LMFDB - Embedded newform 931.2.v.e.275.2

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:	$30$
Relative dimension:	$5$ over $\Q(\zeta_{9})$
Twist minimal:	no (minimal twist has level 133)
Sato-Tate group:	$\mathrm{SU}(2)[C_{9}]$

Embedding invariants

Embedding label			275.2
Character	$\chi$	$=$	931.275
Dual form			931.2.v.e.606.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.52863 - 0.556375i) q^{2} +(1.01101 + 0.367976i) q^{3} +(0.495058 + 0.415403i) q^{4} +(-0.0539084 + 0.0452345i) q^{5} +(-1.34072 - 1.12500i) q^{6} +(1.10109 + 1.90715i) q^{8} +(-1.41140 - 1.18431i) q^{9} +O(q^{10})$	\(q+(-1.52863 - 0.556375i) q^{2} +(1.01101 + 0.367976i) q^{3} +(0.495058 + 0.415403i) q^{4} +(-0.0539084 + 0.0452345i) q^{5} +(-1.34072 - 1.12500i) q^{6} +(1.10109 + 1.90715i) q^{8} +(-1.41140 - 1.18431i) q^{9} +(0.107573 - 0.0391534i) q^{10} +(-0.895617 + 1.55125i) q^{11} +(0.347648 + 0.602145i) q^{12} +(2.27346 + 1.90766i) q^{13} +(-0.0711470 + 0.0258954i) q^{15} +(-0.846511 - 4.80080i) q^{16} +(0.482311 - 0.404707i) q^{17} +(1.49859 + 2.59564i) q^{18} +(-4.10808 + 1.45729i) q^{19} -0.0454783 q^{20} +(2.23214 - 1.87299i) q^{22} +(-0.260520 + 1.47748i) q^{23} +(0.411426 + 2.33331i) q^{24} +(-0.867381 + 4.91916i) q^{25} +(-2.41390 - 4.18100i) q^{26} +(-2.60498 - 4.51196i) q^{27} +(-0.942253 + 5.34378i) q^{29} +0.123165 q^{30} +6.53051 q^{31} +(-0.612235 + 3.47216i) q^{32} +(-1.47630 + 1.23876i) q^{33} +(-0.962442 + 0.350300i) q^{34} +(-0.206761 - 1.17260i) q^{36} +(-0.345571 + 0.598546i) q^{37} +(7.09052 + 0.0579855i) q^{38} +(1.59651 + 2.76524i) q^{39} +(-0.145627 - 0.0530039i) q^{40} +(-5.15375 + 4.32451i) q^{41} +(-1.77256 - 0.645159i) q^{43} +(-1.08778 + 0.395918i) q^{44} +0.129658 q^{45} +(1.22027 - 2.11357i) q^{46} +(1.06525 + 0.893854i) q^{47} +(0.910754 - 5.16514i) q^{48} +(4.06280 - 7.03697i) q^{50} +(0.636542 - 0.231682i) q^{51} +(0.333047 + 1.88881i) q^{52} +(5.65278 + 4.74325i) q^{53} +(1.47170 + 8.34644i) q^{54} +(-0.0218890 - 0.124138i) q^{55} +(-4.68954 - 0.0383506i) q^{57} +(4.41350 - 7.64440i) q^{58} +(-10.6227 + 8.91351i) q^{59} +(-0.0459789 - 0.0167350i) q^{60} +(0.0291876 - 0.165531i) q^{61} +(-9.98271 - 3.63341i) q^{62} +(-2.00716 + 3.47651i) q^{64} -0.208851 q^{65} +(2.94593 - 1.07223i) q^{66} +(8.68050 - 3.15944i) q^{67} +0.406888 q^{68} +(-0.807065 + 1.39788i) q^{69} +(11.0779 + 4.03202i) q^{71} +(0.704565 - 3.99579i) q^{72} +(-10.5484 - 3.83932i) q^{73} +(0.861264 - 0.722686i) q^{74} +(-2.68706 + 4.65413i) q^{75} +(-2.63910 - 0.985067i) q^{76} +(-0.901962 - 5.11528i) q^{78} +(1.81990 + 10.3211i) q^{79} +(0.262796 + 0.220512i) q^{80} +(-0.0135400 - 0.0767891i) q^{81} +(10.2842 - 3.74315i) q^{82} +(-3.37852 + 5.85176i) q^{83} +(-0.00769389 + 0.0436342i) q^{85} +(2.35063 + 1.97242i) q^{86} +(-2.91901 + 5.05588i) q^{87} -3.94463 q^{88} +(-3.87887 + 1.41179i) q^{89} +(-0.198199 - 0.0721386i) q^{90} +(-0.742721 + 0.623217i) q^{92} +(6.60239 + 2.40307i) q^{93} +(-1.13106 - 1.95905i) q^{94} +(0.155540 - 0.264387i) q^{95} +(-1.89665 + 3.28509i) q^{96} +(0.928436 + 5.26542i) q^{97} +(3.10124 - 1.12876i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9}+O(q^{10}) $ 30 * q + 3 * q^3 + 12 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 21 * q^9	$ 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9} - 36 q^{10} - 18 q^{12} - 30 q^{15} + 15 q^{17} + 15 q^{18} - 6 q^{19} + 30 q^{20} + 12 q^{22} + 12 q^{23} + 63 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} - 42 q^{30} + 24 q^{31} + 60 q^{32} - 9 q^{33} + 42 q^{34} - 21 q^{36} + 18 q^{37} + 60 q^{38} + 12 q^{39} - 87 q^{40} - 3 q^{41} - 12 q^{43} - 72 q^{44} + 54 q^{45} + 6 q^{46} + 36 q^{47} - 18 q^{48} - 3 q^{50} + 15 q^{52} - 15 q^{53} + 21 q^{54} - 33 q^{55} - 12 q^{57} + 30 q^{58} - 42 q^{59} + 12 q^{60} + 75 q^{61} - 96 q^{62} + 3 q^{64} - 90 q^{65} - 18 q^{66} + 30 q^{67} + 102 q^{68} - 15 q^{69} + 30 q^{71} + 99 q^{72} + 12 q^{73} - 57 q^{74} - 72 q^{75} - 84 q^{76} + 6 q^{78} + 3 q^{79} - 78 q^{80} - 6 q^{81} + 6 q^{82} - 12 q^{83} + 42 q^{85} + 42 q^{86} - 24 q^{87} - 72 q^{88} - 24 q^{89} - 180 q^{90} - 75 q^{92} + 12 q^{93} - 21 q^{94} + 30 q^{95} + 33 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) $ 30 * q + 3 * q^3 + 12 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 21 * q^9 - 36 * q^10 - 18 * q^12 - 30 * q^15 + 15 * q^17 + 15 * q^18 - 6 * q^19 + 30 * q^20 + 12 * q^22 + 12 * q^23 + 63 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 - 42 * q^30 + 24 * q^31 + 60 * q^32 - 9 * q^33 + 42 * q^34 - 21 * q^36 + 18 * q^37 + 60 * q^38 + 12 * q^39 - 87 * q^40 - 3 * q^41 - 12 * q^43 - 72 * q^44 + 54 * q^45 + 6 * q^46 + 36 * q^47 - 18 * q^48 - 3 * q^50 + 15 * q^52 - 15 * q^53 + 21 * q^54 - 33 * q^55 - 12 * q^57 + 30 * q^58 - 42 * q^59 + 12 * q^60 + 75 * q^61 - 96 * q^62 + 3 * q^64 - 90 * q^65 - 18 * q^66 + 30 * q^67 + 102 * q^68 - 15 * q^69 + 30 * q^71 + 99 * q^72 + 12 * q^73 - 57 * q^74 - 72 * q^75 - 84 * q^76 + 6 * q^78 + 3 * q^79 - 78 * q^80 - 6 * q^81 + 6 * q^82 - 12 * q^83 + 42 * q^85 + 42 * q^86 - 24 * q^87 - 72 * q^88 - 24 * q^89 - 180 * q^90 - 75 * q^92 + 12 * q^93 - 21 * q^94 + 30 * q^95 + 33 * q^96 + 63 * q^97 + 45 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$248$	$344$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{4}{9}\right)$

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 $

$2$	−1.52863	−	0.556375i	−1.08090	−	0.393416i	−0.260659	−	0.965431i	$-0.583940\pi$
$2$	−1.52863	−	0.556375i	−1.08090	−	0.393416i	−0.820243	+	0.572015i	$0.806162\pi$
$3$	1.01101	+	0.367976i	0.583705	+	0.212451i	0.616959	−	0.786996i	$-0.288365\pi$
$3$	1.01101	+	0.367976i	0.583705	+	0.212451i	−0.0332534	+	0.999447i	$0.510587\pi$
$4$	0.495058	+	0.415403i	0.247529	+	0.207701i
$5$	−0.0539084	+	0.0452345i	−0.0241086	+	0.0202295i	−0.654762	−	0.755835i	$-0.727231\pi$
$5$	−0.0539084	+	0.0452345i	−0.0241086	+	0.0202295i	0.630654	+	0.776064i	$0.282787\pi$
$6$	−1.34072	−	1.12500i	−0.547346	−	0.459278i
$7$		0			0
$7$		0			0
$8$	1.10109	+	1.90715i	0.389295	+	0.674278i
$9$	−1.41140	−	1.18431i	−0.470468	−	0.394770i
$10$	0.107573	−	0.0391534i	0.0340176	−	0.0123814i
$11$	−0.895617	+	1.55125i	−0.270039	+	0.467721i	−0.968871	−	0.247564i	$-0.920370\pi$
$11$	−0.895617	+	1.55125i	−0.270039	+	0.467721i	0.698833	+	0.715285i	$0.253703\pi$
$12$	0.347648	+	0.602145i	0.100357	+	0.173824i
$13$	2.27346	+	1.90766i	0.630545	+	0.529090i	0.901098	−	0.433615i	$-0.142762\pi$
$13$	2.27346	+	1.90766i	0.630545	+	0.529090i	−0.270553	+	0.962705i	$0.587207\pi$
$14$		0			0
$15$	−0.0711470	+	0.0258954i	−0.0183701	+	0.00668616i
$16$	−0.846511	−	4.80080i	−0.211628	−	1.20020i
$17$	0.482311	−	0.404707i	0.116978	−	0.0981558i	−0.582423	−	0.812886i	$-0.697895\pi$
$17$	0.482311	−	0.404707i	0.116978	−	0.0981558i	0.699400	+	0.714730i	$0.253451\pi$
$18$	1.49859	+	2.59564i	0.353221	+	0.611797i
$19$	−4.10808	+	1.45729i	−0.942458	+	0.334324i
$19$	−4.10808	+	1.45729i	−0.942458	+	0.334324i
$20$	−0.0454783			−0.0101693
$21$		0			0
$22$	2.23214	−	1.87299i	0.475894	−	0.399323i
$23$	−0.260520	+	1.47748i	−0.0543221	+	0.308076i	−0.999847	−	0.0174729i	$-0.994438\pi$
$23$	−0.260520	+	1.47748i	−0.0543221	+	0.308076i	0.945525	+	0.325549i	$0.105549\pi$
$24$	0.411426	+	2.33331i	0.0839820	+	0.476286i
$25$	−0.867381	+	4.91916i	−0.173476	+	0.983832i
$26$	−2.41390	−	4.18100i	−0.473405	−	0.819962i
$27$	−2.60498	−	4.51196i	−0.501328	−	0.868326i
$28$		0			0
$29$	−0.942253	+	5.34378i	−0.174972	+	0.992316i	0.763204	+	0.646157i	$0.223625\pi$
$29$	−0.942253	+	5.34378i	−0.174972	+	0.992316i	−0.938176	+	0.346158i	$0.887486\pi$
$30$	0.123165			0.0224867
$31$	6.53051			1.17291			0.586457	−	0.809980i	$-0.300522\pi$
$31$	6.53051			1.17291			0.586457	+	0.809980i	$0.300522\pi$
$32$	−0.612235	+	3.47216i	−0.108229	+	0.613796i
$33$	−1.47630	+	1.23876i	−0.256991	+	0.215641i
$34$	−0.962442	+	0.350300i	−0.165057	+	0.0600760i
$35$		0			0
$36$	−0.206761	−	1.17260i	−0.0344602	−	0.195434i
$37$	−0.345571	+	0.598546i	−0.0568115	+	0.0984003i	−0.893032	−	0.449992i	$-0.851427\pi$
$37$	−0.345571	+	0.598546i	−0.0568115	+	0.0984003i	0.836221	+	0.548393i	$0.184760\pi$
$38$	7.09052	+	0.0579855i	1.15023	+	0.00940649i
$39$	1.59651	+	2.76524i	0.255647	+	0.442793i
$40$	−0.145627	−	0.0530039i	−0.0230257	−	0.00838065i
$41$	−5.15375	+	4.32451i	−0.804881	+	0.675376i	−0.949380	−	0.314129i	$-0.898287\pi$
$41$	−5.15375	+	4.32451i	−0.804881	+	0.675376i	0.144499	+	0.989505i	$0.453843\pi$
$42$		0			0
$43$	−1.77256	−	0.645159i	−0.270313	−	0.0983859i	0.203307	−	0.979115i	$-0.434831\pi$
$43$	−1.77256	−	0.645159i	−0.270313	−	0.0983859i	−0.473620	+	0.880729i	$0.657053\pi$
$44$	−1.08778	+	0.395918i	−0.163989	+	0.0596870i
$45$	0.129658			0.0193283
$46$	1.22027	−	2.11357i	0.179919	−	0.311629i
$47$	1.06525	+	0.893854i	0.155383	+	0.130382i	0.717165	−	0.696904i	$-0.245439\pi$
$47$	1.06525	+	0.893854i	0.155383	+	0.130382i	−0.561782	+	0.827286i	$0.689884\pi$
$48$	0.910754	−	5.16514i	0.131456	−	0.745524i
$49$		0			0
$50$	4.06280	−	7.03697i	0.574566	−	0.995178i
$51$	0.636542	−	0.231682i	0.0891337	−	0.0324420i
$52$	0.333047	+	1.88881i	0.0461854	+	0.261930i
$53$	5.65278	+	4.74325i	0.776469	+	0.651535i	0.942357	−	0.334610i	$-0.108604\pi$
$53$	5.65278	+	4.74325i	0.776469	+	0.651535i	−0.165887	+	0.986145i	$0.553049\pi$
$54$	1.47170	+	8.34644i	0.200273	+	1.13581i
$55$	−0.0218890	−	0.124138i	−0.00295151	−	0.0167388i
$56$		0			0
$57$	−4.68954	−	0.0383506i	−0.621145	−	0.00507966i
$58$	4.41350	−	7.64440i	0.579521	−	1.00376i
$59$	−10.6227	+	8.91351i	−1.38296	+	1.16044i	−0.414856	+	0.909887i	$0.636168\pi$
$59$	−10.6227	+	8.91351i	−1.38296	+	1.16044i	−0.968103	+	0.250553i	$0.919388\pi$
$60$	−0.0459789	−	0.0167350i	−0.00593585	−	0.00216047i
$61$	0.0291876	−	0.165531i	0.00373709	−	0.0211941i	−0.982882	−	0.184235i	$-0.941019\pi$
$61$	0.0291876	−	0.165531i	0.00373709	−	0.0211941i	0.986619	+	0.163041i	$0.0521303\pi$
$62$	−9.98271	−	3.63341i	−1.26781	−	0.461444i
$63$		0			0
$64$	−2.00716	+	3.47651i	−0.250896	+	0.434564i
$65$	−0.208851			−0.0259048
$66$	2.94593	−	1.07223i	0.362619	−	0.131982i
$67$	8.68050	−	3.15944i	1.06049	−	0.385987i	0.247878	−	0.968791i	$-0.420267\pi$
$67$	8.68050	−	3.15944i	1.06049	−	0.385987i	0.812613	+	0.582804i	$0.198044\pi$
$68$	0.406888			0.0493424
$69$	−0.807065	+	1.39788i	−0.0971592	+	0.168285i
$70$		0			0
$71$	11.0779	+	4.03202i	1.31470	+	0.478513i	0.901758	−	0.432242i	$-0.142277\pi$
$71$	11.0779	+	4.03202i	1.31470	+	0.478513i	0.412947	+	0.910755i	$0.364500\pi$
$72$	0.704565	−	3.99579i	0.0830338	−	0.470908i
$73$	−10.5484	−	3.83932i	−1.23460	−	0.449358i	−0.359431	−	0.933172i	$-0.617029\pi$
$73$	−10.5484	−	3.83932i	−1.23460	−	0.449358i	−0.875171	+	0.483813i	$0.839251\pi$
$74$	0.861264	−	0.722686i	0.100120	−	0.0840106i
$75$	−2.68706	+	4.65413i	−0.310275	+	0.537413i
$76$	−2.63910	−	0.985067i	−0.302725	−	0.112995i
$77$		0			0
$78$	−0.901962	−	5.11528i	−0.102127	−	0.579191i
$79$	1.81990	+	10.3211i	0.204754	+	1.16122i	0.897826	+	0.440351i	$0.145146\pi$
$79$	1.81990	+	10.3211i	0.204754	+	1.16122i	−0.693071	+	0.720869i	$0.743743\pi$
$80$	0.262796	+	0.220512i	0.0293815	+	0.0246540i
$81$	−0.0135400	−	0.0767891i	−0.00150444	−	0.00853212i
$82$	10.2842	−	3.74315i	1.13570	−	0.413362i
$83$	−3.37852	+	5.85176i	−0.370840	+	0.642315i	−0.989695	−	0.143191i	$-0.954264\pi$
$83$	−3.37852	+	5.85176i	−0.370840	+	0.642315i	0.618855	+	0.785506i	$0.287597\pi$
$84$		0			0
$85$	−0.00769389	+	0.0436342i	−0.000834519	+	0.00473279i
$86$	2.35063	+	1.97242i	0.253475	+	0.212691i
$87$	−2.91901	+	5.05588i	−0.312951	+	0.542047i
$88$	−3.94463			−0.420499
$89$	−3.87887	+	1.41179i	−0.411159	+	0.149650i	−0.539314	−	0.842104i	$-0.681317\pi$
$89$	−3.87887	+	1.41179i	−0.411159	+	0.149650i	0.128156	+	0.991754i	$0.459094\pi$
$90$	−0.198199	−	0.0721386i	−0.0208920	−	0.00760407i
$91$		0			0
$92$	−0.742721	+	0.623217i	−0.0774340	+	0.0649749i
$93$	6.60239	+	2.40307i	0.684636	+	0.249187i
$94$	−1.13106	−	1.95905i	−0.116660	−	0.202061i
$95$	0.155540	−	0.264387i	0.0159581	−	0.0271255i
$96$	−1.89665	+	3.28509i	−0.193576	+	0.335283i
$97$	0.928436	+	5.26542i	0.0942684	+	0.534623i	0.994969	+	0.100182i	$0.0319427\pi$
$97$	0.928436	+	5.26542i	0.0942684	+	0.534623i	−0.900701	+	0.434440i	$0.856946\pi$
$98$		0			0
$99$	3.10124	−	1.12876i	0.311687	−	0.113445i
$100$	−2.47284	+	2.07496i	−0.247284	+	0.207496i
$101$	−0.865924	+	4.91090i	−0.0861626	+	0.488653i	0.910937	+	0.412545i	$0.135360\pi$
$101$	−0.865924	+	4.91090i	−0.0861626	+	0.488653i	−0.997100	+	0.0761071i	$0.975751\pi$
$102$	−1.10194			−0.109108
$103$	3.00139			0.295736			0.147868	−	0.989007i	$-0.452759\pi$
$103$	3.00139			0.295736			0.147868	+	0.989007i	$0.452759\pi$
$104$	−1.13490	+	6.43634i	−0.111286	+	0.631135i
$105$		0			0
$106$	−6.00197	−	10.3957i	−0.582963	−	1.00972i
$107$	6.25942	+	10.8416i	0.605121	+	1.04810i	0.992032	+	0.125983i	$0.0402086\pi$
$107$	6.25942	+	10.8416i	0.605121	+	1.04810i	−0.386912	+	0.922117i	$0.626458\pi$
$108$	0.584664	−	3.31579i	0.0562593	−	0.319062i
$109$	−2.43770	−	13.8249i	−0.233489	−	1.32418i	−0.845772	−	0.533545i	$-0.820860\pi$
$109$	−2.43770	−	13.8249i	−0.233489	−	1.32418i	0.612283	−	0.790639i	$-0.290251\pi$
$110$	−0.0356074	+	0.201940i	−0.00339504	+	0.0192542i
$111$	−0.569625	+	0.477972i	−0.0540664	+	0.0453671i
$112$		0			0
$113$	−0.420510			−0.0395583			−0.0197791	−	0.999804i	$-0.506296\pi$
$113$	−0.420510			−0.0395583			−0.0197791	+	0.999804i	$0.506296\pi$
$114$	7.14722	+	2.66777i	0.669399	+	0.249859i
$115$	−0.0527889	−	0.0914331i	−0.00492259	−	0.00852618i
$116$	−2.68629	+	2.25407i	−0.249416	+	0.209285i
$117$	−0.949515	−	5.38497i	−0.0877827	−	0.497840i
$118$	21.1974	−	7.71522i	1.95138	−	0.710244i
$119$		0			0
$120$	−0.127726	−	0.107175i	−0.0116597	−	0.00978366i
$121$	3.89574	+	6.74762i	0.354158	+	0.613420i
$122$	−0.136714	+	0.236796i	−0.0123775	+	0.0214385i
$123$	−6.80180	+	2.47565i	−0.613298	+	0.223222i
$124$	3.23298	+	2.71279i	0.290330	+	0.243616i
$125$	−0.351688	−	0.609141i	−0.0314559	−	0.0544833i
$126$		0			0
$127$	9.45174	+	7.93095i	0.838707	+	0.703758i	0.957272	−	0.289188i	$-0.0933852\pi$
$127$	9.45174	+	7.93095i	0.838707	+	0.703758i	−0.118566	+	0.992946i	$0.537830\pi$
$128$	10.4042	−	8.73013i	0.919607	−	0.771642i
$129$	−1.55467	−	1.30452i	−0.136881	−	0.114857i
$130$	0.319255	+	0.116199i	0.0280005	+	0.0101914i
$131$	2.80746	+	1.02183i	0.245289	+	0.0892779i	0.461739	−	0.887016i	$-0.347226\pi$
$131$	2.80746	+	1.02183i	0.245289	+	0.0892779i	−0.216450	+	0.976294i	$0.569448\pi$
$132$	−1.24544			−0.108402
$133$		0			0
$134$	−15.0271			−1.29814
$135$	0.344527	+	0.125397i	0.0296521	+	0.0107925i
$136$	1.30290	+	0.474218i	0.111723	+	0.0406639i
$137$	16.3501	+	13.7193i	1.39688	+	1.17212i	0.962464	+	0.271410i	$0.0874899\pi$
$137$	16.3501	+	13.7193i	1.39688	+	1.17212i	0.434417	+	0.900712i	$0.356955\pi$
$138$	2.01144	−	1.68780i	0.171226	−	0.143675i
$139$	5.38233	+	4.51631i	0.456523	+	0.383068i	0.841850	−	0.539712i	$-0.181467\pi$
$139$	5.38233	+	4.51631i	0.456523	+	0.383068i	−0.385327	+	0.922780i	$0.625911\pi$
$140$		0			0
$141$	0.748062	+	1.29568i	0.0629982	+	0.109116i
$142$	−14.6906	−	12.3269i	−1.23281	−	1.03445i
$143$	−4.99542	+	1.81818i	−0.417738	+	0.152044i
$144$	−4.49086	+	7.77841i	−0.374239	+	0.648200i
$145$	−0.190928	−	0.330697i	−0.0158557	−	0.0274629i
$146$	13.9885	+	11.7378i	1.15770	+	0.971425i
$147$		0			0
$148$	−0.419715	+	0.152764i	−0.0345003	+	0.0125571i
$149$	1.40001	+	7.93984i	0.114693	+	0.650457i	0.986902	+	0.161323i	$0.0515760\pi$
$149$	1.40001	+	7.93984i	0.114693	+	0.650457i	−0.872209	+	0.489134i	$0.837313\pi$
$150$	6.69696	−	5.61941i	0.546804	−	0.458823i
$151$	−10.1104	−	17.5117i	−0.822773	−	1.42509i	−0.903609	−	0.428358i	$-0.859092\pi$
$151$	−10.1104	−	17.5117i	−0.822773	−	1.42509i	0.0808356	−	0.996727i	$-0.474241\pi$
$152$	−7.30263	−	6.23011i	−0.592322	−	0.505328i
$153$	−1.16003			−0.0937832
$154$		0			0
$155$	−0.352050	+	0.295405i	−0.0282773	+	0.0237275i
$156$	−0.358323	+	2.03215i	−0.0286888	+	0.162702i
$157$	−3.98880	−	22.6216i	−0.318341	−	1.80540i	−0.552844	−	0.833285i	$-0.686457\pi$
$157$	−3.98880	−	22.6216i	−0.318341	−	1.80540i	0.234503	−	0.972115i	$-0.424654\pi$
$158$	2.96048	−	16.7897i	0.235523	−	1.33572i
$159$	3.96960	+	6.87555i	0.314810	+	0.545266i
$160$	−0.124057	−	0.214873i	−0.00980755	−	0.0169872i
$161$		0			0
$162$	−0.0220259	+	0.124915i	−0.00173052	+	0.00981426i
$163$	−18.0251			−1.41184			−0.705919	−	0.708292i	$-0.749466\pi$
$163$	−18.0251			−1.41184			−0.705919	+	0.708292i	$0.749466\pi$
$164$	−4.34782			−0.339508
$165$	0.0235501	−	0.133560i	0.00183338	−	0.0103976i
$166$	8.42026	−	7.06544i	0.653539	−	0.548385i
$167$	−3.45416	+	1.25721i	−0.267291	+	0.0972860i	−0.472189	−	0.881497i	$-0.656536\pi$
$167$	−3.45416	+	1.25721i	−0.267291	+	0.0972860i	0.204898	+	0.978783i	$0.434314\pi$
$168$		0			0
$169$	−0.727966	−	4.12850i	−0.0559974	−	0.317577i
$170$	0.0360380	−	0.0624197i	0.00276399	−	0.00478737i
$171$	7.52404	+	2.80842i	0.575378	+	0.214765i
$172$	−0.609519	−	1.05572i	−0.0464754	−	0.0804977i
$173$	−10.1517	−	3.69491i	−0.771818	−	0.280919i	−0.0740615	−	0.997254i	$-0.523596\pi$
$173$	−10.1517	−	3.69491i	−0.771818	−	0.280919i	−0.697757	+	0.716335i	$0.745818\pi$
$174$	7.27504	−	6.10448i	0.551519	−	0.462780i
$175$		0			0
$176$	8.20541	+	2.98653i	0.618506	+	0.225118i
$177$	−14.0196	+	5.10271i	−1.05378	+	0.383543i
$178$	6.71482			0.503297
$179$	1.03576	−	1.79399i	0.0774165	−	0.134089i	−0.824718	−	0.565544i	$-0.808666\pi$
$179$	1.03576	−	1.79399i	0.0774165	−	0.134089i	0.902135	+	0.431455i	$0.142000\pi$
$180$	0.0641883	+	0.0538604i	0.00478432	+	0.00401452i
$181$	−0.196089	+	1.11208i	−0.0145752	+	0.0826601i	−0.991228	−	0.132165i	$-0.957807\pi$
$181$	−0.196089	+	1.11208i	−0.0145752	+	0.0826601i	0.976653	+	0.214825i	$0.0689182\pi$
$182$		0			0
$183$	0.0904205	−	0.156613i	0.00668408	−	0.0115772i
$184$	−3.10463	+	1.12999i	−0.228876	+	0.0833041i
$185$	−0.00844578	−	0.0478984i	−0.000620946	−	0.00352156i
$186$	−8.75558	−	7.34681i	−0.641990	−	0.538694i
$187$	0.195837	+	1.11065i	0.0143210	+	0.0812187i
$188$	0.156053	+	0.885019i	0.0113813	+	0.0645466i
$189$		0			0
$190$	−0.384862	+	0.317610i	−0.0279208	+	0.0230419i
$191$	0.150719	−	0.261053i	0.0109056	−	0.0188891i	−0.860521	−	0.509415i	$-0.829862\pi$
$191$	0.150719	−	0.261053i	0.0109056	−	0.0188891i	0.871427	+	0.490526i	$0.163195\pi$
$192$	−3.30853	+	2.77619i	−0.238773	+	0.200354i
$193$	−2.89783	−	1.05473i	−0.208591	−	0.0759208i	0.235612	−	0.971847i	$-0.424291\pi$
$193$	−2.89783	−	1.05473i	−0.208591	−	0.0759208i	−0.444202	+	0.895926i	$0.646513\pi$
$194$	1.51032	−	8.56542i	0.108434	−	0.614962i
$195$	−0.211150	−	0.0768523i	−0.0151208	−	0.00550351i
$196$		0			0
$197$	−13.9602	+	24.1797i	−0.994620	+	1.72273i	−0.407595	+	0.913163i	$0.633632\pi$
$197$	−13.9602	+	24.1797i	−0.994620	+	1.72273i	−0.587025	+	0.809569i	$0.699701\pi$
$198$	−5.36866			−0.381534
$199$	−1.39018	+	0.505985i	−0.0985475	+	0.0358684i	−0.390823	−	0.920466i	$-0.627810\pi$
$199$	−1.39018	+	0.505985i	−0.0985475	+	0.0358684i	0.292276	+	0.956334i	$0.405587\pi$
$200$	−10.3366	+	3.76223i	−0.730910	+	0.266030i
$201$	9.93864			0.701018
$202$	4.05597	−	7.02515i	0.285377	−	0.494288i
$203$		0			0
$204$	0.411367	+	0.149725i	0.0288014	+	0.0104829i
$205$	0.0822134	−	0.466255i	0.00574203	−	0.0325647i
$206$	−4.58800	−	1.66990i	−0.319661	−	0.116347i
$207$	2.11749	−	1.77679i	0.147176	−	0.123495i
$208$	7.23380	−	12.5293i	0.501574	−	0.868751i
$209$	1.41865	−	7.67785i	0.0981298	−	0.531088i
$210$		0			0
$211$	−4.78998	−	27.1653i	−0.329756	−	1.87014i	−0.473894	−	0.880582i	$-0.657152\pi$
$211$	−4.78998	−	27.1653i	−0.329756	−	1.87014i	0.144137	−	0.989558i	$-0.453959\pi$
$212$	0.828095	+	4.69636i	0.0568738	+	0.322547i
$213$	9.71614	+	8.15281i	0.665739	+	0.558621i
$214$	−3.53631	−	20.0554i	−0.241737	−	1.37096i
$215$	0.124739	−	0.0454014i	0.00850716	−	0.00309635i
$216$	5.73664	−	9.93615i	0.390329	−	0.676070i
$217$		0			0
$218$	−3.96548	+	22.4894i	−0.268576	+	1.52317i
$219$	−9.25177	−	7.76316i	−0.625177	−	0.524586i
$220$	0.0407312	−	0.0705484i	0.00274609	−	0.00475637i
$221$	1.86856			0.125693
$222$	1.13668	−	0.413716i	0.0762887	−	0.0277668i
$223$	−8.38245	−	3.05096i	−0.561331	−	0.204308i	0.0457430	−	0.998953i	$-0.485434\pi$
$223$	−8.38245	−	3.05096i	−0.561331	−	0.204308i	−0.607074	+	0.794646i	$0.707657\pi$
$224$		0			0
$225$	7.05003	−	5.91568i	0.470002	−	0.394379i
$226$	0.642803	+	0.233961i	0.0427586	+	0.0155629i
$227$	−12.6725	−	21.9493i	−0.841101	−	1.45683i	−0.888965	−	0.457975i	$-0.848575\pi$
$227$	−12.6725	−	21.9493i	−0.841101	−	1.45683i	0.0478641	−	0.998854i	$-0.484759\pi$
$228$	−2.30566	−	1.96703i	−0.152696	−	0.130270i
$229$	12.4215	−	21.5146i	0.820834	−	1.42173i	−0.0842287	−	0.996446i	$-0.526843\pi$
$229$	12.4215	−	21.5146i	0.820834	−	1.42173i	0.905062	−	0.425279i	$-0.139824\pi$
$230$	0.0298235	+	0.169137i	0.00196650	+	0.0111526i
$231$		0			0
$232$	−11.2289	+	4.08698i	−0.737213	+	0.268323i
$233$	12.1179	−	10.1681i	0.793870	−	0.666136i	−0.152830	−	0.988252i	$-0.548839\pi$
$233$	12.1179	−	10.1681i	0.793870	−	0.666136i	0.946700	+	0.322117i	$0.104394\pi$
$234$	−1.54461	+	8.75989i	−0.100974	+	0.572652i
$235$	−0.0978592			−0.00638363
$236$	−8.96155			−0.583347
$237$	−1.95801	+	11.1044i	−0.127186	+	0.721310i
$238$		0			0
$239$	−2.00385	−	3.47078i	−0.129619	−	0.224506i	0.793910	−	0.608035i	$-0.208042\pi$
$239$	−2.00385	−	3.47078i	−0.129619	−	0.224506i	−0.923529	+	0.383529i	$0.874709\pi$
$240$	0.184545	+	0.319642i	0.0119124	+	0.0206328i
$241$	3.93270	−	22.3034i	0.253327	−	1.43669i	−0.547003	−	0.837131i	$-0.684231\pi$
$241$	3.93270	−	22.3034i	0.253327	−	1.43669i	0.800330	−	0.599559i	$-0.204657\pi$
$242$	−2.20093	−	12.4821i	−0.141481	−	0.802379i
$243$	−2.69953	+	15.3098i	−0.173175	+	0.982124i
$244$	0.0832117	−	0.0698229i	0.00532708	−	0.00446995i
$245$		0			0
$246$	11.7748			0.750734
$247$	−12.1196	−	4.52374i	−0.771150	−	0.287839i
$248$	7.19069	+	12.4546i	0.456609	+	0.790871i
$249$	−5.56902	+	4.67296i	−0.352922	+	0.296137i
$250$	0.198689	+	1.12682i	0.0125662	+	0.0712664i
$251$	25.6565	−	9.33821i	1.61942	−	0.589422i	0.636152	−	0.771563i	$-0.280525\pi$
$251$	25.6565	−	9.33821i	1.61942	−	0.589422i	0.983272	+	0.182141i	$0.0583027\pi$
$252$		0			0
$253$	−2.05862	−	1.72739i	−0.129424	−	0.108600i
$254$	−10.0356	−	17.3822i	−0.629690	−	1.09065i
$255$	−0.0238349	+	0.0412833i	−0.00149260	+	0.00258526i
$256$	−13.2168	+	4.81053i	−0.826052	+	0.300658i
$257$	−9.62015	−	8.07226i	−0.600089	−	0.503534i	0.291386	−	0.956606i	$-0.405884\pi$
$257$	−9.62015	−	8.07226i	−0.600089	−	0.503534i	−0.891474	+	0.453072i	$0.850328\pi$
$258$	1.65070	+	2.85910i	0.102768	+	0.178000i
$259$		0			0
$260$	−0.103393	−	0.0867573i	−0.00641218	−	0.00538046i
$261$	7.65859	−	6.42632i	0.474055	−	0.397779i
$262$	−3.72304	−	3.12400i	−0.230010	−	0.193001i
$263$	−15.5323	−	5.65329i	−0.957761	−	0.348597i	−0.184605	−	0.982813i	$-0.559101\pi$
$263$	−15.5323	−	5.65329i	−0.957761	−	0.348597i	−0.773156	+	0.634216i	$0.781323\pi$
$264$	−3.98804	−	1.45153i	−0.245447	−	0.0893355i
$265$	−0.519291			−0.0318998
$266$		0			0
$267$	−4.44107			−0.271789
$268$	5.60979	+	2.04180i	0.342672	+	0.124722i
$269$	−27.5387	−	10.0233i	−1.67906	−	0.611129i	−0.685883	−	0.727712i	$-0.740584\pi$
$269$	−27.5387	−	10.0233i	−1.67906	−	0.611129i	−0.993181	+	0.116583i	$0.962806\pi$
$270$	−0.456885	−	0.383372i	−0.0278051	−	0.0233313i
$271$	−21.3446	+	17.9102i	−1.29659	+	1.08797i	−0.305867	+	0.952074i	$0.598946\pi$
$271$	−21.3446	+	17.9102i	−1.29659	+	1.08797i	−0.990723	+	0.135894i	$0.956609\pi$
$272$	−2.35120	−	1.97289i	−0.142562	−	0.119624i
$273$		0			0
$274$	−17.3601	−	30.0685i	−1.04876	−	1.81650i
$275$	−6.85403	−	5.75121i	−0.413313	−	0.346811i
$276$	−0.980226	+	0.356773i	−0.0590026	+	0.0214752i
$277$	−3.20279	+	5.54740i	−0.192437	+	0.333311i	−0.946057	−	0.323999i	$-0.894972\pi$
$277$	−3.20279	+	5.54740i	−0.192437	+	0.333311i	0.753620	+	0.657310i	$0.228306\pi$
$278$	−5.71481	−	9.89834i	−0.342752	−	0.593663i
$279$	−9.21719	−	7.73414i	−0.551819	−	0.463031i
$280$		0			0
$281$	−0.456698	+	0.166224i	−0.0272443	+	0.00991612i	−0.355606	−	0.934636i	$-0.615726\pi$
$281$	−0.456698	+	0.166224i	−0.0272443	+	0.00991612i	0.328362	+	0.944552i	$0.393503\pi$
$282$	−0.422623	−	2.39682i	−0.0251668	−	0.142728i
$283$	20.1811	−	16.9339i	1.19964	−	1.00662i	0.200000	−	0.979796i	$-0.435906\pi$
$283$	20.1811	−	16.9339i	1.19964	−	1.00662i	0.999640	−	0.0268214i	$-0.00853855\pi$
$284$	3.80928	+	6.59787i	0.226039	+	0.391512i
$285$	0.254541	−	0.210062i	0.0150777	−	0.0124430i
$286$	8.64773			0.511351
$287$		0			0
$288$	4.97622	−	4.17554i	0.293226	−	0.246046i
$289$	−2.88318	+	16.3513i	−0.169599	+	0.961844i
$290$	0.107866	+	0.611740i	0.00633413	+	0.0359226i
$291$	−0.998896	+	5.66502i	−0.0585563	+	0.332089i
$292$	−3.62722	−	6.28254i	−0.212267	−	0.367658i
$293$	−15.7393	−	27.2613i	−0.919500	−	1.59262i	−0.800176	−	0.599765i	$-0.795261\pi$
$293$	−15.7393	−	27.2613i	−0.919500	−	1.59262i	−0.119324	−	0.992855i	$-0.538073\pi$
$294$		0			0
$295$	0.169455	−	0.961026i	0.00986605	−	0.0559531i
$296$	−1.52202			−0.0884656
$297$	9.33225			0.541512
$298$	2.27743	−	12.9160i	0.131928	−	0.748202i
$299$	−3.41081	+	2.86201i	−0.197253	+	0.165515i
$300$	−3.26359	+	1.18785i	−0.188423	+	0.0685805i
$301$		0			0
$302$	5.71195	+	32.3941i	0.328686	+	1.86407i
$303$	−2.68255	+	4.64631i	−0.154108	+	0.266924i
$304$	10.4737	+	18.4885i	0.600706	+	1.06039i
$305$	0.00591427	+	0.0102438i	0.000338650	+	0.000586559i
$306$	1.77326	+	0.645413i	0.101370	+	0.0368958i
$307$	13.1843	−	11.0629i	0.752468	−	0.631395i	−0.183687	−	0.982985i	$-0.558803\pi$
$307$	13.1843	−	11.0629i	0.752468	−	0.631395i	0.936154	+	0.351589i	$0.114359\pi$
$308$		0			0
$309$	3.03443	+	1.10444i	0.172622	+	0.0628294i
$310$	0.702508	−	0.255692i	0.0398998	−	0.0145223i
$311$	28.7474			1.63012			0.815058	−	0.579379i	$-0.196705\pi$
$311$	28.7474			1.63012			0.815058	+	0.579379i	$0.196705\pi$
$312$	−3.51581	+	6.08957i	−0.199044	+	0.344754i
$313$	5.41462	+	4.54340i	0.306052	+	0.256808i	0.782858	−	0.622200i	$-0.213761\pi$
$313$	5.41462	+	4.54340i	0.306052	+	0.256808i	−0.476806	+	0.879009i	$0.658206\pi$
$314$	−6.48870	+	36.7992i	−0.366179	+	2.07670i
$315$		0			0
$316$	−3.38648	+	5.86555i	−0.190504	+	0.329963i
$317$	5.94003	−	2.16199i	0.333625	−	0.121430i	−0.169775	−	0.985483i	$-0.554304\pi$
$317$	5.94003	−	2.16199i	0.333625	−	0.121430i	0.503401	+	0.864053i	$0.332082\pi$
$318$	−2.24266	−	12.7187i	−0.125762	−	0.713231i
$319$	−7.44567	−	6.24766i	−0.416877	−	0.349802i
$320$	−0.0490553	−	0.278206i	−0.00274227	−	0.0155522i
$321$	2.33885	+	13.2643i	0.130542	+	0.740340i
$322$		0			0
$323$	−1.39160	+	2.36543i	−0.0774306	+	0.131616i
$324$	0.0251953	−	0.0436396i	0.00139974	−	0.00242442i
$325$	−11.3561	+	9.52887i	−0.629921	+	0.528566i
$326$	27.5537	+	10.0287i	1.52606	+	0.555440i
$327$	2.62270	−	14.8741i	0.145036	−	0.822538i
$328$	−13.9222	−	5.06728i	−0.768727	−	0.279794i
$329$		0			0
$330$	−0.110308	+	0.191060i	−0.00607228	+	0.0105175i
$331$	15.6428			0.859808			0.429904	−	0.902875i	$-0.358547\pi$
$331$	15.6428			0.859808			0.429904	+	0.902875i	$0.358547\pi$
$332$	−4.10340	+	1.49352i	−0.225203	+	0.0819673i
$333$	1.19660	−	0.435528i	0.0655735	−	0.0238668i
$334$	5.97961			0.327190
$335$	−0.325036	+	0.562979i	−0.0177586	+	0.0307588i
$336$		0			0
$337$	−7.04290	−	2.56341i	−0.383651	−	0.139638i	0.142992	−	0.989724i	$-0.454328\pi$
$337$	−7.04290	−	2.56341i	−0.383651	−	0.139638i	−0.526644	+	0.850086i	$0.676550\pi$
$338$	−1.18420	+	6.71595i	−0.0644122	+	0.365300i
$339$	−0.425139	−	0.154738i	−0.0230904	−	0.00840420i
$340$	−0.0219347	+	0.0184054i	−0.00118958	+	0.000998172i
$341$	−5.84884	+	10.1305i	−0.316732	+	0.548596i
$342$	−9.93892	−	8.47921i	−0.537435	−	0.458503i
$343$		0			0
$344$	−0.721338	−	4.09091i	−0.0388920	−	0.220567i
$345$	−0.0197247	−	0.111865i	−0.00106194	−	0.00602259i
$346$	13.4624	+	11.2963i	0.723742	+	0.607292i
$347$	1.47528	+	8.36670i	0.0791970	+	0.449148i	0.998459	+	0.0555012i	$0.0176757\pi$
$347$	1.47528	+	8.36670i	0.0791970	+	0.449148i	−0.919262	+	0.393647i	$0.871213\pi$
$348$	−3.54530	+	1.29038i	−0.190048	+	0.0691719i
$349$	0.310773	−	0.538275i	0.0166353	−	0.0288132i	−0.857588	−	0.514337i	$-0.828038\pi$
$349$	0.310773	−	0.538275i	0.0166353	−	0.0288132i	0.874223	+	0.485524i	$0.161371\pi$
$350$		0			0
$351$	2.68496	−	15.2272i	0.143313	−	0.812767i
$352$	−4.83787	−	4.05945i	−0.257859	−	0.216370i
$353$	−13.1627	+	22.7985i	−0.700580	+	1.21344i	0.267683	+	0.963507i	$0.413742\pi$
$353$	−13.1627	+	22.7985i	−0.700580	+	1.21344i	−0.968263	+	0.249933i	$0.919591\pi$
$354$	24.2697			1.28992
$355$	−0.779579	+	0.283743i	−0.0413757	+	0.0150595i
$356$	−2.50672	−	0.912373i	−0.132856	−	0.0483557i
$357$		0			0
$358$	−2.58142	+	2.16607i	−0.136433	+	0.114480i
$359$	8.20713	+	2.98715i	0.433156	+	0.157656i	0.549390	−	0.835566i	$-0.314860\pi$
$359$	8.20713	+	2.98715i	0.433156	+	0.157656i	−0.116234	+	0.993222i	$0.537082\pi$
$360$	0.142766	+	0.247277i	0.00752441	+	0.0130327i
$361$	14.7526	−	11.9733i	0.776455	−	0.630173i
$362$	0.918479	−	1.59085i	0.0482742	−	0.0836134i
$363$	1.45566	+	8.25543i	0.0764021	+	0.433298i
$364$		0			0
$365$	0.742320	−	0.270182i	0.0388548	−	0.0141420i
$366$	−0.225355	+	0.189095i	−0.0117795	+	0.00988415i
$367$	−1.47030	+	8.33846i	−0.0767488	+	0.435264i	0.922085	+	0.386987i	$0.126484\pi$
$367$	−1.47030	+	8.33846i	−0.0767488	+	0.435264i	−0.998834	+	0.0482771i	$0.984627\pi$
$368$	7.31362			0.381249
$369$	12.3956			0.645289
$370$	−0.0137390	+	0.0779178i	−0.000714257	+	0.00405075i
$371$		0			0
$372$	2.27032	+	3.93231i	0.117711	+	0.203881i
$373$	11.8749	+	20.5679i	0.614859	+	1.06497i	0.990409	+	0.138165i	$0.0441205\pi$
$373$	11.8749	+	20.5679i	0.614859	+	1.06497i	−0.375550	+	0.926802i	$0.622546\pi$
$374$	0.318575	−	1.80673i	0.0164731	−	0.0934236i
$375$	−0.131409	−	0.745259i	−0.00678595	−	0.0384850i
$376$	−0.531769	+	3.01581i	−0.0274239	+	0.155529i
$377$	−12.3363	+	10.3514i	−0.635352	+	0.533124i
$378$		0			0
$379$	18.7476			0.962999			0.481500	−	0.876446i	$-0.340092\pi$
$379$	18.7476			0.962999			0.481500	+	0.876446i	$0.340092\pi$
$380$	0.186829	−	0.0662749i	0.00958410	−	0.00339983i
$381$	6.63737	+	11.4963i	0.340043	+	0.588972i
$382$	−0.375636	+	0.315196i	−0.0192192	+	0.0161268i
$383$	2.29354	+	13.0073i	0.117194	+	0.664642i	0.985640	+	0.168858i	$0.0540079\pi$
$383$	2.29354	+	13.0073i	0.117194	+	0.664642i	−0.868446	+	0.495784i	$0.834881\pi$
$384$	13.7312	−	4.99774i	0.700716	−	0.255040i
$385$		0			0
$386$	3.84288	+	3.22456i	0.195598	+	0.164126i
$387$	1.73773	+	3.00984i	0.0883339	+	0.152999i
$388$	−1.72764	+	2.99236i	−0.0877077	+	0.151914i
$389$	−9.00315	+	3.27688i	−0.456478	+	0.166144i	−0.560017	−	0.828481i	$-0.689205\pi$
$389$	−9.00315	+	3.27688i	−0.456478	+	0.166144i	0.103539	+	0.994625i	$0.466983\pi$
$390$	0.280011	+	0.234957i	0.0141789	+	0.0118975i
$391$	0.472295	+	0.818038i	0.0238850	+	0.0413700i
$392$		0			0
$393$	2.46235	+	2.06616i	0.124209	+	0.104224i
$394$	34.7928	−	29.1946i	1.75284	−	1.47081i
$395$	−0.564980	−	0.474075i	−0.0284272	−	0.0238533i
$396$	2.00418	+	0.729463i	0.100714	+	0.0366569i
$397$	15.6578	+	5.69897i	0.785842	+	0.286023i	0.703606	−	0.710590i	$-0.251572\pi$
$397$	15.6578	+	5.69897i	0.785842	+	0.286023i	0.0822355	+	0.996613i	$0.473794\pi$
$398$	2.40659			0.120631
$399$		0			0
$400$	24.3502			1.21751
$401$	−18.8823	−	6.87258i	−0.942936	−	0.343200i	−0.175611	−	0.984460i	$-0.556190\pi$
$401$	−18.8823	−	6.87258i	−0.942936	−	0.343200i	−0.767324	+	0.641259i	$0.778412\pi$
$402$	−15.1925	−	5.52961i	−0.757732	−	0.275792i
$403$	14.8469	+	12.4580i	0.739576	+	0.620578i
$404$	−2.46868	+	2.07147i	−0.122822	+	0.103060i
$405$	0.00420344	+	0.00352710i	0.000208871	+	0.000175263i
$406$		0			0
$407$	−0.618998	−	1.07214i	−0.0306826	−	0.0531438i
$408$	1.14274	+	0.958876i	0.0565742	+	0.0474714i
$409$	−9.85289	+	3.58616i	−0.487194	+	0.177324i	−0.573925	−	0.818908i	$-0.694580\pi$
$409$	−9.85289	+	3.58616i	−0.487194	+	0.177324i	0.0867313	+	0.996232i	$0.472358\pi$
$410$	−0.385086	+	0.666989i	−0.0190181	+	0.0329402i
$411$	11.4816	+	19.8868i	0.566348	+	0.980943i
$412$	1.48586	+	1.24679i	0.0732031	+	0.0614247i
$413$		0			0
$414$	−4.22541	+	1.53792i	−0.207668	+	0.0755849i
$415$	−0.0825713	−	0.468285i	−0.00405327	−	0.0229872i
$416$	−8.01560	+	6.72588i	−0.392997	+	0.329764i
$417$	3.77968	+	6.54659i	0.185092	+	0.320588i
$418$	−6.44034	+	10.9473i	−0.315007	+	0.535448i
$419$	13.0830			0.639145			0.319573	−	0.947562i	$-0.396461\pi$
$419$	13.0830			0.639145			0.319573	+	0.947562i	$0.396461\pi$
$420$		0			0
$421$	18.1411	−	15.2222i	0.884144	−	0.741885i	−0.0828825	−	0.996559i	$-0.526413\pi$
$421$	18.1411	−	15.2222i	0.884144	−	0.741885i	0.967027	+	0.254674i	$0.0819682\pi$
$422$	−7.79201	+	44.1907i	−0.379309	+	2.15117i
$423$	−0.444905	−	2.52318i	−0.0216320	−	0.122681i
$424$	−2.82184	+	16.0034i	−0.137041	+	0.777196i
$425$	1.57247	+	2.72360i	0.0762760	+	0.132114i
$426$	−10.3163	−	17.8684i	−0.499828	−	0.865727i
$427$		0			0
$428$	−1.40487	+	7.96741i	−0.0679069	+	0.385119i
$429$	−5.71946			−0.276138
$430$	−0.215940			−0.0104136
$431$	−1.28158	+	7.26822i	−0.0617317	+	0.350098i	0.938260	+	0.345932i	$0.112437\pi$
$431$	−1.28158	+	7.26822i	−0.0617317	+	0.350098i	−0.999991	+	0.00416584i	$0.998674\pi$
$432$	−19.4559	+	16.3254i	−0.936071	+	0.785457i
$433$	−32.5494	+	11.8470i	−1.56423	+	0.569331i	−0.971700	−	0.236220i	$-0.924091\pi$
$433$	−32.5494	+	11.8470i	−1.56423	+	0.569331i	−0.592526	+	0.805551i	$0.701869\pi$
$434$		0			0
$435$	−0.0713409	−	0.404594i	−0.00342053	−	0.0193988i
$436$	4.53609	−	7.85674i	0.217239	−	0.376270i
$437$	−1.08288	−	6.44926i	−0.0518009	−	0.308510i
$438$	9.82328	+	17.0144i	0.469374	+	0.812980i
$439$	30.3362	+	11.0415i	1.44787	+	0.526981i	0.941995	−	0.335628i	$-0.108948\pi$
$439$	30.3362	+	11.0415i	1.44787	+	0.526981i	0.505873	+	0.862608i	$0.331171\pi$
$440$	0.212649	−	0.178433i	0.0101376	−	0.00850647i
$441$		0			0
$442$	−2.85633	−	1.03962i	−0.135862	−	0.0494496i
$443$	15.5460	−	5.65826i	0.738610	−	0.268832i	0.0548055	−	0.998497i	$-0.482546\pi$
$443$	15.5460	−	5.65826i	0.738610	−	0.268832i	0.683805	+	0.729665i	$0.260324\pi$
$444$	−0.480548			−0.0228058
$445$	0.145242	−	0.251566i	0.00688512	−	0.0119254i
$446$	11.1162	+	9.32757i	0.526365	+	0.441673i
$447$	−1.50626	+	8.54240i	−0.0712434	+	0.404042i
$448$		0			0
$449$	−18.1680	+	31.4678i	−0.857399	+	1.48506i	0.0170021	+	0.999855i	$0.494588\pi$
$449$	−18.1680	+	31.4678i	−0.857399	+	1.48506i	−0.874401	+	0.485204i	$0.838746\pi$
$450$	−14.0682	+	5.12041i	−0.663182	+	0.241378i
$451$	−2.09263	−	11.8679i	−0.0985381	−	0.558837i
$452$	−0.208177	−	0.174681i	−0.00979181	−	0.00821630i
$453$	−3.77779	−	21.4249i	−0.177496	−	1.00663i
$454$	7.15940	+	40.6030i	0.336007	+	1.90559i
$455$		0			0
$456$	−5.09048	−	8.98588i	−0.238383	−	0.420802i
$457$	−13.3009	+	23.0378i	−0.622188	+	1.07766i	0.366889	+	0.930265i	$0.380423\pi$
$457$	−13.3009	+	23.0378i	−0.622188	+	1.07766i	−0.989077	+	0.147397i	$0.952911\pi$
$458$	−30.9580	+	25.9768i	−1.44657	+	1.21382i
$459$	−3.08243	−	1.12191i	−0.143875	−	0.0523664i
$460$	0.0118480	−	0.0671933i	0.000552415	−	0.00313290i
$461$	−0.0577102	−	0.0210048i	−0.00268783	−	0.000978292i	0.340676	−	0.940181i	$-0.389344\pi$
$461$	−0.0577102	−	0.0210048i	−0.00268783	−	0.000978292i	−0.343364	+	0.939203i	$0.611566\pi$
$462$		0			0
$463$	6.51380	−	11.2822i	0.302722	−	0.524329i	−0.674030	−	0.738704i	$-0.735438\pi$
$463$	6.51380	−	11.2822i	0.302722	−	0.524329i	0.976751	+	0.214375i	$0.0687714\pi$
$464$	26.4521			1.22801
$465$	−0.464626	+	0.169110i	−0.0215465	+	0.00784230i
$466$	−24.1810	+	8.80117i	−1.12016	+	0.407706i
$467$	−15.5514			−0.719631			−0.359815	−	0.933023i	$-0.617160\pi$
$467$	−15.5514			−0.719631			−0.359815	+	0.933023i	$0.617160\pi$
$468$	1.76687	−	3.06030i	0.0816734	−	0.141462i
$469$		0			0
$470$	0.149590	+	0.0544464i	0.00690008	+	0.00251142i
$471$	4.29151	−	24.3384i	0.197742	−	1.12145i
$472$	−28.6959	−	10.4445i	−1.32084	−	0.480746i
$473$	2.58834	−	2.17188i	0.119012	−	0.0998630i
$474$	9.17129	−	15.8851i	0.421251	−	0.729629i
$475$	−3.60535	−	21.4723i	−0.165425	−	0.985218i
$476$		0			0
$477$	−2.36089	−	13.3893i	−0.108098	−	0.613053i
$478$	1.13209	+	6.42041i	0.0517807	+	0.293663i
$479$	23.0270	+	19.3220i	1.05213	+	0.882843i	0.993316	−	0.115426i	$-0.0368233\pi$
$479$	23.0270	+	19.3220i	1.05213	+	0.882843i	0.0588153	+	0.998269i	$0.481268\pi$
$480$	−0.0463542	−	0.262888i	−0.00211577	−	0.0119991i
$481$	−1.92747	+	0.701540i	−0.0878849	+	0.0319875i
$482$	−18.4207	+	31.9056i	−0.839039	+	1.45326i
$483$		0			0
$484$	−0.874363	+	4.95876i	−0.0397438	+	0.225398i
$485$	−0.288229	−	0.241853i	−0.0130878	−	0.0109820i
$486$	12.6446	−	21.9010i	0.573569	−	0.993451i
$487$	12.4091			0.562310			0.281155	−	0.959662i	$-0.409283\pi$
$487$	12.4091			0.562310			0.281155	+	0.959662i	$0.409283\pi$
$488$	0.347831	−	0.126600i	0.0157456	−	0.00573091i
$489$	−18.2236	−	6.63283i	−0.824097	−	0.299947i
$490$		0			0
$491$	31.3999	−	26.3477i	1.41706	−	1.18905i	0.464165	−	0.885749i	$-0.346355\pi$
$491$	31.3999	−	26.3477i	1.41706	−	1.18905i	0.952894	−	0.303304i	$-0.0980898\pi$
$492$	−4.39568	−	1.59990i	−0.198172	−	0.0721289i
$493$	1.70821	+	2.95870i	0.0769338	+	0.133253i
$494$	16.0094	+	13.6581i	0.720298	+	0.614509i
$495$	−0.116124	+	0.201133i	−0.00521939	+	0.00904025i
$496$	−5.52815	−	31.3517i	−0.248221	−	1.40773i
$497$		0			0
$498$	11.1129	−	4.04475i	0.497979	−	0.181250i
$499$	5.68646	−	4.77150i	0.254561	−	0.213602i	−0.506572	−	0.862197i	$-0.669088\pi$
$499$	5.68646	−	4.77150i	0.254561	−	0.213602i	0.761133	+	0.648596i	$0.224643\pi$
$500$	0.0789332	−	0.447652i	0.00353000	−	0.0200196i
$501$	−3.95481			−0.176688
$502$	−44.4148			−1.98233
$503$	−3.81927	+	21.6602i	−0.170293	+	0.965779i	0.773145	+	0.634229i	$0.218682\pi$
$503$	−3.81927	+	21.6602i	−0.170293	+	0.965779i	−0.943438	+	0.331549i	$0.892429\pi$
$504$		0			0
$505$	−0.175462	−	0.303908i	−0.00780794	−	0.0135237i
$506$	2.18579	+	3.78590i	0.0971701	+	0.168304i
$507$	0.783212	−	4.44181i	0.0347837	−	0.197268i
$508$	1.38462	+	7.85256i	0.0614325	+	0.348401i
$509$	0.595424	−	3.37682i	0.0263917	−	0.149675i	−0.968764	−	0.247983i	$-0.920232\pi$
$509$	0.595424	−	3.37682i	0.0263917	−	0.149675i	0.995156	+	0.0983086i	$0.0313432\pi$
$510$	0.0594037	−	0.0498456i	0.00263044	−	0.00220720i
$511$		0			0
$512$	−4.28328			−0.189296
$513$	17.2767	+	14.7393i	0.762784	+	0.650755i
$514$	10.2144	+	17.6919i	0.450539	+	0.780356i
$515$	−0.161800	+	0.135766i	−0.00712977	+	0.00598259i
$516$	−0.227749	−	1.29163i	−0.0100261	−	0.0568607i
$517$	−2.34065	+	0.851929i	−0.102942	+	0.0374678i
$518$		0			0
$519$	−8.90378	−	7.47116i	−0.390833	−	0.327948i
$520$	−0.229964	−	0.398310i	−0.0100846	−	0.0174670i
$521$	−6.37820	+	11.0474i	−0.279434	+	0.483994i	−0.971244	−	0.238085i	$-0.923480\pi$
$521$	−6.37820	+	11.0474i	−0.279434	+	0.483994i	0.691810	+	0.722079i	$0.256814\pi$
$522$	−15.2826	+	5.56240i	−0.668900	+	0.243460i
$523$	14.4243	+	12.1034i	0.630728	+	0.529244i	0.901155	−	0.433497i	$-0.142720\pi$
$523$	14.4243	+	12.1034i	0.630728	+	0.529244i	−0.270427	+	0.962741i	$0.587165\pi$
$524$	0.965384	+	1.67209i	0.0421730	+	0.0730457i
$525$		0			0
$526$	20.5977	+	17.2835i	0.898103	+	0.753597i
$527$	3.14974	−	2.64294i	0.137205	−	0.115128i
$528$	7.19676	+	6.03880i	0.313199	+	0.262805i
$529$	19.4979	+	7.09664i	0.847733	+	0.308550i
$530$	0.793802	+	0.288920i	0.0344806	+	0.0125499i
$531$	25.5493			1.10874
$532$		0			0
$533$	−19.9666			−0.864849
$534$	6.78873	+	2.47090i	0.293777	+	0.106926i
$535$	−0.827852	−	0.301313i	−0.0357911	−	0.0130269i
$536$	15.5835	+	13.0761i	0.673106	+	0.564803i
$537$	1.70731	−	1.43260i	0.0736758	−	0.0618214i
$538$	36.5197	+	30.6437i	1.57448	+	1.32114i
$539$		0			0
$540$	0.118470	+	0.205196i	0.00509814	+	0.00883024i
$541$	−23.6015	−	19.8040i	−1.01471	−	0.851440i	−0.0257538	−	0.999668i	$-0.508199\pi$
$541$	−23.6015	−	19.8040i	−1.01471	−	0.851440i	−0.988953	+	0.148228i	$0.952643\pi$
$542$	42.5927	−	15.5025i	1.82951	−	0.665888i
$543$	−0.607466	+	1.05216i	−0.0260689	+	0.0451526i
$544$	1.10992	+	1.92243i	0.0475873	+	0.0824237i
$545$	0.756775	+	0.635009i	0.0324167	+	0.0272008i
$546$		0			0
$547$	−9.70626	+	3.53279i	−0.415010	+	0.151051i	−0.541082	−	0.840970i	$-0.681985\pi$
$547$	−9.70626	+	3.53279i	−0.415010	+	0.151051i	0.126072	+	0.992021i	$0.459763\pi$
$548$	2.39518	+	13.5837i	0.102317	+	0.580268i
$549$	−0.237236	+	0.199064i	−0.0101250	+	0.00849586i
$550$	7.27742	+	12.6049i	0.310310	+	0.537473i
$551$	−3.91657	−	23.3258i	−0.166851	−	0.993713i
$552$	−3.55461			−0.151294
$553$		0			0
$554$	7.98230	−	6.69794i	0.339135	−	0.284568i
$555$	0.00908674	−	0.0515335i	0.000385711	−	0.00218747i
$556$	0.788475	+	4.47167i	0.0334388	+	0.189641i
$557$	−3.61338	+	20.4925i	−0.153104	+	0.868294i	0.807395	+	0.590011i	$0.200876\pi$
$557$	−3.61338	+	20.4925i	−0.153104	+	0.868294i	−0.960499	+	0.278283i	$0.910235\pi$
$558$	9.78657	+	16.9508i	0.414298	+	0.717586i
$559$	−2.79911	−	4.84819i	−0.118390	−	0.205057i
$560$		0			0
$561$	−0.210700	+	1.19494i	−0.00889575	+	0.0504503i
$562$	0.790604			0.0333496
$563$	17.1580			0.723122			0.361561	−	0.932348i	$-0.382244\pi$
$563$	17.1580			0.723122			0.361561	+	0.932348i	$0.382244\pi$
$564$	−0.167896	+	0.952184i	−0.00706968	+	0.0400942i
$565$	0.0226690	−	0.0190216i	0.000953694	−	0.000800244i
$566$	−40.2709	+	14.6574i	−1.69271	+	0.616097i
$567$		0			0
$568$	4.50812	+	25.5668i	0.189156	+	1.07276i
$569$	11.8999	−	20.6112i	0.498869	−	0.864066i	−0.501130	−	0.865372i	$-0.667082\pi$
$569$	11.8999	−	20.6112i	0.498869	−	0.864066i	0.999999	+	0.00130568i	$0.000415612\pi$
$570$	−0.505971	+	0.179486i	−0.0211928	+	0.00751785i
$571$	5.34982	+	9.26617i	0.223883	+	0.387777i	0.955984	−	0.293419i	$-0.0947933\pi$
$571$	5.34982	+	9.26617i	0.223883	+	0.387777i	−0.732101	+	0.681196i	$0.761460\pi$
$572$	−3.22830	−	1.17501i	−0.134982	−	0.0491294i
$573$	0.248439	−	0.208465i	0.0103787	−	0.00870876i
$574$		0			0
$575$	−7.04199	−	2.56308i	−0.293671	−	0.106888i
$576$	6.95019	−	2.52966i	0.289591	−	0.105403i
$577$	21.7342			0.904807			0.452404	−	0.891813i	$-0.350567\pi$
$577$	21.7342			0.904807			0.452404	+	0.891813i	$0.350567\pi$
$578$	13.5048	−	23.3910i	0.561725	−	0.972936i
$579$	−2.54162	−	2.13267i	−0.105626	−	0.0886307i
$580$	0.0428521	−	0.243026i	0.00177934	−	0.0100911i
$581$		0			0
$582$	4.67881	−	8.10394i	0.193943	−	0.335919i
$583$	−12.4207	+	4.52077i	−0.514413	+	0.187231i
$584$	−4.29266	−	24.3449i	−0.177631	−	1.00740i
$585$	0.294773	+	0.247344i	0.0121874	+	0.0102264i
$586$	8.89204	+	50.4293i	0.367327	+	2.08321i
$587$	−4.64746	−	26.3570i	−0.191821	−	1.08787i	−0.916873	−	0.399178i	$-0.869296\pi$
$587$	−4.64746	−	26.3570i	−0.191821	−	1.08787i	0.725052	−	0.688694i	$-0.241816\pi$
$588$		0			0
$589$	−26.8279	+	9.51682i	−1.10542	+	0.392134i
$590$	−0.793724	+	1.37477i	−0.0326771	+	0.0565984i
$591$	−23.0114	+	19.3088i	−0.946561	+	0.794259i
$592$	3.16603	+	1.15234i	0.130123	+	0.0473609i
$593$	5.87022	−	33.2917i	0.241061	−	1.36713i	−0.588404	−	0.808567i	$-0.700243\pi$
$593$	5.87022	−	33.2917i	0.241061	−	1.36713i	0.829465	−	0.558559i	$-0.188645\pi$
$594$	−14.2655	−	5.19223i	−0.585322	−	0.213040i
$595$		0			0
$596$	−2.60514	+	4.51224i	−0.106711	+	0.184829i
$597$	−1.59168			−0.0651430
$598$	6.80621	−	2.47726i	0.278327	−	0.101303i
$599$	−2.60800	+	0.949233i	−0.106560	+	0.0387846i	−0.394750	−	0.918789i	$-0.629169\pi$
$599$	−2.60800	+	0.949233i	−0.106560	+	0.0387846i	0.288190	+	0.957573i	$0.406947\pi$
$600$	−11.8348			−0.483154
$601$	18.6256	−	32.2605i	0.759755	−	1.31594i	−0.183220	−	0.983072i	$-0.558652\pi$
$601$	18.6256	−	32.2605i	0.759755	−	1.31594i	0.942975	−	0.332863i	$-0.108015\pi$
$602$		0			0
$603$	−15.9934	−	5.82114i	−0.651304	−	0.237055i
$604$	2.26919	−	12.8692i	0.0923320	−	0.523641i
$605$	−0.515239	−	0.187532i	−0.0209474	−	0.00762424i
$606$	6.68571	−	5.60997i	0.271588	−	0.227890i
$607$	−19.1436	+	33.1578i	−0.777016	+	1.34583i	0.156638	+	0.987656i	$0.449934\pi$
$607$	−19.1436	+	33.1578i	−0.777016	+	1.34583i	−0.933654	+	0.358176i	$0.883399\pi$
$608$	−2.54481	−	15.1561i	−0.103206	−	0.614661i
$609$		0			0
$610$	−0.00334131	−	0.0189495i	−0.000135286	−	0.000767244i
$611$	0.716644	+	4.06429i	0.0289923	+	0.164424i
$612$	−0.574284	−	0.481881i	−0.0232140	−	0.0194789i
$613$	3.31833	+	18.8192i	0.134026	+	0.760099i	0.975533	+	0.219853i	$0.0705577\pi$
$613$	3.31833	+	18.8192i	0.134026	+	0.760099i	−0.841507	+	0.540246i	$0.818331\pi$
$614$	−26.3090	+	9.57570i	−1.06175	+	0.386444i
$615$	0.254689	−	0.441135i	0.0102701	−	0.0177883i
$616$		0			0
$617$	−0.242442	+	1.37496i	−0.00976036	+	0.0553538i	−0.989299	−	0.145903i	$-0.953391\pi$
$617$	−0.242442	+	1.37496i	−0.00976036	+	0.0553538i	0.979539	+	0.201256i	$0.0645025\pi$
$618$	−4.02402	−	3.37655i	−0.161870	−	0.135825i
$619$	−18.1490	+	31.4350i	−0.729469	+	1.26348i	0.227638	+	0.973746i	$0.426900\pi$
$619$	−18.1490	+	31.4350i	−0.729469	+	1.26348i	−0.957108	+	0.289732i	$0.906434\pi$
$620$	−0.296997			−0.0119277
$621$	7.34497	−	2.67335i	0.294744	−	0.107278i
$622$	−43.9441	−	15.9943i	−1.76200	−	0.641314i
$623$		0			0
$624$	11.9239	−	10.0053i	0.477338	−	0.400535i
$625$	−23.4225	−	8.52511i	−0.936901	−	0.341004i
$626$	−5.74909	−	9.95772i	−0.229780	−	0.397991i
$627$	4.25953	−	7.24033i	0.170109	−	0.289151i
$628$	7.42239	−	12.8560i	0.296186	−	0.513008i
$629$	0.0755631	+	0.428540i	0.00301290	+	0.0170870i
$630$		0			0
$631$	15.0984	−	5.49536i	0.601057	−	0.218767i	−0.0235288	−	0.999723i	$-0.507490\pi$
$631$	15.0984	−	5.49536i	0.601057	−	0.218767i	0.624586	+	0.780956i	$0.285268\pi$
$632$	−17.6801	+	14.8353i	−0.703276	+	0.590118i
$633$	5.15350	−	29.2270i	0.204833	−	1.16167i
$634$	−10.2830			−0.408389
$635$	−0.868282			−0.0344567
$636$	−0.890940	+	5.05277i	−0.0353281	+	0.200356i
$637$		0			0
$638$	7.90561	+	13.6929i	0.312986	+	0.542108i
$639$	−10.8602	−	18.8105i	−0.429624	−	0.744131i
$640$	−0.165969	+	0.941255i	−0.00656049	+	0.0372064i
$641$	−6.75544	−	38.3120i	−0.266824	−	1.51323i	−0.763791	−	0.645463i	$-0.776664\pi$
$641$	−6.75544	−	38.3120i	−0.266824	−	1.51323i	0.496968	−	0.867769i	$-0.334447\pi$
$642$	3.80468	−	21.5774i	0.150159	−	0.851593i
$643$	12.2408	−	10.2712i	0.482729	−	0.405058i	−0.368683	−	0.929555i	$-0.620191\pi$
$643$	12.2408	−	10.2712i	0.482729	−	0.405058i	0.851412	+	0.524498i	$0.175747\pi$
$644$		0			0
$645$	0.142819			0.00562350
$646$	3.44330	−	2.84161i	0.135475	−	0.111802i
$647$	0.912483	+	1.58047i	0.0358734	+	0.0621346i	0.883405	−	0.468611i	$-0.155245\pi$
$647$	0.912483	+	1.58047i	0.0358734	+	0.0621346i	−0.847531	+	0.530745i	$0.821912\pi$
$648$	0.131539	−	0.110375i	0.00516735	−	0.00433592i
$649$	−4.31324	−	24.4616i	−0.169310	−	0.960202i
$650$	22.6608	−	8.24785i	0.888829	−	0.323507i
$651$		0			0
$652$	−8.92349	−	7.48769i	−0.349471	−	0.293241i
$653$	−10.8941	−	18.8692i	−0.426320	−	0.738407i	0.570223	−	0.821490i	$-0.306857\pi$
$653$	−10.8941	−	18.8692i	−0.426320	−	0.738407i	−0.996543	+	0.0830827i	$0.973523\pi$
$654$	−12.2847	+	21.2777i	−0.480369	+	0.832024i
$655$	−0.197568	+	0.0719089i	−0.00771962	+	0.00280971i
$656$	25.1238	+	21.0814i	0.980921	+	0.823091i
$657$	10.3412	+	17.9115i	0.403448	+	0.698792i
$658$		0			0
$659$	13.3023	+	11.1620i	0.518186	+	0.434810i	0.863999	−	0.503494i	$-0.167952\pi$
$659$	13.3023	+	11.1620i	0.518186	+	0.434810i	−0.345813	+	0.938303i	$0.612397\pi$
$660$	0.0671397	−	0.0563369i	0.00261341	−	0.00219291i
$661$	22.8713	+	19.1913i	0.889590	+	0.746455i	0.968128	−	0.250456i	$-0.0805807\pi$
$661$	22.8713	+	19.1913i	0.889590	+	0.746455i	−0.0785377	+	0.996911i	$0.525025\pi$
$662$	−23.9120	−	8.70327i	−0.929368	−	0.338262i
$663$	1.88913	+	0.687586i	0.0733676	+	0.0267036i
$664$	−14.8802			−0.577465
$665$		0			0
$666$	−2.07148			−0.0802681
$667$	−7.64986	−	2.78432i	−0.296204	−	0.107809i
$668$	−2.23226	−	0.812476i	−0.0863687	−	0.0314356i
$669$	−7.35204	−	6.16909i	−0.284246	−	0.238511i
$670$	0.810086	−	0.679743i	0.0312963	−	0.0262607i
$671$	0.230640	+	0.193530i	0.00890376	+	0.00747114i
$672$		0			0
$673$	5.12496	+	8.87669i	0.197553	+	0.342171i	0.947734	−	0.319061i	$-0.103367\pi$
$673$	5.12496	+	8.87669i	0.197553	+	0.342171i	−0.750182	+	0.661232i	$0.770034\pi$
$674$	9.33975	+	7.83698i	0.359754	+	0.301869i
$675$	24.4546	−	8.90073i	0.941256	−	0.342589i
$676$	1.35460	−	2.34624i	0.0521002	−	0.0902401i
$677$	−13.9448	−	24.1531i	−0.535943	−	0.928280i	−0.999117	−	0.0420130i	$-0.986623\pi$
$677$	−13.9448	−	24.1531i	−0.535943	−	0.928280i	0.463174	−	0.886267i	$-0.346710\pi$
$678$	0.563786	+	0.473073i	0.0216521	+	0.0181682i
$679$		0			0
$680$	−0.0916885	+	0.0333719i	−0.00351609	+	0.00127975i
$681$	−4.73510	−	26.8541i	−0.181450	−	1.02905i
$682$	14.5770	−	12.2316i	0.558183	−	0.468371i
$683$	−6.44497	−	11.1630i	−0.246610	−	0.427141i	0.715973	−	0.698128i	$-0.245983\pi$
$683$	−6.44497	−	11.1630i	−0.246610	−	0.427141i	−0.962583	+	0.270987i	$0.912650\pi$
$684$	2.55821	+	4.51583i	0.0978156	+	0.172667i
$685$	−1.50199			−0.0573883
$686$		0			0
$687$	20.4751	−	17.1806i	0.781172	−	0.655481i
$688$	−1.59679	+	9.05585i	−0.0608771	+	0.345251i
$689$	3.80288	+	21.5672i	0.144878	+	0.821645i
$690$	−0.0320868	+	0.181974i	−0.00122153	+	0.00692761i
$691$	−3.96995	−	6.87616i	−0.151024	−	0.261581i	0.780580	−	0.625056i	$-0.214924\pi$
$691$	−3.96995	−	6.87616i	−0.151024	−	0.261581i	−0.931604	+	0.363474i	$0.881590\pi$
$692$	−3.49079	−	6.04623i	−0.132700	−	0.229843i
$693$		0			0
$694$	2.39988	−	13.6104i	0.0910980	−	0.516643i
$695$	−0.494446			−0.0187554
$696$	−12.8564			−0.487320
$697$	−0.735551	+	4.17152i	−0.0278610	+	0.158008i
$698$	−0.774539	+	0.649916i	−0.0293167	+	0.0245997i
$699$	15.9929	−	5.82094i	0.604907	−	0.220168i
$700$		0			0
$701$	4.73725	+	26.8663i	0.178924	+	1.01473i	0.933517	+	0.358533i	$0.116723\pi$
$701$	4.73725	+	26.8663i	0.178924	+	1.01473i	−0.754593	+	0.656193i	$0.772166\pi$
$702$	−12.5763	+	21.7828i	−0.474663	+	0.822140i
$703$	0.547379	−	2.96247i	0.0206448	−	0.111732i
$704$	−3.59530	−	6.22724i	−0.135503	−	0.234698i
$705$	−0.0989364	−	0.0360099i	−0.00372616	−	0.00135621i
$706$	32.8053	−	27.5269i	1.23464	−	1.03599i
$707$		0			0
$708$	−9.06019	−	3.29764i	−0.340503	−	0.123933i
$709$	21.7666	−	7.92241i	0.817463	−	0.297532i	0.100760	−	0.994911i	$-0.467873\pi$
$709$	21.7666	−	7.92241i	0.817463	−	0.297532i	0.716703	+	0.697379i	$0.245650\pi$
$710$	1.34955			0.0506478
$711$	9.65482	−	16.7226i	0.362084	−	0.627148i
$712$	−6.96348	−	5.84305i	−0.260967	−	0.218978i
$713$	−1.70133	+	9.64870i	−0.0637151	+	0.361347i
$714$		0			0
$715$	0.187051	−	0.323981i	0.00699529	−	0.0121162i
$716$	1.25799	−	0.457871i	0.0470133	−	0.0171115i
$717$	−0.748746	−	4.24635i	−0.0279624	−	0.158583i
$718$	−10.8837	−	9.13248i	−0.406175	−	0.340821i
$719$	−8.30929	−	47.1243i	−0.309884	−	1.75744i	−0.599573	−	0.800320i	$-0.704663\pi$
$719$	−8.30929	−	47.1243i	−0.309884	−	1.75744i	0.289689	−	0.957121i	$-0.406448\pi$
$720$	−0.109757	−	0.622464i	−0.00409041	−	0.0231979i
$721$		0			0
$722$	−29.2129	+	10.0947i	−1.08719	+	0.375686i
$723$	12.1831	−	21.1018i	0.453095	−	0.784784i
$724$	−0.559036	+	0.469087i	−0.0207764	+	0.0174335i
$725$	−25.4696	−	9.27019i	−0.945919	−	0.344286i
$726$	2.36796	−	13.4294i	0.0878832	−	0.498410i
$727$	−24.2763	−	8.83586i	−0.900359	−	0.327704i	−0.149963	−	0.988692i	$-0.547915\pi$
$727$	−24.2763	−	8.83586i	−0.900359	−	0.327704i	−0.750397	+	0.660988i	$0.770138\pi$
$728$		0			0
$729$	−8.47985	+	14.6875i	−0.314069	+	0.543983i
$730$	−1.28505			−0.0475619
$731$	−1.11603	+	0.406200i	−0.0412777	+	0.0150239i
$732$	0.109821	−	0.0399715i	0.00405909	−	0.00147739i
$733$	−25.3697			−0.937053			−0.468526	−	0.883450i	$-0.655215\pi$
$733$	−25.3697			−0.937053			−0.468526	+	0.883450i	$0.655215\pi$
$734$	6.88684	−	11.9284i	0.254198	−	0.440284i
$735$		0			0
$736$	−4.97054	−	1.80913i	−0.183217	−	0.0666854i
$737$	−2.87330	+	16.2953i	−0.105839	+	0.600245i
$738$	−18.9482	−	6.89659i	−0.697494	−	0.253867i
$739$	−26.0690	+	21.8745i	−0.958963	+	0.804666i	−0.980784	−	0.195096i	$-0.937498\pi$
$739$	−26.0690	+	21.8745i	−0.958963	+	0.804666i	0.0218211	+	0.999762i	$0.493054\pi$
$740$	0.0157160	−	0.0272209i	0.000577731	−	0.00100066i
$741$	−10.5883	−	9.03326i	−0.388973	−	0.331845i
$742$		0			0
$743$	−0.791920	−	4.49120i	−0.0290527	−	0.164766i	0.966830	−	0.255423i	$-0.0822146\pi$
$743$	−0.791920	−	4.49120i	−0.0290527	−	0.164766i	−0.995882	+	0.0906564i	$0.971103\pi$
$744$	2.68682	+	15.2377i	0.0985037	+	0.558642i
$745$	−0.434627	−	0.364695i	−0.0159235	−	0.0133614i
$746$	−6.70882	−	38.0476i	−0.245627	−	1.39302i
$747$	11.6988	−	4.25800i	0.428035	−	0.155792i
$748$	−0.364416	+	0.631187i	−0.0133244	+	0.0230785i
$749$		0			0
$750$	−0.213768	+	1.21234i	−0.00780569	+	0.0442682i
$751$	−11.1855	−	9.38576i	−0.408165	−	0.342491i	0.415474	−	0.909605i	$-0.363616\pi$
$751$	−11.1855	−	9.38576i	−0.408165	−	0.342491i	−0.823640	+	0.567114i	$0.808060\pi$
$752$	3.38947	−	5.87073i	0.123601	−	0.214084i
$753$	29.3752			1.07049
$754$	24.6169	−	8.95981i	0.896494	−	0.326297i
$755$	1.33717	+	0.486691i	0.0486647	+	0.0177125i
$756$		0			0
$757$	−19.1043	+	16.0304i	−0.694358	+	0.582636i	−0.920162	−	0.391537i	$-0.871943\pi$
$757$	−19.1043	+	16.0304i	−0.694358	+	0.582636i	0.225804	+	0.974173i	$0.427499\pi$
$758$	−28.6581	−	10.4307i	−1.04091	−	0.378860i
$759$	−1.44564	−	2.50393i	−0.0524735	−	0.0908867i
$760$	0.675489	+	0.00552408i	0.0245026	+	0.000200379i
$761$	−22.6403	+	39.2142i	−0.820711	+	1.42151i	0.0844426	+	0.996428i	$0.473089\pi$
$761$	−22.6403	+	39.2142i	−0.820711	+	1.42151i	−0.905154	+	0.425085i	$0.860244\pi$
$762$	−3.74983	−	21.2664i	−0.135842	−	0.770399i
$763$		0			0
$764$	0.183057	−	0.0666271i	0.00662275	−	0.00241048i
$765$	0.0625356	−	0.0524736i	0.00226098	−	0.00189719i
$766$	3.73097	−	21.1594i	0.134805	−	0.764519i
$767$	−41.1543			−1.48600
$768$	−15.1325			−0.546046
$769$	−8.35448	+	47.3806i	−0.301270	+	1.70859i	0.339291	+	0.940682i	$0.389813\pi$
$769$	−8.35448	+	47.3806i	−0.301270	+	1.70859i	−0.640561	+	0.767907i	$0.721298\pi$
$770$		0			0
$771$	−6.75564	−	11.7011i	−0.243298	−	0.421405i
$772$	−0.996459	−	1.72592i	−0.0358634	−	0.0621171i
$773$	4.26192	−	24.1705i	0.153290	−	0.869353i	−0.807042	−	0.590495i	$-0.798933\pi$
$773$	4.26192	−	24.1705i	0.153290	−	0.869353i	0.960332	−	0.278859i	$-0.0899562\pi$
$774$	−0.981745	−	5.56775i	−0.0352881	−	0.200129i
$775$	−5.66444	+	32.1246i	−0.203473	+	1.15395i
$776$	−9.01964	+	7.56838i	−0.323786	+	0.271689i
$777$		0			0
$778$	15.5856			0.558772
$779$	14.8700	−	25.2759i	0.532772	−	0.905605i
$780$	−0.0726067	−	0.125759i	−0.00259974	−	0.00450288i
$781$	−16.1762	+	13.5735i	−0.578831	+	0.485697i
$782$	−0.266826	−	1.51325i	−0.00954170	−	0.0541136i
$783$	26.5655	−	9.66904i	0.949372	−	0.345543i
$784$		0			0
$785$	1.23831	+	1.03906i	0.0441971	+	0.0370858i
$786$	−2.61446	−	4.52838i	−0.0932547	−	0.161522i
$787$	4.59751	−	7.96312i	0.163884	−	0.283855i	−0.772375	−	0.635167i	$-0.780931\pi$
$787$	4.59751	−	7.96312i	0.163884	−	0.283855i	0.936258	+	0.351313i	$0.114265\pi$
$788$	−16.9554	+	6.17126i	−0.604011	+	0.219842i
$789$	−13.6230	−	11.4310i	−0.484990	−	0.406955i
$790$	0.599881	+	1.03902i	0.0213428	+	0.0369668i
$791$		0			0
$792$	5.56746	+	4.67166i	0.197831	+	0.166000i
$793$	0.382135	−	0.320649i	0.0135700	−	0.0113866i
$794$	−20.7642	−	17.4232i	−0.736892	−	0.618326i
$795$	−0.525007	−	0.191087i	−0.0186201	−	0.00677716i
$796$	−0.898409	−	0.326994i	−0.0318432	−	0.0115900i
$797$	50.7437			1.79743			0.898716	−	0.438530i	$-0.144501\pi$
$797$	50.7437			1.79743			0.898716	+	0.438530i	$0.144501\pi$
$798$		0			0
$799$	0.875532			0.0309741
$800$	−16.5491	−	6.02336i	−0.585098	−	0.212958i
$801$	7.14665	+	2.60117i	0.252514	+	0.0919077i
$802$	25.0402	+	21.0112i	0.884200	+	0.741932i
$803$	15.4031	−	12.9248i	0.543564	−	0.456105i
$804$	4.92020	+	4.12854i	0.173522	+	0.145602i
$805$		0			0
$806$	−15.7640	−	27.3041i	−0.555264	−	0.961745i
$807$	−24.1535	−	20.2672i	−0.850243	−	0.713439i
$808$	−10.3193	+	3.75591i	−0.363030	+	0.132132i
$809$	1.11568	−	1.93241i	0.0392252	−	0.0679400i	−0.845746	−	0.533585i	$-0.820844\pi$
$809$	1.11568	−	1.93241i	0.0392252	−	0.0679400i	0.884972	+	0.465645i	$0.154178\pi$
$810$	−0.00446310	−	0.00773031i	−0.000156817	−	0.000271615i
$811$	9.48231	+	7.95660i	0.332969	+	0.279394i	0.793908	−	0.608038i	$-0.208043\pi$
$811$	9.48231	+	7.95660i	0.332969	+	0.279394i	−0.460939	+	0.887432i	$0.652487\pi$
$812$		0			0
$813$	−28.1700	+	10.2531i	−0.987967	+	0.359590i
$814$	0.349707	+	1.98329i	0.0122572	+	0.0695143i
$815$	0.971707	−	0.815359i	0.0340374	−	0.0285608i
$816$	−1.65110	−	2.85979i	−0.0578001	−	0.100113i
$817$	8.22200	+	0.0672386i	0.287651	+	0.00235238i
$818$	17.0566			0.596371
$819$		0			0
$820$	0.234384	−	0.196672i	0.00818505	−	0.00686807i
$821$	−7.84120	+	44.4696i	−0.273660	+	1.55200i	0.469528	+	0.882918i	$0.344424\pi$
$821$	−7.84120	+	44.4696i	−0.273660	+	1.55200i	−0.743187	+	0.669083i	$0.766687\pi$
$822$	−6.48664	−	36.7876i	−0.226248	−	1.28311i
$823$	−1.56995	+	8.90363i	−0.0547250	+	0.310361i	−0.999867	−	0.0162983i	$-0.994812\pi$
$823$	−1.56995	+	8.90363i	−0.0547250	+	0.310361i	0.945142	+	0.326659i	$0.105923\pi$
$824$	3.30481	+	5.72409i	0.115128	+	0.199408i
$825$	−4.81316	−	8.33664i	−0.167573	−	0.290244i
$826$		0			0
$827$	−4.71598	+	26.7457i	−0.163991	+	0.930037i	0.786108	+	0.618089i	$0.212093\pi$
$827$	−4.71598	+	26.7457i	−0.163991	+	0.930037i	−0.950099	+	0.311949i	$0.899018\pi$
$828$	1.78636			0.0620804
$829$	−24.7728			−0.860394			−0.430197	−	0.902735i	$-0.641556\pi$
$829$	−24.7728			−0.860394			−0.430197	+	0.902735i	$0.641556\pi$
$830$	−0.134321	+	0.761774i	−0.00466236	+	0.0264415i
$831$	−5.27935	+	4.42990i	−0.183139	+	0.153672i
$832$	−11.1952	+	4.07473i	−0.388125	+	0.141266i
$833$		0			0
$834$	−2.13536	−	12.1102i	−0.0739413	−	0.419342i
$835$	0.129339	−	0.224022i	0.00447596	−	0.00775260i
$836$	3.89171	−	3.21167i	0.134598	−	0.111078i
$837$	−17.0118	−	29.4654i	−0.588015	−	1.01847i
$838$	−19.9990	−	7.27903i	−0.690853	−	0.251450i
$839$	23.9268	−	20.0769i	0.826043	−	0.693133i	−0.128336	−	0.991731i	$-0.540964\pi$
$839$	23.9268	−	20.0769i	0.826043	−	0.693133i	0.954379	+	0.298598i	$0.0965191\pi$
$840$		0			0
$841$	−0.417095	−	0.151810i	−0.0143826	−	0.00523483i
$842$	−36.2003	+	13.1758i	−1.24754	+	0.454069i
$843$	−0.522891			−0.0180093
$844$	8.91324	−	15.4382i	0.306806	−	0.531404i
$845$	0.225994	+	0.189632i	0.00777444	+	0.00652353i
$846$	−0.723740	+	4.10453i	−0.0248827	+	0.141117i
$847$		0			0
$848$	17.9863	−	31.1531i	0.617650	−	1.06980i
$849$	26.6345	−	9.69416i	0.914093	−	0.332703i
$850$	−0.888379	−	5.03825i	−0.0304712	−	0.172811i
$851$	−0.794311	−	0.666506i	−0.0272286	−	0.0228475i
$852$	1.42335	+	8.07222i	0.0487632	+	0.276550i
$853$	5.23367	+	29.6816i	0.179197	+	1.01628i	0.933187	+	0.359392i	$0.117016\pi$
$853$	5.23367	+	29.6816i	0.179197	+	1.01628i	−0.753989	+	0.656887i	$0.771873\pi$
$854$		0			0
$855$	−0.532647	+	0.188949i	−0.0182161	+	0.00646193i
$856$	−13.7844	+	23.8753i	−0.471141	+	0.816040i
$857$	20.0570	−	16.8298i	0.685133	−	0.574895i	−0.232368	−	0.972628i	$-0.574648\pi$
$857$	20.0570	−	16.8298i	0.685133	−	0.574895i	0.917501	+	0.397733i	$0.130203\pi$
$858$	8.74291	+	3.18216i	0.298478	+	0.108637i
$859$	3.76032	−	21.3259i	0.128301	−	0.727629i	−0.850992	−	0.525179i	$-0.823998\pi$
$859$	3.76032	−	21.3259i	0.128301	−	0.727629i	0.979293	−	0.202450i	$-0.0648904\pi$
$860$	0.0806131	+	0.0293408i	0.00274888	+	0.00100051i
$861$		0			0
$862$	6.00291	−	10.3973i	0.204460	−	0.354135i
$863$	43.2467			1.47214			0.736068	−	0.676908i	$-0.236680\pi$
$863$	43.2467			1.47214			0.736068	+	0.676908i	$0.236680\pi$
$864$	17.2611	−	6.28252i	0.587234	−	0.213736i
$865$	0.714399	−	0.260020i	0.0242903	−	0.00884094i
$866$	56.3473			1.91476
$867$	−8.93183	+	15.4704i	−0.303341	+	0.525402i
$868$		0			0
$869$	−17.6407	−	6.42067i	−0.598418	−	0.217806i
$870$	−0.116052	+	0.658166i	−0.00393455	+	0.0223139i
$871$	25.7619	+	9.37658i	0.872910	+	0.317713i
$872$	23.6819	−	19.8715i	0.801972	−	0.672934i
$873$	4.92549	−	8.53120i	0.166703	−	0.288737i
$874$	−1.93289	+	10.4610i	−0.0653810	+	0.353848i
$875$		0			0
$876$	−1.35532	−	7.68642i	−0.0457921	−	0.259700i
$877$	3.26374	+	18.5096i	0.110209	+	0.625024i	0.989011	+	0.147839i	$0.0472318\pi$
$877$	3.26374	+	18.5096i	0.110209	+	0.625024i	−0.878803	+	0.477185i	$0.841657\pi$
$878$	−40.2295	−	33.7566i	−1.35768	−	1.13923i
$879$	−5.88104	−	33.3530i	−0.198363	−	1.12497i
$880$	−0.577435	+	0.210169i	−0.0194653	+	0.00708480i
$881$	−4.57192	+	7.91881i	−0.154032	+	0.266791i	−0.932706	−	0.360637i	$-0.882559\pi$
$881$	−4.57192	+	7.91881i	−0.154032	+	0.266791i	0.778674	+	0.627429i	$0.215893\pi$
$882$		0			0
$883$	3.57800	−	20.2918i	0.120409	−	0.682874i	−0.863520	−	0.504315i	$-0.831745\pi$
$883$	3.57800	−	20.2918i	0.120409	−	0.682874i	0.983929	−	0.178560i	$-0.0571437\pi$
$884$	0.925045	+	0.776205i	0.0311126	+	0.0261066i
$885$	0.524955	−	0.909249i	0.0176462	−	0.0305641i
$886$	−26.9121			−0.904129
$887$	27.2736	−	9.92680i	0.915759	−	0.333309i	0.159209	−	0.987245i	$-0.449106\pi$
$887$	27.2736	−	9.92680i	0.915759	−	0.333309i	0.756550	+	0.653936i	$0.226883\pi$
$888$	−1.53877	−	0.560067i	−0.0516378	−	0.0187946i
$889$		0			0
$890$	−0.361985	+	0.303742i	−0.0121338	+	0.0101814i
$891$	0.131246	+	0.0477697i	0.00439691	+	0.00160034i
$892$	−2.88242	−	4.99250i	−0.0965105	−	0.167161i
$893$	−5.67875	−	2.11964i	−0.190032	−	0.0709312i
$894$	7.05528	−	12.2201i	0.235964	−	0.408701i
$895$	0.0253141	+	0.143564i	0.000846158	+	0.00479880i
$896$		0			0
$897$	−4.50151	+	1.63842i	−0.150301	+	0.0547051i
$898$	45.2799	−	37.9944i	1.51101	−	1.26789i
$899$	−6.15339	+	34.8976i	−0.205227	+	1.16390i
$900$	5.94756			0.198252
$901$	4.64602			0.154781
$902$	−3.40414	+	19.3059i	−0.113346	+	0.642815i
$903$		0			0
$904$	−0.463020	−	0.801974i	−0.0153998	−	0.0266733i
$905$	−0.0397335	−	0.0688204i	−0.00132078	−	0.00228767i
$906$	−6.14544	+	34.8525i	−0.204169	+	1.15790i
$907$	2.85917	+	16.2152i	0.0949372	+	0.538416i	0.994767	+	0.102174i	$0.0325797\pi$
$907$	2.85917	+	16.2152i	0.0949372	+	0.538416i	−0.899829	+	0.436242i	$0.856309\pi$
$908$	2.84422	−	16.1304i	0.0943887	−	0.535305i
$909$	7.03819	−	5.90574i	0.233442	−	0.195881i
$910$		0			0
$911$	28.9644			0.959634			0.479817	−	0.877368i	$-0.340703\pi$
$911$	28.9644			0.959634			0.479817	+	0.877368i	$0.340703\pi$
$912$	3.78564	+	22.5460i	0.125355	+	0.746574i
$913$	−6.05171	−	10.4819i	−0.200283	−	0.346900i
$914$	33.1497	−	27.8159i	1.09649	−	0.920068i
$915$	0.00220989	+	0.0125329i	7.30566e−5	+	0.000414324i
$916$	15.0866	−	5.49106i	0.498474	−	0.181430i
$917$		0			0
$918$	4.08768	+	3.42997i	0.134914	+	0.113206i
$919$	10.8249	+	18.7493i	0.357081	+	0.618482i	0.987472	−	0.157796i	$-0.0504387\pi$
$919$	10.8249	+	18.7493i	0.357081	+	0.618482i	−0.630391	+	0.776278i	$0.717105\pi$
$920$	0.116251	−	0.201352i	0.00383268	−	0.00663839i
$921$	17.4003	−	6.33320i	0.573360	−	0.208686i
$922$	0.0765309	+	0.0642170i	0.00252041	+	0.00211487i
$923$	17.4934	+	30.2995i	0.575804	+	0.997322i
$924$		0			0
$925$	−2.64460	−	2.21908i	−0.0869540	−	0.0729631i
$926$	−16.2343	+	13.6222i	−0.533492	+	0.447653i
$927$	−4.23618	−	3.55457i	−0.139134	−	0.116748i
$928$	−17.9776	−	6.54330i	−0.590143	−	0.214794i
$929$	16.1983	+	5.89572i	0.531451	+	0.193432i	0.593786	−	0.804623i	$-0.297633\pi$
$929$	16.1983	+	5.89572i	0.531451	+	0.193432i	−0.0623353	+	0.998055i	$0.519855\pi$
$930$	0.804329			0.0263750
$931$		0			0
$932$	10.2229			0.334863
$933$	29.0638	+	10.5784i	0.951508	+	0.346320i
$934$	23.7722	+	8.65238i	0.777851	+	0.283114i
$935$	−0.0607970	−	0.0510147i	−0.00198827	−	0.00166836i
$936$	9.22442	−	7.74021i	0.301510	−	0.252997i
$937$	−10.5786	−	8.87649i	−0.345588	−	0.289982i	0.453428	−	0.891293i	$-0.350201\pi$
$937$	−10.5786	−	8.87649i	−0.345588	−	0.289982i	−0.799015	+	0.601311i	$0.794645\pi$
$938$		0			0
$939$	3.80235	+	6.58586i	0.124085	+	0.214922i
$940$	−0.0484460	−	0.0406510i	−0.00158013	−	0.00132589i
$941$	−40.9538	+	14.9060i	−1.33506	+	0.485921i	−0.908252	−	0.418423i	$-0.862583\pi$
$941$	−40.9538	+	14.9060i	−1.33506	+	0.485921i	−0.426805	+	0.904344i	$0.640361\pi$
$942$	−20.1014	+	34.8166i	−0.654938	+	1.13439i
$943$	−5.04673	−	8.74119i	−0.164344	−	0.284652i
$944$	51.7842	+	43.4521i	1.68543	+	1.41425i
$945$		0			0
$946$	−5.16498	+	1.87990i	−0.167928	+	0.0611208i
$947$	2.61290	+	14.8185i	0.0849078	+	0.481536i	0.997376	+	0.0723895i	$0.0230625\pi$
$947$	2.61290	+	14.8185i	0.0849078	+	0.481536i	−0.912469	+	0.409147i	$0.865826\pi$
$948$	−5.58214	+	4.68397i	−0.181299	+	0.152128i
$949$	−16.6574	−	28.8514i	−0.540721	−	0.936557i
$950$	−6.43542	+	34.8291i	−0.208793	+	1.13001i
$951$	6.80098			0.220537
$952$		0			0
$953$	−27.9792	+	23.4774i	−0.906336	+	0.760506i	−0.971418	−	0.237374i	$-0.923713\pi$
$953$	−27.9792	+	23.4774i	−0.906336	+	0.760506i	0.0650825	+	0.997880i	$0.479269\pi$
$954$	−3.84054	+	21.7808i	−0.124342	+	0.705178i
$955$	0.00368358	+	0.0208906i	0.000119198	+	0.000676005i
$956$	0.449747	−	2.55064i	0.0145458	−	0.0824936i
$957$	−5.22863	−	9.05626i	−0.169018	−	0.292747i
$958$	−24.4495	−	42.3477i	−0.789926	−	1.36819i
$959$		0			0
$960$	0.0527782	−	0.299320i	0.00170341	−	0.00966050i
$961$	11.6476			0.375728
$962$	3.33669			0.107579
$963$	4.00527	−	22.7150i	0.129068	−	0.731981i
$964$	11.2118	−	9.40783i	0.361108	−	0.303006i
$965$	0.203928	−	0.0742236i	0.00656467	−	0.00238934i
$966$		0			0
$967$	2.76506	+	15.6814i	0.0889184	+	0.504281i	0.996442	+	0.0842804i	$0.0268592\pi$
$967$	2.76506	+	15.6814i	0.0889184	+	0.504281i	−0.907524	+	0.420001i	$0.862030\pi$
$968$	−8.57913	+	14.8595i	−0.275744	+	0.477602i
$969$	−2.27734	+	1.87939i	−0.0731587	+	0.0603748i
$970$	0.306034	+	0.530067i	0.00982617	+	0.0170194i
$971$	−0.888704	−	0.323462i	−0.0285199	−	0.0103804i	0.327721	−	0.944775i	$-0.393719\pi$
$971$	−0.888704	−	0.323462i	−0.0285199	−	0.0103804i	−0.356241	+	0.934394i	$0.615942\pi$
$972$	−7.69616	+	6.45784i	−0.246854	+	0.207135i
$973$		0			0
$974$	−18.9689	−	6.90411i	−0.607802	−	0.221222i
$975$	−14.9875	+	5.45499i	−0.479983	+	0.174699i
$976$	−0.819390			−0.0262280
$977$	1.32652	−	2.29761i	0.0424392	−	0.0735069i	−0.844026	−	0.536303i	$-0.819820\pi$
$977$	1.32652	−	2.29761i	0.0424392	−	0.0735069i	0.886465	+	0.462796i	$0.153154\pi$
$978$	24.1667	+	20.2782i	0.772765	+	0.648427i
$979$	1.28393	−	7.28153i	0.0410346	−	0.232719i
$980$		0			0
$981$	−12.9324	+	22.3995i	−0.412898	+	0.715161i
$982$	−62.6579	+	22.8056i	−1.99949	+	0.727756i
$983$	5.83149	+	33.0720i	0.185996	+	1.05483i	0.924669	+	0.380771i	$0.124341\pi$
$983$	5.83149	+	33.0720i	0.185996	+	1.05483i	−0.738674	+	0.674063i	$0.764548\pi$
$984$	−12.2108	−	10.2461i	−0.389267	−	0.326634i
$985$	−0.341187	−	1.93497i	−0.0108711	−	0.0616533i
$986$	−0.965064	−	5.47315i	−0.0307339	−	0.174301i
$987$		0			0
$988$	−4.12071	−	7.27402i	−0.131097	−	0.231417i
$989$	1.41500	−	2.45085i	0.0449943	−	0.0779324i
$990$	0.289416	−	0.242849i	0.00919824	−	0.00771824i
$991$	29.6927	+	10.8073i	0.943221	+	0.343304i	0.767437	−	0.641124i	$-0.221532\pi$
$991$	29.6927	+	10.8073i	0.943221	+	0.343304i	0.175784	+	0.984429i	$0.443754\pi$
$992$	−3.99821	+	22.6750i	−0.126943	+	0.719930i
$993$	15.8150	+	5.75619i	0.501874	+	0.182667i
$994$		0			0
$995$	0.0520546	−	0.0901612i	0.00165024	−	0.00285830i
$996$	−4.69814			−0.148866
$997$	−32.0168	+	11.6532i	−1.01398	+	0.369059i	−0.794961	−	0.606661i	$-0.792509\pi$
$997$	−32.0168	+	11.6532i	−1.01398	+	0.369059i	−0.219022	+	0.975720i	$0.570287\pi$
$998$	−11.3472	+	4.13005i	−0.359190	+	0.130734i
$999$	3.60082			0.113925

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	931.2.v.e.275.2		30
7.2	even	3		931.2.w.b.883.4		30
7.3	odd	6		931.2.x.e.655.4		30
7.4	even	3		931.2.x.d.655.4		30
7.5	odd	6		133.2.v.b.85.4	yes	30
7.6	odd	2		931.2.v.d.275.2		30
19.17	even	9		931.2.x.d.226.4		30
133.17	odd	18		931.2.v.d.606.2		30
133.55	odd	18		931.2.x.e.226.4		30
133.74	even	9	inner	931.2.v.e.606.2		30
133.82	odd	18		2527.2.a.r.1.11		15
133.89	even	18		2527.2.a.s.1.5		15
133.93	even	9		931.2.w.b.834.4		30
133.131	odd	18		133.2.v.b.36.4	✓	30

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
133.2.v.b.36.4	✓	30	133.131	odd	18
133.2.v.b.85.4	yes	30	7.5	odd	6
931.2.v.d.275.2		30	7.6	odd	2
931.2.v.d.606.2		30	133.17	odd	18
931.2.v.e.275.2		30	1.1	even	1	trivial
931.2.v.e.606.2		30	133.74	even	9	inner
931.2.w.b.834.4		30	133.93	even	9
931.2.w.b.883.4		30	7.2	even	3
931.2.x.d.226.4		30	19.17	even	9
931.2.x.d.655.4		30	7.4	even	3
931.2.x.e.226.4		30	133.55	odd	18
931.2.x.e.655.4		30	7.3	odd	6
2527.2.a.r.1.11		15	133.82	odd	18
2527.2.a.s.1.5		15	133.89	even	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)

\(f(q)\)	\(=\)	\(q+(-1.52863 - 0.556375i) q^{2} +(1.01101 + 0.367976i) q^{3} +(0.495058 + 0.415403i) q^{4} +(-0.0539084 + 0.0452345i) q^{5} +(-1.34072 - 1.12500i) q^{6} +(1.10109 + 1.90715i) q^{8} +(-1.41140 - 1.18431i) q^{9} +O(q^{10})\)	\(q+(-1.52863 - 0.556375i) q^{2} +(1.01101 + 0.367976i) q^{3} +(0.495058 + 0.415403i) q^{4} +(-0.0539084 + 0.0452345i) q^{5} +(-1.34072 - 1.12500i) q^{6} +(1.10109 + 1.90715i) q^{8} +(-1.41140 - 1.18431i) q^{9} +(0.107573 - 0.0391534i) q^{10} +(-0.895617 + 1.55125i) q^{11} +(0.347648 + 0.602145i) q^{12} +(2.27346 + 1.90766i) q^{13} +(-0.0711470 + 0.0258954i) q^{15} +(-0.846511 - 4.80080i) q^{16} +(0.482311 - 0.404707i) q^{17} +(1.49859 + 2.59564i) q^{18} +(-4.10808 + 1.45729i) q^{19} -0.0454783 q^{20} +(2.23214 - 1.87299i) q^{22} +(-0.260520 + 1.47748i) q^{23} +(0.411426 + 2.33331i) q^{24} +(-0.867381 + 4.91916i) q^{25} +(-2.41390 - 4.18100i) q^{26} +(-2.60498 - 4.51196i) q^{27} +(-0.942253 + 5.34378i) q^{29} +0.123165 q^{30} +6.53051 q^{31} +(-0.612235 + 3.47216i) q^{32} +(-1.47630 + 1.23876i) q^{33} +(-0.962442 + 0.350300i) q^{34} +(-0.206761 - 1.17260i) q^{36} +(-0.345571 + 0.598546i) q^{37} +(7.09052 + 0.0579855i) q^{38} +(1.59651 + 2.76524i) q^{39} +(-0.145627 - 0.0530039i) q^{40} +(-5.15375 + 4.32451i) q^{41} +(-1.77256 - 0.645159i) q^{43} +(-1.08778 + 0.395918i) q^{44} +0.129658 q^{45} +(1.22027 - 2.11357i) q^{46} +(1.06525 + 0.893854i) q^{47} +(0.910754 - 5.16514i) q^{48} +(4.06280 - 7.03697i) q^{50} +(0.636542 - 0.231682i) q^{51} +(0.333047 + 1.88881i) q^{52} +(5.65278 + 4.74325i) q^{53} +(1.47170 + 8.34644i) q^{54} +(-0.0218890 - 0.124138i) q^{55} +(-4.68954 - 0.0383506i) q^{57} +(4.41350 - 7.64440i) q^{58} +(-10.6227 + 8.91351i) q^{59} +(-0.0459789 - 0.0167350i) q^{60} +(0.0291876 - 0.165531i) q^{61} +(-9.98271 - 3.63341i) q^{62} +(-2.00716 + 3.47651i) q^{64} -0.208851 q^{65} +(2.94593 - 1.07223i) q^{66} +(8.68050 - 3.15944i) q^{67} +0.406888 q^{68} +(-0.807065 + 1.39788i) q^{69} +(11.0779 + 4.03202i) q^{71} +(0.704565 - 3.99579i) q^{72} +(-10.5484 - 3.83932i) q^{73} +(0.861264 - 0.722686i) q^{74} +(-2.68706 + 4.65413i) q^{75} +(-2.63910 - 0.985067i) q^{76} +(-0.901962 - 5.11528i) q^{78} +(1.81990 + 10.3211i) q^{79} +(0.262796 + 0.220512i) q^{80} +(-0.0135400 - 0.0767891i) q^{81} +(10.2842 - 3.74315i) q^{82} +(-3.37852 + 5.85176i) q^{83} +(-0.00769389 + 0.0436342i) q^{85} +(2.35063 + 1.97242i) q^{86} +(-2.91901 + 5.05588i) q^{87} -3.94463 q^{88} +(-3.87887 + 1.41179i) q^{89} +(-0.198199 - 0.0721386i) q^{90} +(-0.742721 + 0.623217i) q^{92} +(6.60239 + 2.40307i) q^{93} +(-1.13106 - 1.95905i) q^{94} +(0.155540 - 0.264387i) q^{95} +(-1.89665 + 3.28509i) q^{96} +(0.928436 + 5.26542i) q^{97} +(3.10124 - 1.12876i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9}+O(q^{10}) \) 30 * q + 3 * q^3 + 12 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 21 * q^9	\( 30 q + 3 q^{3} + 12 q^{4} - 3 q^{5} + 9 q^{6} + 9 q^{8} - 21 q^{9} - 36 q^{10} - 18 q^{12} - 30 q^{15} + 15 q^{17} + 15 q^{18} - 6 q^{19} + 30 q^{20} + 12 q^{22} + 12 q^{23} + 63 q^{24} + 21 q^{25} + 45 q^{26} - 27 q^{27} - 42 q^{30} + 24 q^{31} + 60 q^{32} - 9 q^{33} + 42 q^{34} - 21 q^{36} + 18 q^{37} + 60 q^{38} + 12 q^{39} - 87 q^{40} - 3 q^{41} - 12 q^{43} - 72 q^{44} + 54 q^{45} + 6 q^{46} + 36 q^{47} - 18 q^{48} - 3 q^{50} + 15 q^{52} - 15 q^{53} + 21 q^{54} - 33 q^{55} - 12 q^{57} + 30 q^{58} - 42 q^{59} + 12 q^{60} + 75 q^{61} - 96 q^{62} + 3 q^{64} - 90 q^{65} - 18 q^{66} + 30 q^{67} + 102 q^{68} - 15 q^{69} + 30 q^{71} + 99 q^{72} + 12 q^{73} - 57 q^{74} - 72 q^{75} - 84 q^{76} + 6 q^{78} + 3 q^{79} - 78 q^{80} - 6 q^{81} + 6 q^{82} - 12 q^{83} + 42 q^{85} + 42 q^{86} - 24 q^{87} - 72 q^{88} - 24 q^{89} - 180 q^{90} - 75 q^{92} + 12 q^{93} - 21 q^{94} + 30 q^{95} + 33 q^{96} + 63 q^{97} + 45 q^{99}+O(q^{100}) \) 30 * q + 3 * q^3 + 12 * q^4 - 3 * q^5 + 9 * q^6 + 9 * q^8 - 21 * q^9 - 36 * q^10 - 18 * q^12 - 30 * q^15 + 15 * q^17 + 15 * q^18 - 6 * q^19 + 30 * q^20 + 12 * q^22 + 12 * q^23 + 63 * q^24 + 21 * q^25 + 45 * q^26 - 27 * q^27 - 42 * q^30 + 24 * q^31 + 60 * q^32 - 9 * q^33 + 42 * q^34 - 21 * q^36 + 18 * q^37 + 60 * q^38 + 12 * q^39 - 87 * q^40 - 3 * q^41 - 12 * q^43 - 72 * q^44 + 54 * q^45 + 6 * q^46 + 36 * q^47 - 18 * q^48 - 3 * q^50 + 15 * q^52 - 15 * q^53 + 21 * q^54 - 33 * q^55 - 12 * q^57 + 30 * q^58 - 42 * q^59 + 12 * q^60 + 75 * q^61 - 96 * q^62 + 3 * q^64 - 90 * q^65 - 18 * q^66 + 30 * q^67 + 102 * q^68 - 15 * q^69 + 30 * q^71 + 99 * q^72 + 12 * q^73 - 57 * q^74 - 72 * q^75 - 84 * q^76 + 6 * q^78 + 3 * q^79 - 78 * q^80 - 6 * q^81 + 6 * q^82 - 12 * q^83 + 42 * q^85 + 42 * q^86 - 24 * q^87 - 72 * q^88 - 24 * q^89 - 180 * q^90 - 75 * q^92 + 12 * q^93 - 21 * q^94 + 30 * q^95 + 33 * q^96 + 63 * q^97 + 45 * q^99

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