889	+	0.0465477i	0.00505130	+	0.00183852i	−0.339493	+	0.940608i	$0.610256\pi$
$642$	−1.56283	+	0.568825i	−0.0616801	+	0.0224497i
$643$	−8.36602	−	47.4461i	−0.329924	−	1.87109i	−0.472536	−	0.881311i	$-0.656661\pi$
$643$	−8.36602	−	47.4461i	−0.329924	−	1.87109i	0.142613	−	0.989779i	$-0.454450\pi$
$644$		0			0
$645$	−6.46791			−0.254674
$646$	5.21048	+	3.60331i	0.205004	+	0.141771i
$647$	−18.4859	−	32.0186i	−0.726756	−	1.25878i	−0.958247	−	0.285942i	$-0.907694\pi$
$647$	−18.4859	−	32.0186i	−0.726756	−	1.25878i	0.231490	−	0.972837i	$-0.425640\pi$
$648$	−3.21853	−	18.2532i	−0.126436	−	0.717053i
$649$	−34.4898	−	12.5533i	−1.35384	−	0.492758i
$650$	5.03074	+	4.22130i	0.197322	+	0.165573i
$651$		0			0
$652$	0.430770	−	2.44302i	0.0168702	−	0.0956759i
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	−0.999456	−	0.0329874i	$-0.989498\pi$
$653$	−13.5000	−	23.3827i	−0.528296	−	0.915035i	0.471160	−	0.882048i	$-0.343835\pi$
$654$	1.72416	−	2.98632i	0.0674198	−	0.116775i
$655$	5.89053	+	4.94274i	0.230162	+	0.193129i
$656$	−0.0326615	+	0.185233i	−0.00127522	+	0.00723212i
$657$	10.2121	+	17.6879i	0.398413	+	0.690072i
$658$		0			0
$659$	3.27760	−	18.5882i	0.127677	−	0.724093i	−0.852005	−	0.523534i	$-0.824613\pi$
$659$	3.27760	−	18.5882i	0.127677	−	0.724093i	0.979682	−	0.200559i	$-0.0642757\pi$
$660$	0.979055	+	5.55250i	0.0381097	+	0.216131i
$661$	5.31567	−	30.1467i	0.206756	−	1.17257i	−0.687897	−	0.725808i	$-0.741466\pi$
$661$	5.31567	−	30.1467i	0.206756	−	1.17257i	0.894653	−	0.446762i	$-0.147423\pi$
$662$	−1.15199	+	0.966633i	−0.0447733	+	0.0375693i
$663$	3.56418	−	2.99070i	0.138421	−	0.116149i
$664$	7.12918			0.276666
$665$		0			0
$666$	2.00093			0.0775346
$667$	−4.67230	+	3.92053i	−0.180912	+	0.151803i
$668$	−21.8542	+	18.3378i	−0.845563	+	0.709511i
$669$	−0.278533	+	1.57964i	−0.0107687	+	0.0610724i
$670$	5.49525	+	31.1651i	0.212300	+	1.20401i
$671$	−2.60014	+	14.7461i	−0.100377	+	0.569267i
$672$		0			0
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	0.728134	−	0.685435i	$-0.240388\pi$
$673$	−5.95471	−	10.3139i	−0.229537	−	0.397570i	−0.957671	+	0.287865i	$0.907055\pi$
$674$	3.88460	−	22.0307i	0.149629	−	0.848589i
$675$	3.28905	+	2.75984i	0.126596	+	0.106226i
$676$	9.19594	−	15.9278i	0.353690	−	0.612609i
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	0.916211	−	0.400696i	$-0.131232\pi$
$677$	2.89053	+	5.00654i	0.111092	+	0.192417i	−0.805119	+	0.593114i	$0.797898\pi$
$678$	−0.599422	+	3.39949i	−0.0230207	+	0.130557i
$679$		0			0
$680$	9.09627	+	7.63267i	0.348826	+	0.292700i
$681$	6.86097	+	2.49719i	0.262913	+	0.0956924i
$682$	−1.01249	−	5.74211i	−0.0387702	−	0.219877i
$683$	−10.5248	−	18.2295i	−0.402721	−	0.697533i	0.591332	−	0.806428i	$-0.298602\pi$
$683$	−10.5248	−	18.2295i	−0.402721	−	0.697533i	−0.994053	+	0.108895i	$0.965269\pi$
$684$	14.0538	+	3.67799i	0.537361	+	0.140631i
$685$	49.4766			1.89040
$686$		0			0
$687$	0.869833	+	4.93307i	0.0331862	+	0.188208i
$688$	0.188968	−	0.0687786i	0.00720432	−	0.00262216i
$689$	30.3580	+	11.0494i	1.15655	+	0.420949i
$690$	1.95811	−	0.712694i	0.0745440	−	0.0271318i
$691$	−16.4688	−	28.5249i	−0.626504	−	1.08514i	−0.988248	−	0.152860i	$-0.951152\pi$
$691$	−16.4688	−	28.5249i	−0.626504	−	1.08514i	0.361744	−	0.932278i	$-0.382182\pi$
$692$	−0.549935	−	0.952515i	−0.0209054	−	0.0362092i
$693$		0			0
$694$	−6.36484	+	2.31661i	−0.241606	+	0.0879374i
$695$	−38.9864			−1.47884
$696$	−5.23585			−0.198464
$697$	6.97343	−	2.53812i	0.264138	−	0.0961382i
$698$	−3.47508	−	19.7082i	−0.131534	−	0.745965i
$699$	9.85819	+	8.27201i	0.372871	+	0.312876i
$700$		0			0
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.0660380	−	0.997817i	$-0.521036\pi$
$701$	−20.0694	−	7.30466i	−0.758010	−	0.275893i	−0.691973	+	0.721924i	$0.743258\pi$
$702$	−7.07650	+	12.2569i	−0.267085	+	0.462606i
$703$	−1.52347	+	3.31747i	−0.0574588	+	0.125121i
$704$	−8.60014	−	14.8959i	−0.324130	−	0.561409i
$705$	0.739885	−	0.620838i	0.0278657	−	0.0233821i
$706$	1.74779	+	9.91220i	0.0657789	+	0.373051i
$707$		0			0
$708$	5.37939	−	4.51384i	0.202170	−	0.169641i
$709$	−12.0810	−	10.1372i	−0.453712	−	0.380709i	0.387099	−	0.922038i	$-0.373477\pi$
$709$	−12.0810	−	10.1372i	−0.453712	−	0.380709i	−0.840811	+	0.541329i	$0.817921\pi$
$710$	−30.6364			−1.14976
$711$	−9.45904	+	16.3835i	−0.354742	+	0.614431i
$712$	−1.12495	+	6.37992i	−0.0421594	+	0.239098i
$713$	3.21213	−	1.16912i	0.120295	−	0.0437839i
$714$		0			0
$715$	−22.8516	+	39.5802i	−0.854603	+	1.48022i
$716$	20.0326	+	16.8093i	0.748652	+	0.628193i
$717$	−11.6630	−	4.24497i	−0.435562	−	0.158531i
$718$	1.58569	−	8.99292i	0.0591776	−	0.335613i
$719$	−33.1977	−	12.0830i	−1.23807	−	0.450620i	−0.361714	−	0.932289i	$-0.617808\pi$
$719$	−33.1977	−	12.0830i	−1.23807	−	0.450620i	−0.876353	+	0.481669i	$0.840031\pi$
$720$	−0.270792	−	0.0985603i	−0.0100918	−	0.00367313i
$721$		0			0
$722$	10.5899	−	12.9237i	0.394114	−	0.480971i
$723$	−0.0791925	+	0.137165i	−0.00294520	+	0.00510124i
$724$	−3.42932	−	19.4486i	−0.127450	−	0.722803i
$725$	−3.74969	+	3.14636i	−0.139260	+	0.116853i
$726$	0.280592	−	0.102127i	0.0104138	−	0.00379030i
$727$	−30.9647	+	25.9825i	−1.14842	+	0.963637i	−0.999681	−	0.0252396i	$-0.991965\pi$
$727$	−30.9647	+	25.9825i	−1.14842	+	0.963637i	−0.148737	+	0.988877i	$0.547521\pi$
$728$		0			0
$729$	6.44562	−	11.1641i	0.238727	−	0.413487i
$730$	16.7392			0.619544
$731$	−6.07785	−	5.09992i	−0.224797	−	0.188627i
$732$	−2.19459	−	1.84148i	−0.0811145	−	0.0680631i
$733$	36.2763			1.33990			0.669948	−	0.742408i	$-0.266316\pi$
$733$	36.2763			1.33990			0.669948	+	0.742408i	$0.266316\pi$
$734$	−14.3045	+	24.7762i	−0.527990	+	0.914505i
$735$		0			0
$736$	7.59627	−	6.37402i	0.280002	−	0.234950i
$737$	−45.5604	+	16.5826i	−1.67824	+	0.610829i
$738$	−8.21806	+	6.89577i	−0.302511	+	0.253837i
$739$	−3.59034	−	20.3618i	−0.132073	−	0.749021i	−0.976854	−	0.213909i	$-0.931380\pi$
$739$	−3.59034	−	20.3618i	−0.132073	−	0.749021i	0.844781	−	0.535112i	$-0.179731\pi$
$740$	−1.30066	+	2.25281i	−0.0478132	+	0.0828149i
$741$	−7.09698	−	10.0108i	−0.260714	−	0.367754i
$742$		0			0
$743$	−6.29978	−	2.29293i	−0.231117	−	0.0841196i	0.223866	−	0.974620i	$-0.428132\pi$
$743$	−6.29978	−	2.29293i	−0.231117	−	0.0841196i	−0.454982	+	0.890500i	$0.650354\pi$
$744$	2.75743	+	1.00362i	0.101092	+	0.0367945i
$745$	−1.65611	+	9.39225i	−0.0606751	+	0.344105i
$746$	−25.1920	−	9.16912i	−0.922343	−	0.335705i
$747$	5.22912	+	4.38775i	0.191324	+	0.160540i
$748$	−3.45811	+	5.98962i	−0.126441	+	0.219002i
$749$		0			0
$750$	−3.99525	+	1.45415i	−0.145886	+	0.0530982i
$751$	1.85932	−	10.5447i	0.0678475	−	0.384782i	−0.931909	−	0.362693i	$-0.881857\pi$
$751$	1.85932	−	10.5447i	0.0678475	−	0.384782i	0.999756	−	0.0220888i	$-0.00703166\pi$
$752$	−0.0150147	+	0.0260063i	−0.000547531	+	0.000948352i
$753$	−8.61856			−0.314078
$754$	−12.3603	−	10.3715i	−0.450134	−	0.377707i
$755$	−28.3123	+	23.7568i	−1.03039	+	0.864599i
$756$		0			0
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	0.969301	−	0.245878i	$-0.0790764\pi$
$757$	−0.705432	−	4.00071i	−0.0256394	−	0.145408i	−0.994940	+	0.100470i	$0.967965\pi$
$758$	12.0312	−	10.0954i	0.436993	−	0.366681i
$759$	1.59627	+	2.76481i	0.0579408	+	0.100356i
$760$	22.0155	−	22.2738i	0.798585	−	0.807956i
$761$	−5.50387	+	9.53298i	−0.199515	+	0.345570i	−0.948371	−	0.317162i	$-0.897270\pi$
$761$	−5.50387	+	9.53298i	−0.199515	+	0.345570i	0.748856	+	0.662733i	$0.230603\pi$
$762$	−0.0444153	−	0.0161658i	−0.00160900	−	0.000585627i
$763$		0			0
$764$	−17.8059	−	14.9409i	−0.644194	−	0.540543i
$765$	1.97431	+	11.1969i	0.0713812	+	0.404823i
$766$	−19.3830	+	7.05482i	−0.700334	+	0.254901i
$767$	56.9231			2.05538
$768$	8.56717			0.309141
$769$	20.0599	−	7.30121i	0.723378	−	0.263288i	0.0460191	−	0.998941i	$-0.485346\pi$
$769$	20.0599	−	7.30121i	0.723378	−	0.263288i	0.677359	+	0.735652i	$0.263124\pi$
$770$		0			0
$771$	−4.08512	−	7.07564i	−0.147122	−	0.254823i
$772$	7.91312	+	13.7059i	0.284800	+	0.493287i
$773$	16.8366	−	6.12803i	0.605571	−	0.220410i	−0.0209932	−	0.999780i	$-0.506683\pi$
$773$	16.8366	−	6.12803i	0.605571	−	0.220410i	0.626564	+	0.779370i	$0.284461\pi$
$774$	10.7780	+	3.92286i	0.387406	+	0.141004i
$775$	2.57785	−	0.938260i	0.0925990	−	0.0337033i
$776$	−0.898214	−	5.09403i	−0.0322440	−	0.182865i
$777$		0			0
$778$	3.43788			0.123254
$779$	−5.17587	−	18.8755i	−0.185445	−	0.676287i
$780$	−4.37211	−	7.57272i	−0.156547	−	0.271147i
$781$	−8.15064	−	46.2246i	−0.291653	−	1.65405i
$782$	2.40198	+	0.874249i	0.0858946	+	0.0312631i
$783$	−8.08100	−	6.78077i	−0.288792	−	0.242325i
$784$		0			0
$785$	4.56165	−	25.8704i	0.162812	−	0.923355i
$786$	0.710485	+	1.23060i	0.0253422	+	0.0438939i
$787$	24.4158	−	42.2894i	0.870330	−	1.50746i	0.00867371	−	0.999962i	$-0.497239\pi$
$787$	24.4158	−	42.2894i	0.870330	−	1.50746i	0.861656	−	0.507493i	$-0.169428\pi$
$788$	21.8011	+	18.2933i	0.776633	+	0.651672i
$789$	−0.890996	+	5.05309i	−0.0317203	+	0.179895i
$790$	7.75237	+	13.4275i	0.275817	+	0.477729i
$791$		0			0
$792$	4.56687	−	25.9000i	0.162277	−	0.920316i
$793$	−4.03256	−	22.8698i	−0.143200	−	0.812129i
$794$	−1.36808	+	7.75876i	−0.0485513	+	0.275348i
$795$	6.30200	−	5.28801i	0.223509	−	0.187546i
$796$	8.66550	−	7.27122i	0.307140	−	0.257721i
$797$	28.5262			1.01045			0.505225	−	0.862988i	$-0.331409\pi$
$797$	28.5262			1.01045			0.505225	+	0.862988i	$0.331409\pi$
$798$		0			0
$799$	1.18479			0.0419149
$800$	6.09627	−	5.11538i	0.215536	−	0.180856i
$801$	−4.75174	+	3.98719i	−0.167895	+	0.140880i
$802$	−0.309582	+	1.75573i	−0.0109317	+	0.0619969i
$803$	4.45336	+	25.2563i	0.157156	+	0.891275i
$804$	1.61081	−	9.13538i	0.0568091	−	0.322180i
$805$		0			0
$806$	4.52141	+	7.83131i	0.159260	+	0.275846i
$807$	−1.68891	+	9.57829i	−0.0594525	+	0.337172i
$808$	−17.2181	−	14.4477i	−0.605729	−	0.508267i
$809$	7.41834	−	12.8489i	0.260815	−	0.451745i	−0.705644	−	0.708567i	$-0.749342\pi$
$809$	7.41834	−	12.8489i	0.260815	−	0.451745i	0.966459	+	0.256822i	$0.0826755\pi$
$810$	−7.27244	−	12.5962i	−0.255528	−	0.442587i
$811$	1.45471	−	8.25006i	0.0510817	−	0.289699i	−0.948556	−	0.316609i	$-0.897456\pi$
$811$	1.45471	−	8.25006i	0.0510817	−	0.289699i	0.999638	+	0.0269103i	$0.00856684\pi$
$812$		0			0
$813$	7.72984	+	6.48610i	0.271097	+	0.227478i
$814$	2.36097	+	0.859322i	0.0827518	+	0.0301192i
$815$	−0.889185	−	5.04282i	−0.0311468	−	0.176642i
$816$	0.0184183	+	0.0319015i	0.000644770	+	0.00111677i
$817$	−14.7101	+	14.8827i	−0.514640	+	0.520679i
$818$	28.3233			0.990299
$819$		0			0
$820$	−2.42185	−	13.7350i	−0.0845746	−	0.479646i
$821$	−5.90033	+	2.14754i	−0.205923	+	0.0749498i	−0.442922	−	0.896560i	$-0.646058\pi$
$821$	−5.90033	+	2.14754i	−0.205923	+	0.0749498i	0.236999	+	0.971510i	$0.423836\pi$
$822$	8.59152	+	3.12706i	0.299664	+	0.109069i
$823$	−10.3614	+	3.77125i	−0.361177	+	0.131458i	−0.516233	−	0.856448i	$-0.672666\pi$
$823$	−10.3614	+	3.77125i	−0.361177	+	0.131458i	0.155056	+	0.987906i	$0.450444\pi$
$824$	0.0206398	+	0.0357492i	0.000719023	+	0.00124538i
$825$	1.28106	+	2.21886i	0.0446008	+	0.0772508i
$826$		0			0
$827$	−31.8892	+	11.6067i	−1.10890	+	0.403606i	−0.830589	−	0.556886i	$-0.811996\pi$
$827$	−31.8892	+	11.6067i	−1.10890	+	0.403606i	−0.278309	+	0.960492i	$0.589774\pi$
$828$	5.86154			0.203703
$829$	20.3669			0.707372			0.353686	−	0.935364i	$-0.384928\pi$
$829$	20.3669			0.707372			0.353686	+	0.935364i	$0.384928\pi$
$830$	5.25712	−	1.91344i	0.182477	−	0.0664163i
$831$	−1.27173	−	7.21232i	−0.0441157	−	0.250192i
$832$	20.4349	+	17.1470i	0.708454	+	0.594464i
$833$		0			0
$834$	−6.76991	−	2.46405i	−0.234423	−	0.0853230i
$835$	−29.4440	+	50.9986i	−1.01895	+	1.76488i
$836$	15.0030	+	10.3753i	0.518889	+	0.358838i
$837$	2.95605	+	5.12003i	0.102176	+	0.176974i
$838$	15.6623	−	13.1422i	0.541044	−	0.453990i
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	−0.994815	−	0.101697i	$-0.967573\pi$
$839$	−2.74526	−	15.5692i	−0.0947770	−	0.537507i	0.900038	−	0.435810i	$-0.143538\pi$
$840$		0			0
$841$	−13.0025	+	10.9104i	−0.448363	+	0.376221i
$842$	4.34730	+	3.64781i	0.149818	+	0.125712i
$843$	−6.97628			−0.240276
$844$	8.96926	−	15.5352i	0.308734	−	0.534744i
$845$	6.59240	−	37.3873i	0.226785	−	1.28616i
$846$	−1.60947	+	0.585799i	−0.0553347	+	0.0201402i
$847$		0			0
$848$	−0.127889	+	0.221510i	−0.00439172	+	0.00760668i
$849$	−7.08306	−	5.94340i	−0.243090	−	0.203977i
$850$	1.92767	+	0.701615i	0.0661186	+	0.0240652i
$851$	−0.255777	+	1.45059i	−0.00876794	+	0.0497254i
$852$	8.43882	+	3.07148i	0.289109	+	0.105227i
$853$	−49.4741	−	18.0071i	−1.69396	−	0.616551i	−0.698845	−	0.715274i	$-0.746302\pi$
$853$	−49.4741	−	18.0071i	−1.69396	−	0.616551i	−0.995115	+	0.0987227i	$0.968524\pi$
$854$		0			0
$855$	29.8567	−	2.78768i	1.02108	−	0.0953368i
$856$	−5.04277	+	8.73433i	−0.172358	+	0.298533i
$857$	3.99866	+	22.6775i	0.136591	+	0.774649i	0.973738	+	0.227670i	$0.0731109\pi$
$857$	3.99866	+	22.6775i	0.136591	+	0.774649i	−0.837147	+	0.546978i	$0.815778\pi$
$858$	−6.46972	+	5.42874i	−0.220873	+	0.185334i
$859$	8.37211	−	3.04720i	0.285653	−	0.103969i	−0.195220	−	0.980759i	$-0.562542\pi$
$859$	8.37211	−	3.04720i	0.285653	−	0.103969i	0.480873	+	0.876790i	$0.340320\pi$
$860$	−11.4226	+	9.58471i	−0.389508	+	0.326836i
$861$		0			0
$862$	6.15451	−	10.6599i	0.209624	−	0.363079i
$863$	29.7698			1.01338			0.506688	−	0.862129i	$-0.330870\pi$
$863$	29.7698			1.01338			0.506688	+	0.862129i	$0.330870\pi$
$864$	13.1382	+	11.0242i	0.446969	+	0.375052i
$865$	−1.73917	−	1.45934i	−0.0591336	−	0.0496189i
$866$	25.2321			0.857420
$867$	−3.79607	+	6.57499i	−0.128921	+	0.223298i
$868$		0			0
$869$	−18.1971	+	15.2692i	−0.617295	+	0.517972i
$870$	−3.86097	+	1.40528i	−0.130899	+	0.0476434i
$871$	57.6023	−	48.3340i	1.95178	−	1.63774i
$872$	−3.63119	−	20.5935i	−0.122967	−	0.697383i
$873$	2.47637	−	4.28919i	0.0838123	−	0.145167i
$874$	2.81345	−	6.12651i	0.0951665	−	0.207232i
$875$		0			0
$876$	−4.61081	−	1.67820i	−0.155785	−	0.0567011i
$877$	23.5205	+	8.56077i	0.794232	+	0.289077i	0.707094	−	0.707119i	$-0.250006\pi$
$877$	23.5205	+	8.56077i	0.794232	+	0.289077i	0.0871379	+	0.996196i	$0.472228\pi$
$878$	2.03741	−	11.5547i	0.0687592	−	0.389953i
$879$	−7.80200	−	2.83970i	−0.263155	−	0.0957806i
$880$	−0.277189	−	0.232589i	−0.00934403	−	0.00784057i
$881$	10.1980	−	17.6634i	0.343579	−	0.595097i	−0.641515	−	0.767110i	$-0.721694\pi$
$881$	10.1980	−	17.6634i	0.343579	−	0.595097i	0.985095	+	0.172014i	$0.0550273\pi$
$882$		0			0
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	−0.168460	−	0.985708i	$-0.553880\pi$
$883$	9.98710	−	3.63501i	0.336093	−	0.122328i	0.504553	+	0.863381i	$0.331657\pi$
$884$	1.86262	−	10.5634i	0.0626465	−	0.355286i
$885$	7.24763	−	12.5533i	0.243626	−	0.421973i
$886$	29.7962			1.00102
$887$	43.1580	+	36.2138i	1.44910	+	1.21594i	0.933231	+	0.359276i	$0.116976\pi$
$887$	43.1580	+	36.2138i	1.44910	+	1.21594i	0.515872	+	0.856666i	$0.327468\pi$
$888$	−0.968626	+	0.812774i	−0.0325050	+	0.0272749i
$889$		0			0
$890$	0.882789	+	5.00654i	0.0295911	+	0.167820i
$891$	17.0706	−	14.3239i	0.571886	−	0.479869i
$892$	1.84895	+	3.20247i	0.0619073	+	0.107227i
$893$	0.254185	−	3.11446i	0.00850597	−	0.104221i
$894$	−0.881196	+	1.52628i	−0.0294716	+	0.0510463i
$895$	50.7242	+	18.4621i	1.69552	+	0.617120i
$896$		0			0
$897$	−3.79292	−	3.18264i	−0.126642	−	0.106265i
$898$	2.87696	+	16.3161i	0.0960056	+	0.544475i
$899$	−6.33363	+	2.30525i	−0.211238	+	0.0768844i
$900$	4.70409			0.156803
$901$	10.0915			0.336197
$902$	−12.6582	+	4.60722i	−0.421473	+	0.153404i
$903$		0			0
$904$	10.4666	+	18.1286i	0.348113	+	0.602949i
$905$	−20.3824	−	35.3033i	−0.677533	−	1.17352i
$906$	−6.41787	+	2.33591i	−0.213219	+	0.0776055i
$907$	5.56640	+	2.02600i	0.184829	+	0.0672723i	0.432777	−	0.901501i	$-0.357534\pi$
$907$	5.56640	+	2.02600i	0.184829	+	0.0672723i	−0.247948	+	0.968773i	$0.579756\pi$
$908$	15.8173	−	5.75703i	0.524916	−	0.191054i
$909$	−3.73711	−	21.1942i	−0.123952	−	0.702968i
$910$		0			0
$911$	−34.0591			−1.12843			−0.564215	−	0.825628i	$-0.690821\pi$
$911$	−34.0591			−1.12843			−0.564215	+	0.825628i	$0.690821\pi$
$912$	0.0878107	−	0.0415720i	0.00290770	−	0.00137659i
$913$	4.28564	+	7.42295i	0.141834	+	0.245664i
$914$	2.18046	+	12.3660i	0.0721231	+	0.409030i
$915$	−5.55690	−	2.02255i	−0.183706	−	0.0668634i
$916$	8.84642	+	7.42303i	0.292294	+	0.245264i
$917$		0			0
$918$	−0.767693	+	4.35381i	−0.0253377	+	0.143697i
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	0.913116	−	0.407700i	$-0.133669\pi$
$919$	3.13697	+	5.43340i	0.103479	+	0.179231i	−0.809637	+	0.586931i	$0.800336\pi$
$920$	6.31820	−	10.9434i	0.208305	−	0.360795i
$921$	8.77173	+	7.36035i	0.289038	+	0.242532i
$922$	2.12687	−	12.0621i	0.0700447	−	0.397243i
$923$	36.3979	+	63.0429i	1.19805	+	2.07508i
$924$		0			0
$925$	−0.205270	+	1.16415i	−0.00674924	+	0.0382769i
$926$	−0.269200	−	1.52671i	−0.00884645	−	0.0501707i
$927$	−0.00686344	+	0.0389245i	−0.000225425	+	0.00127845i
$928$	−14.9782	+	12.5682i	−0.491683	+	0.412571i
$929$	−21.6969	+	18.2058i	−0.711851	+	0.597314i	−0.925118	−	0.379680i	$-0.876034\pi$
$929$	−21.6969	+	18.2058i	−0.711851	+	0.597314i	0.213267	+	0.976994i	$0.431590\pi$
$930$	2.30272			0.0755091
$931$		0			0
$932$	29.6682			0.971814
$933$	5.90832	−	4.95767i	0.193430	−	0.162307i
$934$	−14.8485	+	12.4594i	−0.485857	+	0.407682i
$935$	−2.47906	+	14.0594i	−0.0810738	+	0.459792i
$936$	7.08276	+	40.1683i	0.231507	+	1.31294i
$937$	3.48545	−	19.7670i	0.113865	−	0.645759i	−0.873441	−	0.486930i	$-0.838117\pi$
$937$	3.48545	−	19.7670i	0.113865	−	0.645759i	0.987306	−	0.158830i	$-0.0507720\pi$
$938$		0			0
$939$	−5.19278	−	8.99416i	−0.169460	−	0.293513i
$940$	0.386659	−	2.19285i	0.0126114	−	0.0715230i
$941$	−4.13294	−	3.46795i	−0.134730	−	0.113052i	0.572932	−	0.819603i	$-0.305806\pi$
$941$	−4.13294	−	3.46795i	−0.134730	−	0.113052i	−0.707662	+	0.706551i	$0.750250\pi$
$942$	2.42720	−	4.20404i	0.0790826	−	0.136975i
$943$	−3.94862	−	6.83920i	−0.128585	−	0.222715i
$944$	−0.0782589	+	0.443828i	−0.00254711	+	0.0144454i
$945$		0			0
$946$	11.0326	+	9.25741i	0.358699	+	0.300984i
$947$	−6.24257	−	2.27211i	−0.202856	−	0.0738337i	0.238594	−	0.971119i	$-0.423314\pi$
$947$	−6.24257	−	2.27211i	−0.202856	−	0.0738337i	−0.441450	+	0.897286i	$0.645536\pi$
$948$	−0.789210	−	4.47584i	−0.0256324	−	0.145368i
$949$	−19.8871	−	34.4455i	−0.645563	−	1.11815i
$950$	2.25789	−	4.91673i	0.0732557	−	0.159520i
$951$	−15.0833			−0.489109
$952$		0			0
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	−0.997693	−	0.0678799i	$-0.978377\pi$
$953$	−2.57414	−	14.5987i	−0.0833846	−	0.472897i	0.914309	−	0.405018i	$-0.132735\pi$
$954$	−13.7087	+	4.98957i	−0.443837	+	0.161543i
$955$	−45.0861	−	16.4100i	−1.45895	−	0.531015i
$956$	−26.8879	+	9.78639i	−0.869617	+	0.316515i
$957$	−3.14749	−	5.45161i	−0.101744	−	0.176226i
$958$	−11.1932	−	19.3873i	−0.361637	−	0.626374i
$959$		0			0
$960$	6.38326	−	2.32332i	0.206019	−	0.0749847i
$961$	−27.2226			−0.878147
$962$	−3.89662			−0.125632
$963$	−9.07444	+	3.30283i	−0.292420	+	0.106432i
$964$	0.0634062	+	0.359595i	0.00204218	+	0.0115818i
$965$	25.0253	+	20.9987i	0.805592	+	0.675972i
$966$		0			0
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	0.000850519	−	1.00000i	$-0.499729\pi$
$967$	−19.9418	−	7.25822i	−0.641285	−	0.233409i	−0.642136	+	0.766591i	$0.721951\pi$
$968$	0.905382	−	1.56817i	0.0291001	−	0.0504028i
$969$	−3.15270	−	2.18025i	−0.101279	−	0.0700399i
$970$	−2.02956	−	3.51531i	−0.0651653	−	0.112870i
$971$	28.8084	−	24.1731i	0.924506	−	0.775752i	−0.0503172	−	0.998733i	$-0.516023\pi$
$971$	28.8084	−	24.1731i	0.924506	−	0.775752i	0.974823	+	0.222981i	$0.0715788\pi$
$972$	2.68422	+	15.2230i	0.0860964	+	0.488277i
$973$		0			0
$974$	−15.1643	+	12.7244i	−0.485896	+	0.407715i
$975$	−3.04395	−	2.55418i	−0.0974844	−	0.0817991i
$976$	0.183859			0.00588518
$977$	23.0107	−	39.8558i	0.736179	−	1.27510i	−0.218026	−	0.975943i	$-0.569962\pi$
$977$	23.0107	−	39.8558i	0.736179	−	1.27510i	0.954204	−	0.299156i	$-0.0967050\pi$
$978$	0.164315	−	0.931876i	0.00525421	−	0.0297981i
$979$	−7.31908	+	2.66393i	−0.233919	+	0.0851395i
$980$		0			0
$981$	10.0111	−	17.3398i	0.319631	−	0.553618i
$982$	10.5318	+	8.83726i	0.336085	+	0.282008i
$983$	56.9420	+	20.7252i	1.81617	+	0.661031i	0.996046	+	0.0888404i	$0.0283161\pi$
$983$	56.9420	+	20.7252i	1.81617	+	0.661031i	0.820121	+	0.572190i	$0.193906\pi$
$984$	1.17721	−	6.67631i	0.0375282	−	0.212833i
$985$	55.2024	+	20.0920i	1.75889	+	0.640185i
$986$	−4.73618	−	1.72383i	−0.150831	−	0.0548979i
$987$		0			0
$988$	−27.3684	−	7.16252i	−0.870705	−	0.227870i
$989$	−4.22163	+	7.31208i	−0.134240	+	0.232510i
$990$	−3.58378	−	20.3246i	−0.113900	−	0.645959i
$991$	32.0959	−	26.9316i	1.01956	−	0.855511i	0.0299865	−	0.999550i	$-0.490454\pi$
$991$	32.0959	−	26.9316i	1.01956	−	0.855511i	0.989572	+	0.144039i	$0.0460091\pi$
$992$	10.2973	−	3.74789i	0.326938	−	0.118996i
$993$	0.697033	−	0.584880i	0.0221197	−	0.0185606i
$994$		0			0
$995$	11.6750	−	20.2217i	0.370122	−	0.641070i
$996$	−1.63991			−0.0519626
$997$	−25.8273	−	21.6717i	−0.817958	−	0.686349i	0.134535	−	0.990909i	$-0.457046\pi$
$997$	−25.8273	−	21.6717i	−0.817958	−	0.686349i	−0.952493	+	0.304560i	$0.901490\pi$
$998$	−19.2777	−	16.1759i	−0.610224	−	0.512038i
$999$	−2.54757			−0.0806016

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.v.a.422.1		6
7.2	even	3		931.2.w.a.99.1		6
7.3	odd	6		931.2.x.a.802.1		6
7.4	even	3		931.2.x.b.802.1		6
7.5	odd	6		19.2.e.a.4.1	✓	6
7.6	odd	2		931.2.v.b.422.1		6
19.5	even	9		931.2.x.b.765.1		6
21.5	even	6		171.2.u.c.118.1		6
28.19	even	6		304.2.u.b.289.1		6
35.12	even	12		475.2.u.a.99.2		12
35.19	odd	6		475.2.l.a.251.1		6
35.33	even	12		475.2.u.a.99.1		12
133.5	odd	18		19.2.e.a.5.1	yes	6
133.12	even	6		361.2.e.b.234.1		6
133.24	odd	18		931.2.v.b.214.1		6
133.26	odd	6		361.2.e.f.234.1		6
133.33	even	18		361.2.e.h.62.1		6
133.40	even	18		361.2.e.b.54.1		6
133.47	odd	18		361.2.a.g.1.3		3
133.54	odd	18		361.2.e.g.245.1		6
133.61	odd	18		361.2.c.i.292.1		6
133.62	odd	18		931.2.x.a.765.1		6
133.68	odd	6		361.2.e.g.28.1		6
133.75	even	6		361.2.e.h.99.1		6
133.81	even	9	inner	931.2.v.a.214.1		6
133.82	odd	18		361.2.c.i.68.1		6
133.89	even	18		361.2.c.h.68.3		6
133.100	even	9		931.2.w.a.442.1		6
133.103	even	6		361.2.e.a.28.1		6
133.110	even	18		361.2.c.h.292.3		6
133.117	even	18		361.2.e.a.245.1		6
133.124	even	18		361.2.a.h.1.1		3
133.131	odd	18		361.2.e.f.54.1		6
399.5	even	18		171.2.u.c.100.1		6
399.47	even	18		3249.2.a.z.1.1		3
399.257	odd	18		3249.2.a.s.1.3		3
532.47	even	18		5776.2.a.br.1.1		3
532.271	even	18		304.2.u.b.81.1		6
532.523	odd	18		5776.2.a.bi.1.3		3
665.124	even	18		9025.2.a.x.1.3		3
665.138	even	36		475.2.u.a.24.2		12
665.404	odd	18		475.2.l.a.176.1		6
665.537	even	36		475.2.u.a.24.1		12
665.579	odd	18		9025.2.a.bd.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.2.e.a.4.1	✓	6	7.5	odd	6
19.2.e.a.5.1	yes	6	133.5	odd	18
171.2.u.c.100.1		6	399.5	even	18
171.2.u.c.118.1		6	21.5	even	6
304.2.u.b.81.1		6	532.271	even	18
304.2.u.b.289.1		6	28.19	even	6
361.2.a.g.1.3		3	133.47	odd	18
361.2.a.h.1.1		3	133.124	even	18
361.2.c.h.68.3		6	133.89	even	18
361.2.c.h.292.3		6	133.110	even	18
361.2.c.i.68.1		6	133.82	odd	18
361.2.c.i.292.1		6	133.61	odd	18
361.2.e.a.28.1		6	133.103	even	6
361.2.e.a.245.1		6	133.117	even	18
361.2.e.b.54.1		6	133.40	even	18
361.2.e.b.234.1		6	133.12	even	6
361.2.e.f.54.1		6	133.131	odd	18
361.2.e.f.234.1		6	133.26	odd	6
361.2.e.g.28.1		6	133.68	odd	6
361.2.e.g.245.1		6	133.54	odd	18
361.2.e.h.62.1		6	133.33	even	18
361.2.e.h.99.1		6	133.75	even	6
475.2.l.a.176.1		6	665.404	odd	18
475.2.l.a.251.1		6	35.19	odd	6
475.2.u.a.24.1		12	665.537	even	36
475.2.u.a.24.2		12	665.138	even	36
475.2.u.a.99.1		12	35.33	even	12
475.2.u.a.99.2		12	35.12	even	12
931.2.v.a.214.1		6	133.81	even	9	inner
931.2.v.a.422.1		6	1.1	even	1	trivial
931.2.v.b.214.1		6	133.24	odd	18
931.2.v.b.422.1		6	7.6	odd	2
931.2.w.a.99.1		6	7.2	even	3
931.2.w.a.442.1		6	133.100	even	9
931.2.x.a.765.1		6	133.62	odd	18
931.2.x.a.802.1		6	7.3	odd	6
931.2.x.b.765.1		6	19.5	even	9
931.2.x.b.802.1		6	7.4	even	3
3249.2.a.s.1.3		3	399.257	odd	18
3249.2.a.z.1.1		3	399.47	even	18
5776.2.a.bi.1.3		3	532.523	odd	18
5776.2.a.br.1.1		3	532.47	even	18
9025.2.a.x.1.3		3	665.124	even	18
9025.2.a.bd.1.1		3	665.579	odd	18

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:	\( N \)	\(=\)	\( 931 = 7^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	931.v (of order \(9\), degree \(6\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.673648 - 0.565258i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-0.0812519 + 0.460802i) q^{6} +(1.41875 + 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +O(q^{10})\)	\(q+(0.673648 - 0.565258i) q^{2} +(-0.407604 + 0.342020i) q^{3} +(-0.213011 + 1.20805i) q^{4} +(0.439693 + 2.49362i) q^{5} +(-0.0812519 + 0.460802i) q^{6} +(1.41875 + 2.45734i) q^{8} +(-0.471782 + 2.67561i) q^{9} +(1.70574 + 1.43128i) q^{10} +(-1.70574 + 2.95442i) q^{11} +(-0.326352 - 0.565258i) q^{12} +(0.918748 - 5.21048i) q^{13} +(-1.03209 - 0.866025i) q^{15} +(0.0393628 + 0.0143269i) q^{16} +(-0.286989 - 1.62760i) q^{17} +(1.19459 + 2.06910i) q^{18} +(-4.34002 + 0.405223i) q^{19} -3.10607 q^{20} +(0.520945 + 2.95442i) q^{22} +(-1.65270 + 0.601535i) q^{23} +(-1.41875 - 0.516382i) q^{24} +(-1.32635 + 0.482753i) q^{25} +(-2.32635 - 4.02936i) q^{26} +(-1.52094 - 2.63435i) q^{27} +(3.25877 - 1.18610i) q^{29} -1.18479 q^{30} -1.94356 q^{31} +(-5.29813 + 1.92836i) q^{32} +(-0.315207 - 1.78763i) q^{33} +(-1.11334 - 0.934204i) q^{34} +(-3.13176 - 1.13987i) q^{36} +(0.418748 - 0.725293i) q^{37} +(-2.69459 + 2.72621i) q^{38} +(1.40760 + 2.43804i) q^{39} +(-5.50387 + 4.61830i) q^{40} +(0.779715 + 4.42198i) q^{41} +(3.67752 - 3.08580i) q^{43} +(-3.20574 - 2.68993i) q^{44} -6.87939 q^{45} +(-0.773318 + 1.33943i) q^{46} +(-0.124485 + 0.705990i) q^{47} +(-0.0209445 + 0.00762319i) q^{48} +(-0.620615 + 1.07494i) q^{50} +(0.673648 + 0.565258i) q^{51} +(6.09879 + 2.21978i) q^{52} +(-1.06031 + 6.01330i) q^{53} +(-2.51367 - 0.914901i) q^{54} +(-8.11721 - 2.95442i) q^{55} +(1.63041 - 1.64955i) q^{57} +(1.52481 - 2.64106i) q^{58} +(1.86824 + 10.5953i) q^{59} +(1.26604 - 1.06234i) q^{60} +(4.12449 - 1.50119i) q^{61} +(-1.30928 + 1.09861i) q^{62} +(-2.52094 + 4.36640i) q^{64} +13.3969 q^{65} +(-1.22281 - 1.02606i) q^{66} +(10.8871 + 9.13538i) q^{67} +2.02734 q^{68} +(0.467911 - 0.810446i) q^{69} +(-10.5398 + 8.84397i) q^{71} +(-7.24422 + 2.63668i) q^{72} +(5.75877 - 4.83218i) q^{73} +(-0.127889 - 0.725293i) q^{74} +(0.375515 - 0.650411i) q^{75} +(0.434945 - 5.32926i) q^{76} +(2.32635 + 0.846723i) q^{78} +(6.54323 + 2.38154i) q^{79} +(-0.0184183 + 0.104455i) q^{80} +(-6.13816 - 2.23411i) q^{81} +(3.02481 + 2.53812i) q^{82} +(1.25624 - 2.17588i) q^{83} +(3.93242 - 1.43128i) q^{85} +(0.733078 - 4.15749i) q^{86} +(-0.922618 + 1.59802i) q^{87} -9.68004 q^{88} +(1.74897 + 1.46756i) q^{89} +(-4.63429 + 3.88863i) q^{90} +(-0.374638 - 2.12467i) q^{92} +(0.792204 - 0.664738i) q^{93} +(0.315207 + 0.545955i) q^{94} +(-2.91875 - 10.6442i) q^{95} +(1.50000 - 2.59808i) q^{96} +(-1.71301 - 0.623485i) q^{97} +(-7.10014 - 5.95772i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9	\( 6 q + 3 q^{2} - 6 q^{3} - 9 q^{4} - 3 q^{5} - 3 q^{6} + 6 q^{8} + 12 q^{9} - 3 q^{12} + 3 q^{13} + 3 q^{15} + 9 q^{16} + 6 q^{17} + 3 q^{18} - 6 q^{19} + 6 q^{20} - 12 q^{23} - 6 q^{24} - 9 q^{25} - 15 q^{26} - 6 q^{27} - 3 q^{29} + 18 q^{31} - 18 q^{32} - 9 q^{33} - 24 q^{36} - 12 q^{38} + 12 q^{39} - 9 q^{40} - 21 q^{41} - 3 q^{43} - 9 q^{44} - 30 q^{45} - 18 q^{46} + 12 q^{47} + 3 q^{48} - 15 q^{50} + 3 q^{51} - 6 q^{52} - 12 q^{53} + 6 q^{54} - 18 q^{55} + 24 q^{57} - 18 q^{58} + 6 q^{59} + 3 q^{60} + 12 q^{61} + 12 q^{62} - 12 q^{64} + 24 q^{65} - 18 q^{66} + 6 q^{67} - 30 q^{68} + 12 q^{69} - 6 q^{71} + 15 q^{72} + 12 q^{73} - 30 q^{74} + 15 q^{75} - 36 q^{76} + 15 q^{78} + 24 q^{79} - 12 q^{80} - 3 q^{81} - 9 q^{82} - 48 q^{86} + 21 q^{87} - 18 q^{88} - 15 q^{89} - 18 q^{90} + 42 q^{92} - 36 q^{93} + 9 q^{94} - 15 q^{95} + 9 q^{96} - 18 q^{97} + 9 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 - 6 * q^3 - 9 * q^4 - 3 * q^5 - 3 * q^6 + 6 * q^8 + 12 * q^9 - 3 * q^12 + 3 * q^13 + 3 * q^15 + 9 * q^16 + 6 * q^17 + 3 * q^18 - 6 * q^19 + 6 * q^20 - 12 * q^23 - 6 * q^24 - 9 * q^25 - 15 * q^26 - 6 * q^27 - 3 * q^29 + 18 * q^31 - 18 * q^32 - 9 * q^33 - 24 * q^36 - 12 * q^38 + 12 * q^39 - 9 * q^40 - 21 * q^41 - 3 * q^43 - 9 * q^44 - 30 * q^45 - 18 * q^46 + 12 * q^47 + 3 * q^48 - 15 * q^50 + 3 * q^51 - 6 * q^52 - 12 * q^53 + 6 * q^54 - 18 * q^55 + 24 * q^57 - 18 * q^58 + 6 * q^59 + 3 * q^60 + 12 * q^61 + 12 * q^62 - 12 * q^64 + 24 * q^65 - 18 * q^66 + 6 * q^67 - 30 * q^68 + 12 * q^69 - 6 * q^71 + 15 * q^72 + 12 * q^73 - 30 * q^74 + 15 * q^75 - 36 * q^76 + 15 * q^78 + 24 * q^79 - 12 * q^80 - 3 * q^81 - 9 * q^82 - 48 * q^86 + 21 * q^87 - 18 * q^88 - 15 * q^89 - 18 * q^90 + 42 * q^92 - 36 * q^93 + 9 * q^94 - 15 * q^95 + 9 * q^96 - 18 * q^97 + 9 * q^99

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