LMFDB - Embedded newform 429.2.m.b.109.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [429,2,Mod(109,429)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(429, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 2, 3]))

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

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

chi := DirichletCharacter("429.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 429 = 3 \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	429.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.42558224671$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			109.13
Character	$\chi$	$=$	429.109
Dual form			429.2.m.b.307.13

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.63677 + 1.63677i) q^{2} +1.00000 q^{3} +3.35804i q^{4} +(0.440340 - 0.440340i) q^{5} +(1.63677 + 1.63677i) q^{6} +(-2.71876 + 2.71876i) q^{7} +(-2.22281 + 2.22281i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(1.63677 + 1.63677i) q^{2} +1.00000 q^{3} +3.35804i q^{4} +(0.440340 - 0.440340i) q^{5} +(1.63677 + 1.63677i) q^{6} +(-2.71876 + 2.71876i) q^{7} +(-2.22281 + 2.22281i) q^{8} +1.00000 q^{9} +1.44147 q^{10} +(2.64974 + 1.99471i) q^{11} +3.35804i q^{12} +(-2.23697 - 2.82772i) q^{13} -8.89999 q^{14} +(0.440340 - 0.440340i) q^{15} -0.560371 q^{16} +3.11687 q^{17} +(1.63677 + 1.63677i) q^{18} +(-2.98040 - 2.98040i) q^{19} +(1.47868 + 1.47868i) q^{20} +(-2.71876 + 2.71876i) q^{21} +(1.07213 + 7.60191i) q^{22} -6.31611i q^{23} +(-2.22281 + 2.22281i) q^{24} +4.61220i q^{25} +(0.966925 - 8.28973i) q^{26} +1.00000 q^{27} +(-9.12973 - 9.12973i) q^{28} +4.54764i q^{29} +1.44147 q^{30} +(5.18868 - 5.18868i) q^{31} +(3.52842 + 3.52842i) q^{32} +(2.64974 + 1.99471i) q^{33} +(5.10161 + 5.10161i) q^{34} +2.39436i q^{35} +3.35804i q^{36} +(-5.30931 - 5.30931i) q^{37} -9.75645i q^{38} +(-2.23697 - 2.82772i) q^{39} +1.95758i q^{40} +(-7.97044 - 7.97044i) q^{41} -8.89999 q^{42} +10.8771 q^{43} +(-6.69834 + 8.89794i) q^{44} +(0.440340 - 0.440340i) q^{45} +(10.3380 - 10.3380i) q^{46} +(-1.66486 - 1.66486i) q^{47} -0.560371 q^{48} -7.78335i q^{49} +(-7.54912 + 7.54912i) q^{50} +3.11687 q^{51} +(9.49560 - 7.51183i) q^{52} -8.11308 q^{53} +(1.63677 + 1.63677i) q^{54} +(2.04514 - 0.288433i) q^{55} -12.0866i q^{56} +(-2.98040 - 2.98040i) q^{57} +(-7.44344 + 7.44344i) q^{58} +(-0.774163 - 0.774163i) q^{59} +(1.47868 + 1.47868i) q^{60} +9.66220i q^{61} +16.9854 q^{62} +(-2.71876 + 2.71876i) q^{63} +12.6712i q^{64} +(-2.23018 - 0.260131i) q^{65} +(1.07213 + 7.60191i) q^{66} +(8.11379 - 8.11379i) q^{67} +10.4666i q^{68} -6.31611i q^{69} +(-3.91902 + 3.91902i) q^{70} +(-6.86968 + 6.86968i) q^{71} +(-2.22281 + 2.22281i) q^{72} +(1.27729 - 1.27729i) q^{73} -17.3803i q^{74} +4.61220i q^{75} +(10.0083 - 10.0083i) q^{76} +(-12.6272 + 1.78086i) q^{77} +(0.966925 - 8.28973i) q^{78} -4.85714i q^{79} +(-0.246753 + 0.246753i) q^{80} +1.00000 q^{81} -26.0916i q^{82} +(-7.42906 - 7.42906i) q^{83} +(-9.12973 - 9.12973i) q^{84} +(1.37248 - 1.37248i) q^{85} +(17.8034 + 17.8034i) q^{86} +4.54764i q^{87} +(-10.3237 + 1.45599i) q^{88} +(1.31899 + 1.31899i) q^{89} +1.44147 q^{90} +(13.7697 + 1.60611i) q^{91} +21.2098 q^{92} +(5.18868 - 5.18868i) q^{93} -5.45000i q^{94} -2.62477 q^{95} +(3.52842 + 3.52842i) q^{96} +(-9.60861 + 9.60861i) q^{97} +(12.7396 - 12.7396i) q^{98} +(2.64974 + 1.99471i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	$ 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) $ 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

$n$	$67$	$79$	$287$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	1.63677	+	1.63677i	1.15737	+	1.15737i	0.985039	+	0.172334i	$0.0551308\pi$
$2$	1.63677	+	1.63677i	1.15737	+	1.15737i	0.172334	+	0.985039i	$0.444869\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$			3.35804i			1.67902i
$5$	0.440340	−	0.440340i	0.196926	−	0.196926i	−0.601755	−	0.798681i	$-0.705532\pi$
$5$	0.440340	−	0.440340i	0.196926	−	0.196926i	0.798681	+	0.601755i	$0.205532\pi$
$6$	1.63677	+	1.63677i	0.668209	+	0.668209i
$7$	−2.71876	+	2.71876i	−1.02760	+	1.02760i	−0.0279879	+	0.999608i	$0.508910\pi$
$7$	−2.71876	+	2.71876i	−1.02760	+	1.02760i	−0.999608	+	0.0279879i	$0.991090\pi$
$8$	−2.22281	+	2.22281i	−0.785881	+	0.785881i
$9$	1.00000			0.333333
$10$	1.44147			0.455833
$11$	2.64974	+	1.99471i	0.798926	+	0.601429i
$11$	2.64974	+	1.99471i	0.798926	+	0.601429i
$12$			3.35804i			0.969384i
$13$	−2.23697	−	2.82772i	−0.620423	−	0.784268i
$13$	−2.23697	−	2.82772i	−0.620423	−	0.784268i
$14$	−8.89999			−2.37862
$15$	0.440340	−	0.440340i	0.113695	−	0.113695i
$16$	−0.560371			−0.140093
$17$	3.11687			0.755953			0.377976	−	0.925815i	$-0.376620\pi$
$17$	3.11687			0.755953			0.377976	+	0.925815i	$0.376620\pi$
$18$	1.63677	+	1.63677i	0.385791	+	0.385791i
$19$	−2.98040	−	2.98040i	−0.683750	−	0.683750i	0.277093	−	0.960843i	$-0.410629\pi$
$19$	−2.98040	−	2.98040i	−0.683750	−	0.683750i	−0.960843	+	0.277093i	$0.910629\pi$
$20$	1.47868	+	1.47868i	0.330643	+	0.330643i
$21$	−2.71876	+	2.71876i	−0.593283	+	0.593283i
$22$	1.07213	+	7.60191i	0.228578	+	1.62073i
$23$		−	6.31611i		−	1.31700i	−0.752581	−	0.658500i	$-0.771191\pi$
$23$		−	6.31611i		−	1.31700i	0.752581	−	0.658500i	$-0.228809\pi$
$24$	−2.22281	+	2.22281i	−0.453729	+	0.453729i
$25$			4.61220i			0.922440i
$26$	0.966925	−	8.28973i	0.189630	−	1.62575i
$27$	1.00000			0.192450
$28$	−9.12973	−	9.12973i	−1.72536	−	1.72536i
$29$			4.54764i			0.844475i	0.906485	+	0.422237i	$0.138755\pi$
$29$			4.54764i			0.844475i	−0.906485	+	0.422237i	$0.861245\pi$
$30$	1.44147			0.263175
$31$	5.18868	−	5.18868i	0.931914	−	0.931914i	−0.0659114	−	0.997825i	$-0.520995\pi$
$31$	5.18868	−	5.18868i	0.931914	−	0.931914i	0.997825	+	0.0659114i	$0.0209955\pi$
$32$	3.52842	+	3.52842i	0.623742	+	0.623742i
$33$	2.64974	+	1.99471i	0.461260	+	0.347235i
$34$	5.10161	+	5.10161i	0.874919	+	0.874919i
$35$			2.39436i			0.404721i
$36$			3.35804i			0.559674i
$37$	−5.30931	−	5.30931i	−0.872846	−	0.872846i	0.119936	−	0.992782i	$-0.461731\pi$
$37$	−5.30931	−	5.30931i	−0.872846	−	0.872846i	−0.992782	+	0.119936i	$0.961731\pi$
$38$		−	9.75645i		−	1.58271i
$39$	−2.23697	−	2.82772i	−0.358201	−	0.452797i
$40$			1.95758i			0.309521i
$41$	−7.97044	−	7.97044i	−1.24477	−	1.24477i	−0.957998	−	0.286775i	$-0.907417\pi$
$41$	−7.97044	−	7.97044i	−1.24477	−	1.24477i	−0.286775	−	0.957998i	$-0.592583\pi$
$42$	−8.89999			−1.37330
$43$	10.8771			1.65875			0.829373	−	0.558695i	$-0.188698\pi$
$43$	10.8771			1.65875			0.829373	+	0.558695i	$0.188698\pi$
$44$	−6.69834	+	8.89794i	−1.00981	+	1.34141i
$45$	0.440340	−	0.440340i	0.0656420	−	0.0656420i
$46$	10.3380	−	10.3380i	1.52426	−	1.52426i
$47$	−1.66486	−	1.66486i	−0.242845	−	0.242845i	0.575181	−	0.818026i	$-0.304932\pi$
$47$	−1.66486	−	1.66486i	−0.242845	−	0.242845i	−0.818026	+	0.575181i	$0.804932\pi$
$48$	−0.560371			−0.0808825
$49$		−	7.78335i		−	1.11191i
$50$	−7.54912	+	7.54912i	−1.06761	+	1.06761i
$51$	3.11687			0.436449
$52$	9.49560	−	7.51183i	1.31680	−	1.04170i
$53$	−8.11308			−1.11442			−0.557208	−	0.830373i	$-0.688128\pi$
$53$	−8.11308			−1.11442			−0.557208	+	0.830373i	$0.688128\pi$
$54$	1.63677	+	1.63677i	0.222736	+	0.222736i
$55$	2.04514	−	0.288433i	0.275766	−	0.0388923i
$56$		−	12.0866i		−	1.61514i
$57$	−2.98040	−	2.98040i	−0.394763	−	0.394763i
$58$	−7.44344	+	7.44344i	−0.977372	+	0.977372i
$59$	−0.774163	−	0.774163i	−0.100787	−	0.100787i	0.654915	−	0.755702i	$-0.272704\pi$
$59$	−0.774163	−	0.774163i	−0.100787	−	0.100787i	−0.755702	+	0.654915i	$0.772704\pi$
$60$	1.47868	+	1.47868i	0.190897	+	0.190897i
$61$			9.66220i			1.23712i	0.785738	+	0.618559i	$0.212283\pi$
$61$			9.66220i			1.23712i	−0.785738	+	0.618559i	$0.787717\pi$
$62$	16.9854			2.15714
$63$	−2.71876	+	2.71876i	−0.342532	+	0.342532i
$64$			12.6712i			1.58390i
$65$	−2.23018	−	0.260131i	−0.276620	−	0.0322653i
$66$	1.07213	+	7.60191i	0.131970	+	0.935730i
$67$	8.11379	−	8.11379i	0.991257	−	0.991257i	−0.00870525	−	0.999962i	$-0.502771\pi$
$67$	8.11379	−	8.11379i	0.991257	−	0.991257i	0.999962	+	0.00870525i	$0.00277100\pi$
$68$			10.4666i			1.26926i
$69$		−	6.31611i		−	0.760370i
$70$	−3.91902	+	3.91902i	−0.468412	+	0.468412i
$71$	−6.86968	+	6.86968i	−0.815282	+	0.815282i	−0.985420	−	0.170139i	$-0.945578\pi$
$71$	−6.86968	+	6.86968i	−0.815282	+	0.815282i	0.170139	+	0.985420i	$0.445578\pi$
$72$	−2.22281	+	2.22281i	−0.261960	+	0.261960i
$73$	1.27729	−	1.27729i	0.149496	−	0.149496i	−0.628397	−	0.777893i	$-0.716289\pi$
$73$	1.27729	−	1.27729i	0.149496	−	0.149496i	0.777893	+	0.628397i	$0.216289\pi$
$74$		−	17.3803i		−	2.02042i
$75$			4.61220i			0.532571i
$76$	10.0083	−	10.0083i	1.14803	−	1.14803i
$77$	−12.6272	+	1.78086i	−1.43900	+	0.202948i
$78$	0.966925	−	8.28973i	0.109483	−	0.938627i
$79$		−	4.85714i		−	0.546471i	−0.961947	−	0.273236i	$-0.911906\pi$
$79$		−	4.85714i		−	0.546471i	0.961947	−	0.273236i	$-0.0880939\pi$
$80$	−0.246753	+	0.246753i	−0.0275879	+	0.0275879i
$81$	1.00000			0.111111
$82$		−	26.0916i		−	2.88133i
$83$	−7.42906	−	7.42906i	−0.815446	−	0.815446i	0.169999	−	0.985444i	$-0.445624\pi$
$83$	−7.42906	−	7.42906i	−0.815446	−	0.815446i	−0.985444	+	0.169999i	$0.945624\pi$
$84$	−9.12973	−	9.12973i	−0.996135	−	0.996135i
$85$	1.37248	−	1.37248i	0.148867	−	0.148867i
$86$	17.8034	+	17.8034i	1.91979	+	1.91979i
$87$			4.54764i			0.487558i
$88$	−10.3237	+	1.45599i	−1.10051	+	0.155209i
$89$	1.31899	+	1.31899i	0.139813	+	0.139813i	0.773549	−	0.633736i	$-0.218480\pi$
$89$	1.31899	+	1.31899i	0.139813	+	0.139813i	−0.633736	+	0.773549i	$0.718480\pi$
$90$	1.44147			0.151944
$91$	13.7697	+	1.60611i	1.44345	+	0.168366i
$92$	21.2098			2.21127
$93$	5.18868	−	5.18868i	0.538041	−	0.538041i
$94$		−	5.45000i		−	0.562124i
$95$	−2.62477			−0.269296
$96$	3.52842	+	3.52842i	0.360118	+	0.360118i
$97$	−9.60861	+	9.60861i	−0.975606	+	0.975606i	−0.999709	−	0.0241030i	$-0.992327\pi$
$97$	−9.60861	+	9.60861i	−0.975606	+	0.975606i	0.0241030	+	0.999709i	$0.492327\pi$
$98$	12.7396	−	12.7396i	1.28689	−	1.28689i
$99$	2.64974	+	1.99471i	0.266309	+	0.200476i
$100$	−15.4880			−1.54880
$101$	−3.07578			−0.306051			−0.153026	−	0.988222i	$-0.548902\pi$
$101$	−3.07578			−0.306051			−0.153026	+	0.988222i	$0.548902\pi$
$102$	5.10161	+	5.10161i	0.505135	+	0.505135i
$103$			10.6106i			1.04550i	0.852487	+	0.522748i	$0.175093\pi$
$103$			10.6106i			1.04550i	−0.852487	+	0.522748i	$0.824907\pi$
$104$	11.2578	+	1.31313i	1.10392	+	0.128763i
$105$			2.39436i			0.233666i
$106$	−13.2793	−	13.2793i	−1.28980	−	1.28980i
$107$			5.84091i			0.564662i	0.959317	+	0.282331i	$0.0911077\pi$
$107$			5.84091i			0.564662i	−0.959317	+	0.282331i	$0.908892\pi$
$108$			3.35804i			0.323128i
$109$	7.48558	+	7.48558i	0.716989	+	0.716989i	0.967987	−	0.250999i	$-0.0807590\pi$
$109$	7.48558	+	7.48558i	0.716989	+	0.716989i	−0.250999	+	0.967987i	$0.580759\pi$
$110$	3.81952	+	2.87532i	0.364177	+	0.274151i
$111$	−5.30931	−	5.30931i	−0.503938	−	0.503938i
$112$	1.52352	−	1.52352i	0.143959	−	0.143959i
$113$	1.32031			0.124204			0.0621021	−	0.998070i	$-0.480220\pi$
$113$	1.32031			0.124204			0.0621021	+	0.998070i	$0.480220\pi$
$114$		−	9.75645i		−	0.913776i
$115$	−2.78123	−	2.78123i	−0.259351	−	0.259351i
$116$	−15.2712			−1.41789
$117$	−2.23697	−	2.82772i	−0.206808	−	0.261423i
$118$		−	2.53426i		−	0.233297i
$119$	−8.47404	+	8.47404i	−0.776814	+	0.776814i
$120$			1.95758i			0.178702i
$121$	3.04223	+	10.5709i	0.276566	+	0.960995i
$122$	−15.8148	+	15.8148i	−1.43181	+	1.43181i
$123$	−7.97044	−	7.97044i	−0.718670	−	0.718670i
$124$	17.4238	+	17.4238i	1.56470	+	1.56470i
$125$	4.23263	+	4.23263i	0.378578	+	0.378578i
$126$	−8.89999			−0.792874
$127$	−2.18796			−0.194150			−0.0970748	−	0.995277i	$-0.530949\pi$
$127$	−2.18796			−0.194150			−0.0970748	+	0.995277i	$0.530949\pi$
$128$	−13.6830	+	13.6830i	−1.20942	+	1.20942i
$129$	10.8771			0.957678
$130$	−3.22452	−	4.07607i	−0.282809	−	0.357495i
$131$			7.32444i			0.639940i	0.947428	+	0.319970i	$0.103673\pi$
$131$			7.32444i			0.639940i	−0.947428	+	0.319970i	$0.896327\pi$
$132$	−6.69834	+	8.89794i	−0.583015	+	0.774466i
$133$	16.2060			1.40524
$134$	26.5608			2.29451
$135$	0.440340	−	0.440340i	0.0378984	−	0.0378984i
$136$	−6.92821	+	6.92821i	−0.594089	+	0.594089i
$137$	8.29459	+	8.29459i	0.708655	+	0.708655i	0.966252	−	0.257598i	$-0.0829309\pi$
$137$	8.29459	+	8.29459i	0.708655	+	0.708655i	−0.257598	+	0.966252i	$0.582931\pi$
$138$	10.3380	−	10.3380i	0.880032	−	0.880032i
$139$		−	14.7415i		−	1.25035i	−0.780483	−	0.625177i	$-0.785027\pi$
$139$		−	14.7415i		−	1.25035i	0.780483	−	0.625177i	$-0.214973\pi$
$140$	−8.04036			−0.679535
$141$	−1.66486	−	1.66486i	−0.140207	−	0.140207i
$142$	−22.4882			−1.88717
$143$	−0.286888	−	11.9548i	−0.0239908	−	0.999712i
$144$	−0.560371			−0.0466975
$145$	2.00250	+	2.00250i	0.166299	+	0.166299i
$146$	4.18127			0.346045
$147$		−	7.78335i		−	0.641960i
$148$	17.8289	−	17.8289i	1.46553	−	1.46553i
$149$	2.00568	+	2.00568i	0.164312	+	0.164312i	0.784474	−	0.620162i	$-0.212933\pi$
$149$	2.00568	+	2.00568i	0.164312	+	0.164312i	−0.620162	+	0.784474i	$0.712933\pi$
$150$	−7.54912	+	7.54912i	−0.616383	+	0.616383i
$151$	2.84242	−	2.84242i	0.231313	−	0.231313i	−0.581928	−	0.813240i	$-0.697701\pi$
$151$	2.84242	−	2.84242i	0.231313	−	0.231313i	0.813240	+	0.581928i	$0.197701\pi$
$152$	13.2497			1.07469
$153$	3.11687			0.251984
$154$	−23.5827	−	17.7529i	−1.90034	−	1.43057i
$155$		−	4.56956i		−	0.367036i
$156$	9.49560	−	7.51183i	0.760256	−	0.601428i
$157$	−12.0466			−0.961423			−0.480712	−	0.876879i	$-0.659622\pi$
$157$	−12.0466			−0.961423			−0.480712	+	0.876879i	$0.659622\pi$
$158$	7.95004	−	7.95004i	0.632471	−	0.632471i
$159$	−8.11308			−0.643409
$160$	3.10740			0.245662
$161$	17.1720	+	17.1720i	1.35334	+	1.35334i
$162$	1.63677	+	1.63677i	0.128597	+	0.128597i
$163$	−12.7861	−	12.7861i	−1.00148	−	1.00148i	−0.999999	−	0.00148186i	$-0.999528\pi$
$163$	−12.7861	−	12.7861i	−1.00148	−	1.00148i	−0.00148186	−	0.999999i	$-0.500472\pi$
$164$	26.7651	−	26.7651i	2.09000	−	2.09000i
$165$	2.04514	−	0.288433i	0.159214	−	0.0224545i
$166$		−	24.3194i		−	1.88755i
$167$	2.97568	−	2.97568i	0.230265	−	0.230265i	−0.582538	−	0.812803i	$-0.697940\pi$
$167$	2.97568	−	2.97568i	0.230265	−	0.230265i	0.812803	+	0.582538i	$0.197940\pi$
$168$		−	12.0866i		−	0.932500i
$169$	−2.99197	+	12.6510i	−0.230151	+	0.973155i
$170$	4.49288			0.344588
$171$	−2.98040	−	2.98040i	−0.227917	−	0.227917i
$172$			36.5259i			2.78507i
$173$	−3.40269			−0.258702			−0.129351	−	0.991599i	$-0.541289\pi$
$173$	−3.40269			−0.258702			−0.129351	+	0.991599i	$0.541289\pi$
$174$	−7.44344	+	7.44344i	−0.564286	+	0.564286i
$175$	−12.5395	−	12.5395i	−0.947896	−	0.947896i
$176$	−1.48484	−	1.11778i	−0.111924	−	0.0842558i
$177$	−0.774163	−	0.774163i	−0.0581896	−	0.0581896i
$178$			4.31778i			0.323631i
$179$			23.5848i			1.76281i	0.472363	+	0.881404i	$0.343401\pi$
$179$			23.5848i			1.76281i	−0.472363	+	0.881404i	$0.656599\pi$
$180$	1.47868	+	1.47868i	0.110214	+	0.110214i
$181$		−	16.3445i		−	1.21488i	−0.794366	−	0.607439i	$-0.792197\pi$
$181$		−	16.3445i		−	1.21488i	0.794366	−	0.607439i	$-0.207803\pi$
$182$	19.9090	+	25.1667i	1.47575	+	1.86548i
$183$			9.66220i			0.714250i
$184$	14.0395	+	14.0395i	1.03501	+	1.03501i
$185$	−4.67580			−0.343772
$186$	16.9854			1.24543
$187$	8.25890	+	6.21727i	0.603950	+	0.454652i
$188$	5.59068	−	5.59068i	0.407742	−	0.407742i
$189$	−2.71876	+	2.71876i	−0.197761	+	0.197761i
$190$	−4.29615	−	4.29615i	−0.311676	−	0.311676i
$191$	−11.9686			−0.866017			−0.433009	−	0.901390i	$-0.642548\pi$
$191$	−11.9686			−0.866017			−0.433009	+	0.901390i	$0.642548\pi$
$192$			12.6712i			0.914463i
$193$	−9.11717	+	9.11717i	−0.656268	+	0.656268i	−0.954495	−	0.298227i	$-0.903605\pi$
$193$	−9.11717	+	9.11717i	−0.656268	+	0.656268i	0.298227	+	0.954495i	$0.403605\pi$
$194$	−31.4542			−2.25828
$195$	−2.23018	−	0.260131i	−0.159707	−	0.0186284i
$196$	26.1368			1.86692
$197$	−13.5536	−	13.5536i	−0.965655	−	0.965655i	0.0337747	−	0.999429i	$-0.489247\pi$
$197$	−13.5536	−	13.5536i	−0.965655	−	0.965655i	−0.999429	+	0.0337747i	$0.989247\pi$
$198$	1.07213	+	7.60191i	0.0761927	+	0.540244i
$199$			9.74611i			0.690883i	0.938440	+	0.345442i	$0.112271\pi$
$199$			9.74611i			0.690883i	−0.938440	+	0.345442i	$0.887729\pi$
$200$	−10.2520	−	10.2520i	−0.724929	−	0.724929i
$201$	8.11379	−	8.11379i	0.572302	−	0.572302i
$202$	−5.03434	−	5.03434i	−0.354215	−	0.354215i
$203$	−12.3639	−	12.3639i	−0.867779	−	0.867779i
$204$			10.4666i			0.732808i
$205$	−7.01940			−0.490256
$206$	−17.3672	+	17.3672i	−1.21003	+	1.21003i
$207$		−	6.31611i		−	0.439000i
$208$	1.25353	+	1.58457i	0.0869167	+	0.109870i
$209$	−1.95223	−	13.8423i	−0.135039	−	0.957492i
$210$	−3.91902	+	3.91902i	−0.270438	+	0.270438i
$211$			0.301318i			0.0207436i	0.999946	+	0.0103718i	$0.00330150\pi$
$211$			0.301318i			0.0207436i	−0.999946	+	0.0103718i	$0.996698\pi$
$212$		−	27.2441i		−	1.87113i
$213$	−6.86968	+	6.86968i	−0.470703	+	0.470703i
$214$	−9.56024	+	9.56024i	−0.653524	+	0.653524i
$215$	4.78963	−	4.78963i	0.326650	−	0.326650i
$216$	−2.22281	+	2.22281i	−0.151243	+	0.151243i
$217$			28.2136i			1.91526i
$218$			24.5044i			1.65965i
$219$	1.27729	−	1.27729i	0.0863114	−	0.0863114i
$220$	0.968572	+	6.86766i	0.0653011	+	0.463017i
$221$	−6.97234	−	8.81363i	−0.469010	−	0.592869i
$222$		−	17.3803i		−	1.16649i
$223$	0.853776	−	0.853776i	0.0571731	−	0.0571731i	−0.677942	−	0.735115i	$-0.737128\pi$
$223$	0.853776	−	0.853776i	0.0571731	−	0.0571731i	0.735115	+	0.677942i	$0.237128\pi$
$224$	−19.1859			−1.28191
$225$			4.61220i			0.307480i
$226$	2.16104	+	2.16104i	0.143751	+	0.143751i
$227$	3.13060	+	3.13060i	0.207786	+	0.207786i	0.803326	−	0.595540i	$-0.203062\pi$
$227$	3.13060	+	3.13060i	0.207786	+	0.207786i	−0.595540	+	0.803326i	$0.703062\pi$
$228$	10.0083	−	10.0083i	0.662816	−	0.662816i
$229$	−8.95456	−	8.95456i	−0.591734	−	0.591734i	0.346366	−	0.938100i	$-0.387416\pi$
$229$	−8.95456	−	8.95456i	−0.591734	−	0.591734i	−0.938100	+	0.346366i	$0.887416\pi$
$230$		−	9.10449i		−	0.600332i
$231$	−12.6272	+	1.78086i	−0.830807	+	0.117172i
$232$	−10.1085	−	10.1085i	−0.663657	−	0.663657i
$233$	11.9165			0.780676			0.390338	−	0.920672i	$-0.372358\pi$
$233$	11.9165			0.780676			0.390338	+	0.920672i	$0.372358\pi$
$234$	0.966925	−	8.28973i	0.0632098	−	0.541917i
$235$	−1.46621			−0.0956449
$236$	2.59967	−	2.59967i	0.169224	−	0.169224i
$237$		−	4.85714i		−	0.315505i
$238$	−27.7401			−1.79813
$239$	1.16552	+	1.16552i	0.0753913	+	0.0753913i	0.743797	−	0.668406i	$-0.233023\pi$
$239$	1.16552	+	1.16552i	0.0753913	+	0.0753913i	−0.668406	+	0.743797i	$0.733023\pi$
$240$	−0.246753	+	0.246753i	−0.0159279	+	0.0159279i
$241$	−4.08744	+	4.08744i	−0.263295	+	0.263295i	−0.826391	−	0.563096i	$-0.809610\pi$
$241$	−4.08744	+	4.08744i	−0.263295	+	0.263295i	0.563096	+	0.826391i	$0.309610\pi$
$242$	−12.3228	+	22.2817i	−0.792138	+	1.43232i
$243$	1.00000			0.0641500
$244$	−32.4461			−2.07715
$245$	−3.42732	−	3.42732i	−0.218963	−	0.218963i
$246$		−	26.0916i		−	1.66354i
$247$	−1.76067	+	15.0948i	−0.112029	+	0.960456i
$248$			23.0669i			1.46475i
$249$	−7.42906	−	7.42906i	−0.470798	−	0.470798i
$250$			13.8557i			0.876312i
$251$			11.6991i			0.738440i	0.929342	+	0.369220i	$0.120375\pi$
$251$			11.6991i			0.738440i	−0.929342	+	0.369220i	$0.879625\pi$
$252$	−9.12973	−	9.12973i	−0.575119	−	0.575119i
$253$	12.5988	−	16.7360i	0.792082	−	1.05219i
$254$	−3.58118	−	3.58118i	−0.224704	−	0.224704i
$255$	1.37248	−	1.37248i	0.0859482	−	0.0859482i
$256$	−19.4495			−1.21559
$257$		−	15.6236i		−	0.974574i	−0.873242	−	0.487287i	$-0.837986\pi$
$257$		−	15.6236i		−	0.974574i	0.873242	−	0.487287i	$-0.162014\pi$
$258$	17.8034	+	17.8034i	1.10839	+	1.10839i
$259$	28.8695			1.79387
$260$	0.873532	−	7.48904i	0.0541741	−	0.464451i
$261$			4.54764i			0.281492i
$262$	−11.9884	+	11.9884i	−0.740648	+	0.740648i
$263$		−	25.4067i		−	1.56665i	−0.621615	−	0.783323i	$-0.713523\pi$
$263$		−	25.4067i		−	1.56665i	0.621615	−	0.783323i	$-0.286477\pi$
$264$	−10.3237	+	1.45599i	−0.635381	+	0.0896102i
$265$	−3.57251	+	3.57251i	−0.219458	+	0.219458i
$266$	26.5255	+	26.5255i	1.62638	+	1.62638i
$267$	1.31899	+	1.31899i	0.0807211	+	0.0807211i
$268$	27.2465	+	27.2465i	1.66434	+	1.66434i
$269$	−20.3398			−1.24014			−0.620071	−	0.784546i	$-0.712896\pi$
$269$	−20.3398			−1.24014			−0.620071	+	0.784546i	$0.712896\pi$
$270$	1.44147			0.0877251
$271$	6.16624	−	6.16624i	0.374573	−	0.374573i	−0.494567	−	0.869140i	$-0.664673\pi$
$271$	6.16624	−	6.16624i	0.374573	−	0.374573i	0.869140	+	0.494567i	$0.164673\pi$
$272$	−1.74660			−0.105903
$273$	13.7697	+	1.60611i	0.833379	+	0.0972064i
$274$			27.1527i			1.64035i
$275$	−9.20002	+	12.2211i	−0.554782	+	0.736962i
$276$	21.2098			1.27668
$277$	13.4973			0.810972			0.405486	−	0.914101i	$-0.367102\pi$
$277$	13.4973			0.810972			0.405486	+	0.914101i	$0.367102\pi$
$278$	24.1284	−	24.1284i	1.44712	−	1.44712i
$279$	5.18868	−	5.18868i	0.310638	−	0.310638i
$280$	−5.32220	−	5.32220i	−0.318062	−	0.318062i
$281$	−21.7122	+	21.7122i	−1.29524	+	1.29524i	−0.363745	+	0.931499i	$0.618502\pi$
$281$	−21.7122	+	21.7122i	−1.29524	+	1.29524i	−0.931499	+	0.363745i	$0.881498\pi$
$282$		−	5.45000i		−	0.324543i
$283$	23.5532			1.40009			0.700047	−	0.714097i	$-0.253162\pi$
$283$	23.5532			1.40009			0.700047	+	0.714097i	$0.253162\pi$
$284$	−23.0687	−	23.0687i	−1.36888	−	1.36888i
$285$	−2.62477			−0.155478
$286$	19.0977	−	20.0369i	1.12927	−	1.18481i
$287$	43.3395			2.55825
$288$	3.52842	+	3.52842i	0.207914	+	0.207914i
$289$	−7.28511			−0.428536
$290$			6.55529i			0.384940i
$291$	−9.60861	+	9.60861i	−0.563267	+	0.563267i
$292$	4.28921	+	4.28921i	0.251007	+	0.251007i
$293$	−4.64872	+	4.64872i	−0.271581	+	0.271581i	−0.829737	−	0.558155i	$-0.811509\pi$
$293$	−4.64872	+	4.64872i	−0.271581	+	0.271581i	0.558155	+	0.829737i	$0.311509\pi$
$294$	12.7396	−	12.7396i	0.742987	−	0.742987i
$295$	−0.681789			−0.0396953
$296$	23.6032			1.37191
$297$	2.64974	+	1.99471i	0.153753	+	0.115745i
$298$			6.56568i			0.380340i
$299$	−17.8602	+	14.1289i	−1.03288	+	0.817097i
$300$	−15.4880			−0.894199
$301$	−29.5723	+	29.5723i	−1.70452	+	1.70452i
$302$	9.30478			0.535430
$303$	−3.07578			−0.176699
$304$	1.67013	+	1.67013i	0.0957883	+	0.0957883i
$305$	4.25465	+	4.25465i	0.243621	+	0.243621i
$306$	5.10161	+	5.10161i	0.291640	+	0.291640i
$307$	8.38481	−	8.38481i	0.478547	−	0.478547i	−0.426120	−	0.904667i	$-0.640120\pi$
$307$	8.38481	−	8.38481i	0.478547	−	0.478547i	0.904667	+	0.426120i	$0.140120\pi$
$308$	−5.98020	−	42.4026i	−0.340753	−	2.41611i
$309$			10.6106i			0.603618i
$310$	7.47933	−	7.47933i	0.424797	−	0.424797i
$311$			3.95370i			0.224193i	0.993697	+	0.112097i	$0.0357567\pi$
$311$			3.95370i			0.224193i	−0.993697	+	0.112097i	$0.964243\pi$
$312$	11.2578	+	1.31313i	0.637348	+	0.0743411i
$313$	29.7537			1.68178			0.840889	−	0.541208i	$-0.182033\pi$
$313$	29.7537			1.68178			0.840889	+	0.541208i	$0.182033\pi$
$314$	−19.7175	−	19.7175i	−1.11272	−	1.11272i
$315$			2.39436i			0.134907i
$316$	16.3105			0.917538
$317$	1.56178	−	1.56178i	0.0877183	−	0.0877183i	−0.661886	−	0.749604i	$-0.730244\pi$
$317$	1.56178	−	1.56178i	0.0877183	−	0.0877183i	0.749604	+	0.661886i	$0.230244\pi$
$318$	−13.2793	−	13.2793i	−0.744664	−	0.744664i
$319$	−9.07123	+	12.0500i	−0.507892	+	0.674673i
$320$	5.57962	+	5.57962i	0.311910	+	0.311910i
$321$			5.84091i			0.326008i
$322$			56.2133i			3.13265i
$323$	−9.28951	−	9.28951i	−0.516882	−	0.516882i
$324$			3.35804i			0.186558i
$325$	13.0420	−	10.3173i	0.723440	−	0.572303i
$326$		−	41.8557i		−	2.31817i
$327$	7.48558	+	7.48558i	0.413954	+	0.413954i
$328$	35.4335			1.95649
$329$	9.05273			0.499093
$330$	3.81952	+	2.87532i	0.210258	+	0.158281i
$331$	−12.5690	+	12.5690i	−0.690857	+	0.690857i	−0.962420	−	0.271564i	$-0.912459\pi$
$331$	−12.5690	+	12.5690i	−0.690857	+	0.690857i	0.271564	+	0.962420i	$0.412459\pi$
$332$	24.9471	−	24.9471i	1.36915	−	1.36915i
$333$	−5.30931	−	5.30931i	−0.290949	−	0.290949i
$334$	9.74102			0.533005
$335$		−	7.14564i		−	0.390408i
$336$	1.52352	−	1.52352i	0.0831146	−	0.0831146i
$337$	25.3068			1.37855			0.689276	−	0.724499i	$-0.257929\pi$
$337$	25.3068			1.37855			0.689276	+	0.724499i	$0.257929\pi$
$338$	−25.6040	+	15.8097i	−1.39267	+	0.859932i
$339$	1.32031			0.0717093
$340$	4.60886	+	4.60886i	0.249950	+	0.249950i
$341$	24.0986	−	3.39871i	1.30501	−	0.184051i
$342$		−	9.75645i		−	0.527569i
$343$	2.12975	+	2.12975i	0.114996	+	0.114996i
$344$	−24.1778	+	24.1778i	−1.30358	+	1.30358i
$345$	−2.78123	−	2.78123i	−0.149737	−	0.149737i
$346$	−5.56942	−	5.56942i	−0.299414	−	0.299414i
$347$		−	13.7207i		−	0.736568i	−0.929713	−	0.368284i	$-0.879945\pi$
$347$		−	13.7207i		−	0.736568i	0.929713	−	0.368284i	$-0.120055\pi$
$348$	−15.2712			−0.818620
$349$	2.46015	−	2.46015i	0.131689	−	0.131689i	−0.638190	−	0.769879i	$-0.720317\pi$
$349$	2.46015	−	2.46015i	0.131689	−	0.131689i	0.769879	+	0.638190i	$0.220317\pi$
$350$		−	41.0486i		−	2.19414i
$351$	−2.23697	−	2.82772i	−0.119400	−	0.150932i
$352$	2.31120	+	16.3876i	0.123187	+	0.873460i
$353$	−5.02997	+	5.02997i	−0.267718	+	0.267718i	−0.828180	−	0.560462i	$-0.810624\pi$
$353$	−5.02997	+	5.02997i	−0.267718	+	0.267718i	0.560462	+	0.828180i	$0.310624\pi$
$354$		−	2.53426i		−	0.134694i
$355$			6.04999i			0.321100i
$356$	−4.42924	+	4.42924i	−0.234749	+	0.234749i
$357$	−8.47404	+	8.47404i	−0.448494	+	0.448494i
$358$	−38.6029	+	38.6029i	−2.04023	+	2.04023i
$359$	−11.0971	+	11.0971i	−0.585685	+	0.585685i	−0.936460	−	0.350775i	$-0.885918\pi$
$359$	−11.0971	+	11.0971i	−0.585685	+	0.585685i	0.350775	+	0.936460i	$0.385918\pi$
$360$			1.95758i			0.103174i
$361$		−	1.23449i		−	0.0649731i
$362$	26.7522	−	26.7522i	1.40607	−	1.40607i
$363$	3.04223	+	10.5709i	0.159676	+	0.554831i
$364$	−5.39340	+	46.2392i	−0.282691	+	2.42359i
$365$		−	1.12489i		−	0.0588792i
$366$	−15.8148	+	15.8148i	−0.826654	+	0.826654i
$367$	25.1602			1.31335			0.656675	−	0.754173i	$-0.271962\pi$
$367$	25.1602			1.31335			0.656675	+	0.754173i	$0.271962\pi$
$368$			3.53936i			0.184502i
$369$	−7.97044	−	7.97044i	−0.414924	−	0.414924i
$370$	−7.65322	−	7.65322i	−0.397872	−	0.397872i
$371$	22.0575	−	22.0575i	1.14517	−	1.14517i
$372$	17.4238	+	17.4238i	0.903382	+	0.903382i
$373$			26.6611i			1.38046i	0.723590	+	0.690230i	$0.242491\pi$
$373$			26.6611i			1.38046i	−0.723590	+	0.690230i	$0.757509\pi$
$374$	3.34168	+	23.6942i	0.172794	+	1.22520i
$375$	4.23263	+	4.23263i	0.218572	+	0.218572i
$376$	7.40133			0.381695
$377$	12.8594	−	10.1729i	0.662294	−	0.523931i
$378$	−8.89999			−0.457766
$379$	20.7109	−	20.7109i	1.06385	−	1.06385i	0.0660322	−	0.997817i	$-0.478966\pi$
$379$	20.7109	−	20.7109i	1.06385	−	1.06385i	0.997817	−	0.0660322i	$-0.0210340\pi$
$380$		−	8.81410i		−	0.452154i
$381$	−2.18796			−0.112092
$382$	−19.5899	−	19.5899i	−1.00230	−	1.00230i
$383$	6.01453	−	6.01453i	0.307328	−	0.307328i	−0.536544	−	0.843872i	$-0.680270\pi$
$383$	6.01453	−	6.01453i	0.307328	−	0.307328i	0.843872	+	0.536544i	$0.180270\pi$
$384$	−13.6830	+	13.6830i	−0.698256	+	0.698256i
$385$	−4.77606	+	6.34443i	−0.243411	+	0.323342i
$386$	−29.8454			−1.51909
$387$	10.8771			0.552916
$388$	−32.2661	−	32.2661i	−1.63806	−	1.63806i
$389$		−	18.8623i		−	0.956355i	−0.878263	−	0.478177i	$-0.841298\pi$
$389$		−	18.8623i		−	0.956355i	0.878263	−	0.478177i	$-0.158702\pi$
$390$	−3.22452	−	4.07607i	−0.163280	−	0.206400i
$391$		−	19.6865i		−	0.995590i
$392$	17.3009	+	17.3009i	0.873827	+	0.873827i
$393$			7.32444i			0.369469i
$394$		−	44.3683i		−	2.23524i
$395$	−2.13879	−	2.13879i	−0.107614	−	0.107614i
$396$	−6.69834	+	8.89794i	−0.336604	+	0.447138i
$397$	5.11109	+	5.11109i	0.256518	+	0.256518i	0.823636	−	0.567118i	$-0.191942\pi$
$397$	5.11109	+	5.11109i	0.256518	+	0.256518i	−0.567118	+	0.823636i	$0.691942\pi$
$398$	−15.9522	+	15.9522i	−0.799609	+	0.799609i
$399$	16.2060			0.811314
$400$		−	2.58454i		−	0.129227i
$401$	21.4291	+	21.4291i	1.07012	+	1.07012i	0.997349	+	0.0727671i	$0.0231830\pi$
$401$	21.4291	+	21.4291i	1.07012	+	1.07012i	0.0727671	+	0.997349i	$0.476817\pi$
$402$	26.5608			1.32473
$403$	−26.2790	−	3.06522i	−1.30905	−	0.152689i
$404$		−	10.3286i		−	0.513866i
$405$	0.440340	−	0.440340i	0.0218807	−	0.0218807i
$406$		−	40.4739i		−	2.00869i
$407$	−3.47773	−	24.6589i	−0.172385	−	1.22229i
$408$	−6.92821	+	6.92821i	−0.342997	+	0.342997i
$409$	3.49848	+	3.49848i	0.172989	+	0.172989i	0.788291	−	0.615302i	$-0.210966\pi$
$409$	3.49848	+	3.49848i	0.172989	+	0.172989i	−0.615302	+	0.788291i	$0.710966\pi$
$410$	−11.4892	−	11.4892i	−0.567409	−	0.567409i
$411$	8.29459	+	8.29459i	0.409142	+	0.409142i
$412$	−35.6310			−1.75541
$413$	4.20953			0.207138
$414$	10.3380	−	10.3380i	0.508087	−	0.508087i
$415$	−6.54262			−0.321165
$416$	2.08442	−	17.8703i	0.102197	−	0.876164i
$417$		−	14.7415i		−	0.721892i
$418$	19.4613	−	25.8521i	0.951885	−	1.26447i
$419$	−2.18413			−0.106702			−0.0533509	−	0.998576i	$-0.516990\pi$
$419$	−2.18413			−0.106702			−0.0533509	+	0.998576i	$0.516990\pi$
$420$	−8.04036			−0.392330
$421$	7.48874	−	7.48874i	0.364979	−	0.364979i	−0.500663	−	0.865642i	$-0.666911\pi$
$421$	7.48874	−	7.48874i	0.364979	−	0.364979i	0.865642	+	0.500663i	$0.166911\pi$
$422$	−0.493189	+	0.493189i	−0.0240081	+	0.0240081i
$423$	−1.66486	−	1.66486i	−0.0809483	−	0.0809483i
$424$	18.0338	−	18.0338i	0.875799	−	0.875799i
$425$			14.3756i			0.697321i
$426$	−22.4882			−1.08956
$427$	−26.2692	−	26.2692i	−1.27126	−	1.27126i
$428$	−19.6140			−0.948080
$429$	−0.286888	−	11.9548i	−0.0138511	−	0.577184i
$430$	15.6791			0.756112
$431$	−11.9955	−	11.9955i	−0.577802	−	0.577802i	0.356495	−	0.934297i	$-0.383972\pi$
$431$	−11.9955	−	11.9955i	−0.577802	−	0.577802i	−0.934297	+	0.356495i	$0.883972\pi$
$432$	−0.560371			−0.0269608
$433$		−	18.3318i		−	0.880972i	−0.897759	−	0.440486i	$-0.854806\pi$
$433$		−	18.3318i		−	0.880972i	0.897759	−	0.440486i	$-0.145194\pi$
$434$	−46.1792	+	46.1792i	−2.21667	+	2.21667i
$435$	2.00250	+	2.00250i	0.0960127	+	0.0960127i
$436$	−25.1369	+	25.1369i	−1.20384	+	1.20384i
$437$	−18.8245	+	18.8245i	−0.900498	+	0.900498i
$438$	4.18127			0.199789
$439$	16.5121			0.788082			0.394041	−	0.919093i	$-0.371077\pi$
$439$	16.5121			0.788082			0.394041	+	0.919093i	$0.371077\pi$
$440$	−3.90481	+	5.18708i	−0.186155	+	0.247284i
$441$		−	7.78335i		−	0.370636i
$442$	3.01378	−	25.8380i	0.143351	−	1.22899i
$443$	29.8790			1.41960			0.709798	−	0.704406i	$-0.248786\pi$
$443$	29.8790			1.41960			0.709798	+	0.704406i	$0.248786\pi$
$444$	17.8289	−	17.8289i	0.846123	−	0.846123i
$445$	1.16161			0.0550656
$446$	2.79487			0.132341
$447$	2.00568	+	2.00568i	0.0948655	+	0.0948655i
$448$	−34.4499	−	34.4499i	−1.62761	−	1.62761i
$449$	−19.4059	−	19.4059i	−0.915823	−	0.915823i	0.0808989	−	0.996722i	$-0.474221\pi$
$449$	−19.4059	−	19.4059i	−0.915823	−	0.915823i	−0.996722	+	0.0808989i	$0.974221\pi$
$450$	−7.54912	+	7.54912i	−0.355869	+	0.355869i
$451$	−5.22083	−	37.0183i	−0.245839	−	1.74312i
$452$			4.43365i			0.208542i
$453$	2.84242	−	2.84242i	0.133548	−	0.133548i
$454$			10.2482i			0.480970i
$455$	6.77057	−	5.35610i	0.317409	−	0.251098i
$456$	13.2497			0.620474
$457$	−3.84032	−	3.84032i	−0.179643	−	0.179643i	0.611557	−	0.791200i	$-0.290543\pi$
$457$	−3.84032	−	3.84032i	−0.179643	−	0.179643i	−0.791200	+	0.611557i	$0.790543\pi$
$458$		−	29.3131i		−	1.36971i
$459$	3.11687			0.145483
$460$	9.33951	−	9.33951i	0.435457	−	0.435457i
$461$	25.1497	+	25.1497i	1.17134	+	1.17134i	0.981890	+	0.189450i	$0.0606703\pi$
$461$	25.1497	+	25.1497i	1.17134	+	1.17134i	0.189450	+	0.981890i	$0.439330\pi$
$462$	−23.5827	−	17.7529i	−1.09716	−	0.825942i
$463$	−4.47195	−	4.47195i	−0.207829	−	0.207829i	0.595515	−	0.803344i	$-0.296948\pi$
$463$	−4.47195	−	4.47195i	−0.207829	−	0.207829i	−0.803344	+	0.595515i	$0.796948\pi$
$464$		−	2.54836i		−	0.118305i
$465$		−	4.56956i		−	0.211908i
$466$	19.5046	+	19.5046i	0.903532	+	0.903532i
$467$			3.40679i			0.157648i	0.996889	+	0.0788238i	$0.0251164\pi$
$467$			3.40679i			0.157648i	−0.996889	+	0.0788238i	$0.974884\pi$
$468$	9.49560	−	7.51183i	0.438934	−	0.347234i
$469$			44.1189i			2.03722i
$470$	−2.39985	−	2.39985i	−0.110697	−	0.110697i
$471$	−12.0466			−0.555078
$472$	3.44163			0.158414
$473$	28.8215	+	21.6968i	1.32522	+	0.997618i
$474$	7.95004	−	7.95004i	0.365157	−	0.365157i
$475$	13.7462	−	13.7462i	0.630718	−	0.630718i
$476$	−28.4562	−	28.4562i	−1.30429	−	1.30429i
$477$	−8.11308			−0.371472
$478$			3.81538i			0.174512i
$479$	−4.08095	+	4.08095i	−0.186463	+	0.186463i	−0.794165	−	0.607702i	$-0.792092\pi$
$479$	−4.08095	+	4.08095i	−0.186463	+	0.186463i	0.607702	+	0.794165i	$0.292092\pi$
$480$	3.10740			0.141833
$481$	−3.13648	+	26.8900i	−0.143011	+	1.22608i
$482$	−13.3804			−0.609462
$483$	17.1720	+	17.1720i	0.781354	+	0.781354i
$484$	−35.4977	+	10.2159i	−1.61353	+	0.464361i
$485$			8.46210i			0.384244i
$486$	1.63677	+	1.63677i	0.0742455	+	0.0742455i
$487$	1.43086	−	1.43086i	0.0648384	−	0.0648384i	−0.673944	−	0.738782i	$-0.735401\pi$
$487$	1.43086	−	1.43086i	0.0648384	−	0.0648384i	0.738782	+	0.673944i	$0.235401\pi$
$488$	−21.4772	−	21.4772i	−0.972228	−	0.972228i
$489$	−12.7861	−	12.7861i	−0.578205	−	0.578205i
$490$		−	11.2195i		−	0.506844i
$491$	39.5788			1.78617			0.893083	−	0.449892i	$-0.148538\pi$
$491$	39.5788			1.78617			0.893083	+	0.449892i	$0.148538\pi$
$492$	26.7651	−	26.7651i	1.20666	−	1.20666i
$493$			14.1744i			0.638383i
$494$	−27.5885	+	21.8249i	−1.24126	+	0.981947i
$495$	2.04514	−	0.288433i	0.0919221	−	0.0129641i
$496$	−2.90758	+	2.90758i	−0.130554	+	0.130554i
$497$		−	37.3541i		−	1.67556i
$498$		−	24.3194i		−	1.08978i
$499$	0.186322	−	0.186322i	0.00834093	−	0.00834093i	−0.702924	−	0.711265i	$-0.748123\pi$
$499$	0.186322	−	0.186322i	0.00834093	−	0.00834093i	0.711265	+	0.702924i	$0.248123\pi$
$500$	−14.2134	+	14.2134i	−0.635641	+	0.635641i
$501$	2.97568	−	2.97568i	0.132944	−	0.132944i
$502$	−19.1487	+	19.1487i	−0.854650	+	0.854650i
$503$			26.0955i			1.16354i	0.813353	+	0.581770i	$0.197640\pi$
$503$			26.0955i			1.16354i	−0.813353	+	0.581770i	$0.802360\pi$
$504$		−	12.0866i		−	0.538379i
$505$	−1.35439	+	1.35439i	−0.0602694	+	0.0602694i
$506$	48.0145	−	6.77167i	2.13451	−	0.301037i
$507$	−2.99197	+	12.6510i	−0.132878	+	0.561851i
$508$		−	7.34725i		−	0.325982i
$509$	17.5324	−	17.5324i	0.777111	−	0.777111i	−0.202228	−	0.979339i	$-0.564818\pi$
$509$	17.5324	−	17.5324i	0.777111	−	0.777111i	0.979339	+	0.202228i	$0.0648181\pi$
$510$	4.49288			0.198948
$511$			6.94531i			0.307243i
$512$	−4.46841	−	4.46841i	−0.197478	−	0.197478i
$513$	−2.98040	−	2.98040i	−0.131588	−	0.131588i
$514$	25.5723	−	25.5723i	1.12795	−	1.12795i
$515$	4.67228	+	4.67228i	0.205885	+	0.205885i
$516$			36.5259i			1.60796i
$517$	−1.09053	−	7.73237i	−0.0479612	−	0.340069i
$518$	47.2529	+	47.2529i	2.07617	+	2.07617i
$519$	−3.40269			−0.149361
$520$	5.53548	−	4.37904i	0.242747	−	0.192034i
$521$	−30.1446			−1.32066			−0.660330	−	0.750976i	$-0.729584\pi$
$521$	−30.1446			−1.32066			−0.660330	+	0.750976i	$0.729584\pi$
$522$	−7.44344	+	7.44344i	−0.325791	+	0.325791i
$523$		−	10.2008i		−	0.446051i	−0.974813	−	0.223025i	$-0.928407\pi$
$523$		−	10.2008i		−	0.446051i	0.974813	−	0.223025i	$-0.0715933\pi$
$524$	−24.5958			−1.07447
$525$	−12.5395	−	12.5395i	−0.547268	−	0.547268i
$526$	41.5850	−	41.5850i	1.81319	−	1.81319i
$527$	16.1724	−	16.1724i	0.704483	−	0.704483i
$528$	−1.48484	−	1.11778i	−0.0646192	−	0.0486451i
$529$	−16.8933			−0.734489
$530$	−11.6948			−0.507988
$531$	−0.774163	−	0.774163i	−0.0335958	−	0.0335958i
$532$			54.4204i			2.35942i
$533$	−4.70854	+	40.3677i	−0.203950	+	1.74852i
$534$			4.31778i			0.186849i
$535$	2.57198	+	2.57198i	0.111197	+	0.111197i
$536$			36.0708i			1.55802i
$537$			23.5848i			1.01776i
$538$	−33.2917	−	33.2917i	−1.43531	−	1.43531i
$539$	15.5256	−	20.6239i	0.668733	−	0.888332i
$540$	1.47868	+	1.47868i	0.0636323	+	0.0636323i
$541$	−0.236940	+	0.236940i	−0.0101869	+	0.0101869i	−0.712182	−	0.701995i	$-0.752293\pi$
$541$	−0.236940	+	0.236940i	−0.0101869	+	0.0101869i	0.701995	+	0.712182i	$0.252293\pi$
$542$	20.1855			0.867040
$543$		−	16.3445i		−	0.701410i
$544$	10.9976	+	10.9976i	0.471519	+	0.471519i
$545$	6.59240			0.282387
$546$	19.9090	+	25.1667i	0.852026	+	1.07703i
$547$		−	32.4864i		−	1.38902i	−0.719484	−	0.694509i	$-0.755622\pi$
$547$		−	32.4864i		−	1.38902i	0.719484	−	0.694509i	$-0.244378\pi$
$548$	−27.8536	+	27.8536i	−1.18985	+	1.18985i
$549$			9.66220i			0.412373i
$550$	−35.0615	+	4.94486i	−1.49503	+	0.210850i
$551$	13.5538	−	13.5538i	0.577409	−	0.577409i
$552$	14.0395	+	14.0395i	0.597561	+	0.597561i
$553$	13.2054	+	13.2054i	0.561552	+	0.561552i
$554$	22.0919	+	22.0919i	0.938596	+	0.938596i
$555$	−4.67580			−0.198477
$556$	49.5024			2.09937
$557$	21.3322	−	21.3322i	0.903872	−	0.903872i	−0.0918963	−	0.995769i	$-0.529293\pi$
$557$	21.3322	−	21.3322i	0.903872	−	0.903872i	0.995769	+	0.0918963i	$0.0292928\pi$
$558$	16.9854			0.719048
$559$	−24.3318	−	30.7574i	−1.02912	−	1.30090i
$560$		−	1.34173i		−	0.0566984i
$561$	8.25890	+	6.21727i	0.348691	+	0.262493i
$562$	−71.0760			−2.99816
$563$	−10.0912			−0.425292			−0.212646	−	0.977129i	$-0.568208\pi$
$563$	−10.0912			−0.425292			−0.212646	+	0.977129i	$0.568208\pi$
$564$	5.59068	−	5.59068i	0.235410	−	0.235410i
$565$	0.581384	−	0.581384i	0.0244590	−	0.0244590i
$566$	38.5512	+	38.5512i	1.62043	+	1.62043i
$567$	−2.71876	+	2.71876i	−0.114177	+	0.114177i
$568$		−	30.5400i		−	1.28143i
$569$	−3.76424			−0.157805			−0.0789025	−	0.996882i	$-0.525142\pi$
$569$	−3.76424			−0.157805			−0.0789025	+	0.996882i	$0.525142\pi$
$570$	−4.29615	−	4.29615i	−0.179946	−	0.179946i
$571$	7.10330			0.297264			0.148632	−	0.988893i	$-0.452513\pi$
$571$	7.10330			0.297264			0.148632	+	0.988893i	$0.452513\pi$
$572$	40.1448	−	0.963383i	1.67854	−	0.0402811i
$573$	−11.9686			−0.499995
$574$	70.9368	+	70.9368i	2.96085	+	2.96085i
$575$	29.1312			1.21485
$576$			12.6712i			0.527965i
$577$	1.61787	−	1.61787i	0.0673529	−	0.0673529i	−0.672628	−	0.739981i	$-0.734835\pi$
$577$	1.61787	−	1.61787i	0.0673529	−	0.0673529i	0.739981	+	0.672628i	$0.234835\pi$
$578$	−11.9241	−	11.9241i	−0.495975	−	0.495975i
$579$	−9.11717	+	9.11717i	−0.378896	+	0.378896i
$580$	−6.72450	+	6.72450i	−0.279220	+	0.279220i
$581$	40.3957			1.67590
$582$	−31.4542			−1.30382
$583$	−21.4975	−	16.1833i	−0.890337	−	0.670243i
$584$			5.67835i			0.234972i
$585$	−2.23018	−	0.260131i	−0.0922066	−	0.0107551i
$586$	−15.2178			−0.628642
$587$	22.0484	−	22.0484i	0.910034	−	0.910034i	−0.0862400	−	0.996274i	$-0.527485\pi$
$587$	22.0484	−	22.0484i	0.910034	−	0.910034i	0.996274	+	0.0862400i	$0.0274852\pi$
$588$	26.1368			1.07787
$589$	−30.9286			−1.27439
$590$	−1.11593	−	1.11593i	−0.0459422	−	0.0459422i
$591$	−13.5536	−	13.5536i	−0.557521	−	0.557521i
$592$	2.97518	+	2.97518i	0.122279	+	0.122279i
$593$	−11.9152	+	11.9152i	−0.489299	+	0.489299i	−0.908085	−	0.418786i	$-0.862456\pi$
$593$	−11.9152	+	11.9152i	−0.489299	+	0.489299i	0.418786	+	0.908085i	$0.362456\pi$
$594$	1.07213	+	7.60191i	0.0439899	+	0.311910i
$595$			7.46291i			0.305950i
$596$	−6.73516	+	6.73516i	−0.275883	+	0.275883i
$597$			9.74611i			0.398882i
$598$	−52.3589	−	6.10720i	−2.14111	−	0.249742i
$599$	−41.4860			−1.69507			−0.847536	−	0.530737i	$-0.821915\pi$
$599$	−41.4860			−1.69507			−0.847536	+	0.530737i	$0.821915\pi$
$600$	−10.2520	−	10.2520i	−0.418538	−	0.418538i
$601$		−	2.57219i		−	0.104922i	−0.998623	−	0.0524609i	$-0.983294\pi$
$601$		−	2.57219i		−	0.104922i	0.998623	−	0.0524609i	$-0.0167065\pi$
$602$	−96.8064			−3.94553
$603$	8.11379	−	8.11379i	0.330419	−	0.330419i
$604$	9.54496	+	9.54496i	0.388379	+	0.388379i
$605$	5.99442	+	3.31519i	0.243708	+	0.134782i
$606$	−5.03434	−	5.03434i	−0.204506	−	0.204506i
$607$		−	23.9187i		−	0.970829i	−0.874284	−	0.485415i	$-0.838669\pi$
$607$		−	23.9187i		−	0.970829i	0.874284	−	0.485415i	$-0.161331\pi$
$608$		−	21.0322i		−	0.852966i
$609$	−12.3639	−	12.3639i	−0.501012	−	0.501012i
$610$			13.9278i			0.563919i
$611$	−0.983519	+	8.43200i	−0.0397889	+	0.341122i
$612$			10.4666i			0.423087i
$613$	12.3929	+	12.3929i	0.500546	+	0.500546i	0.911608	−	0.411061i	$-0.134842\pi$
$613$	12.3929	+	12.3929i	0.500546	+	0.500546i	−0.411061	+	0.911608i	$0.634842\pi$
$614$	27.4480			1.10771
$615$	−7.01940			−0.283049
$616$	24.1093	−	32.0263i	0.971390	−	1.29038i
$617$	−30.7416	+	30.7416i	−1.23761	+	1.23761i	−0.276633	+	0.960976i	$0.589219\pi$
$617$	−30.7416	+	30.7416i	−1.23761	+	1.23761i	−0.960976	+	0.276633i	$0.910781\pi$
$618$	−17.3672	+	17.3672i	−0.698611	+	0.698611i
$619$	29.1449	+	29.1449i	1.17143	+	1.17143i	0.981868	+	0.189566i	$0.0607080\pi$
$619$	29.1449	+	29.1449i	1.17143	+	1.17143i	0.189566	+	0.981868i	$0.439292\pi$
$620$	15.3448			0.616262
$621$		−	6.31611i		−	0.253457i
$622$	−6.47130	+	6.47130i	−0.259475	+	0.259475i
$623$	−7.17206			−0.287343
$624$	1.25353	+	1.58457i	0.0501814	+	0.0634335i
$625$	−19.3334			−0.773337
$626$	48.7000	+	48.7000i	1.94644	+	1.94644i
$627$	−1.95223	−	13.8423i	−0.0779646	−	0.552808i
$628$		−	40.4530i		−	1.61425i
$629$	−16.5485	−	16.5485i	−0.659830	−	0.659830i
$630$	−3.91902	+	3.91902i	−0.156137	+	0.156137i
$631$	28.9801	+	28.9801i	1.15368	+	1.15368i	0.985809	+	0.167869i	$0.0536885\pi$
$631$	28.9801	+	28.9801i	1.15368	+	1.15368i	0.167869	+	0.985809i	$0.446312\pi$
$632$	10.7965	+	10.7965i	0.429462	+	0.429462i
$633$			0.301318i			0.0119763i
$634$	5.11255			0.203045
$635$	−0.963444	+	0.963444i	−0.0382331	+	0.0382331i
$636$		−	27.2441i		−	1.08030i
$637$	−22.0091	+	17.4111i	−0.872033	+	0.689853i
$638$	−34.5707	+	4.87564i	−1.36867	+	0.193028i
$639$	−6.86968	+	6.86968i	−0.271761	+	0.271761i
$640$			12.0503i			0.476330i
$641$			39.9060i			1.57619i	0.615552	+	0.788096i	$0.288933\pi$
$641$			39.9060i			1.57619i	−0.615552	+	0.788096i	$0.711067\pi$
$642$	−9.56024	+	9.56024i	−0.377312	+	0.377312i
$643$	−13.3720	+	13.3720i	−0.527341	+	0.527341i	−0.919779	−	0.392438i	$-0.871632\pi$
$643$	−13.3720	+	13.3720i	−0.527341	+	0.527341i	0.392438	+	0.919779i	$0.371632\pi$
$644$	−57.6644	+	57.6644i	−2.27229	+	2.27229i
$645$	4.78963	−	4.78963i	0.188592	−	0.188592i
$646$		−	30.4096i		−	1.19645i
$647$		−	7.30888i		−	0.287342i	−0.989626	−	0.143671i	$-0.954109\pi$
$647$		−	7.30888i		−	0.287342i	0.989626	−	0.143671i	$-0.0458907\pi$
$648$	−2.22281	+	2.22281i	−0.0873201	+	0.0873201i
$649$	−0.507096	−	3.59556i	−0.0199052	−	0.141138i
$650$	38.2339	+	4.45965i	1.49966	+	0.174922i
$651$			28.2136i			1.10578i
$652$	42.9361	−	42.9361i	1.68151	−	1.68151i
$653$	3.19992			0.125223			0.0626113	−	0.998038i	$-0.480057\pi$
$653$	3.19992			0.125223			0.0626113	+	0.998038i	$0.480057\pi$
$654$			24.5044i			0.958197i
$655$	3.22524	+	3.22524i	0.126021	+	0.126021i
$656$	4.46640	+	4.46640i	0.174384	+	0.174384i
$657$	1.27729	−	1.27729i	0.0498319	−	0.0498319i
$658$	14.8173	+	14.8173i	0.577637	+	0.577637i
$659$			24.5643i			0.956890i	0.878117	+	0.478445i	$0.158799\pi$
$659$			24.5643i			0.956890i	−0.878117	+	0.478445i	$0.841201\pi$
$660$	0.968572	+	6.86766i	0.0377016	+	0.267323i
$661$	34.8454	+	34.8454i	1.35533	+	1.35533i	0.879584	+	0.475743i	$0.157821\pi$
$661$	34.8454	+	34.8454i	1.35533	+	1.35533i	0.475743	+	0.879584i	$0.342179\pi$
$662$	−41.1453			−1.59916
$663$	−6.97234	−	8.81363i	−0.270783	−	0.342293i
$664$	33.0268			1.28169
$665$	7.13614	−	7.13614i	0.276728	−	0.276728i
$666$		−	17.3803i		−	0.673472i
$667$	28.7234			1.11217
$668$	9.99246	+	9.99246i	0.386620	+	0.386620i
$669$	0.853776	−	0.853776i	0.0330089	−	0.0330089i
$670$	11.6958	−	11.6958i	0.451848	−	0.451848i
$671$	−19.2733	+	25.6023i	−0.744038	+	0.988366i
$672$	−19.1859			−0.740111
$673$	−44.2849			−1.70706			−0.853528	−	0.521047i	$-0.825542\pi$
$673$	−44.2849			−1.70706			−0.853528	+	0.521047i	$0.825542\pi$
$674$	41.4215	+	41.4215i	1.59550	+	1.59550i
$675$			4.61220i			0.177524i
$676$	−42.4827	−	10.0472i	−1.63395	−	0.386429i
$677$		−	10.2638i		−	0.394471i	−0.980356	−	0.197235i	$-0.936804\pi$
$677$		−	10.2638i		−	0.394471i	0.980356	−	0.197235i	$-0.0631963\pi$
$678$	2.16104	+	2.16104i	0.0829944	+	0.0829944i
$679$		−	52.2471i		−	2.00506i
$680$			6.10153i			0.233983i
$681$	3.13060	+	3.13060i	0.119965	+	0.119965i
$682$	45.0068	+	33.8809i	1.72340	+	1.29737i
$683$	−7.58719	−	7.58719i	−0.290316	−	0.290316i	0.546889	−	0.837205i	$-0.315812\pi$
$683$	−7.58719	−	7.58719i	−0.290316	−	0.290316i	−0.837205	+	0.546889i	$0.815812\pi$
$684$	10.0083	−	10.0083i	0.382677	−	0.382677i
$685$	7.30487			0.279105
$686$			6.97184i			0.266186i
$687$	−8.95456	−	8.95456i	−0.341638	−	0.341638i
$688$	−6.09522			−0.232378
$689$	18.1487	+	22.9415i	0.691410	+	0.874001i
$690$		−	9.10449i		−	0.346602i
$691$	−31.9004	+	31.9004i	−1.21355	+	1.21355i	−0.243695	+	0.969852i	$0.578360\pi$
$691$	−31.9004	+	31.9004i	−1.21355	+	1.21355i	−0.969852	+	0.243695i	$0.921640\pi$
$692$		−	11.4264i		−	0.434366i
$693$	−12.6272	+	1.78086i	−0.479667	+	0.0676492i
$694$	22.4577	−	22.4577i	0.852483	−	0.852483i
$695$	−6.49125	−	6.49125i	−0.246227	−	0.246227i
$696$	−10.1085	−	10.1085i	−0.383162	−	0.383162i
$697$	−24.8428	−	24.8428i	−0.940989	−	0.940989i
$698$	8.05340			0.304826
$699$	11.9165			0.450723
$700$	42.1081	−	42.1081i	1.59154	−	1.59154i
$701$	5.30607			0.200407			0.100204	−	0.994967i	$-0.468051\pi$
$701$	5.30607			0.200407			0.100204	+	0.994967i	$0.468051\pi$
$702$	0.966925	−	8.28973i	0.0364942	−	0.312876i
$703$			31.6477i			1.19362i
$704$	−25.2754	+	33.5753i	−0.952601	+	1.26542i
$705$	−1.46621			−0.0552206
$706$	−16.4658			−0.619700
$707$	8.36231	−	8.36231i	0.314497	−	0.314497i
$708$	2.59967	−	2.59967i	0.0977017	−	0.0977017i
$709$	−6.96375	−	6.96375i	−0.261529	−	0.261529i	0.564146	−	0.825675i	$-0.309206\pi$
$709$	−6.96375	−	6.96375i	−0.261529	−	0.261529i	−0.825675	+	0.564146i	$0.809206\pi$
$710$	−9.90245	+	9.90245i	−0.371632	+	0.371632i
$711$		−	4.85714i		−	0.182157i
$712$	−5.86374			−0.219753
$713$	−32.7723	−	32.7723i	−1.22733	−	1.22733i
$714$	−27.7401			−1.03815
$715$	−5.39051	−	5.13785i	−0.201594	−	0.192145i
$716$	−79.1987			−2.95979
$717$	1.16552	+	1.16552i	0.0435272	+	0.0435272i
$718$	−36.3270			−1.35571
$719$			14.0512i			0.524020i	0.965065	+	0.262010i	$0.0843854\pi$
$719$			14.0512i			0.524020i	−0.965065	+	0.262010i	$0.915615\pi$
$720$	−0.246753	+	0.246753i	−0.00919596	+	0.00919596i
$721$	−28.8478	−	28.8478i	−1.07435	−	1.07435i
$722$	2.02058	−	2.02058i	0.0751981	−	0.0751981i
$723$	−4.08744	+	4.08744i	−0.152014	+	0.152014i
$724$	54.8856			2.03981
$725$	−20.9746			−0.778978
$726$	−12.3228	+	22.2817i	−0.457341	+	0.826950i
$727$			35.1587i			1.30396i	0.758235	+	0.651981i	$0.226062\pi$
$727$			35.1587i			1.30396i	−0.758235	+	0.651981i	$0.773938\pi$
$728$	−34.1774	+	27.0373i	−1.26670	+	1.00207i
$729$	1.00000			0.0370370
$730$	1.84118	−	1.84118i	0.0681452	−	0.0681452i
$731$	33.9026			1.25393
$732$	−32.4461			−1.19924
$733$	35.2758	+	35.2758i	1.30294	+	1.30294i	0.926400	+	0.376541i	$0.122887\pi$
$733$	35.2758	+	35.2758i	1.30294	+	1.30294i	0.376541	+	0.926400i	$0.377113\pi$
$734$	41.1815	+	41.1815i	1.52004	+	1.52004i
$735$	−3.42732	−	3.42732i	−0.126419	−	0.126419i
$736$	22.2859	−	22.2859i	0.821468	−	0.821468i
$737$	37.6841	−	5.31473i	1.38811	−	0.195771i
$738$		−	26.0916i		−	0.960444i
$739$	−20.8319	+	20.8319i	−0.766313	+	0.766313i	−0.977455	−	0.211142i	$-0.932282\pi$
$739$	−20.8319	+	20.8319i	−0.766313	+	0.766313i	0.211142	+	0.977455i	$0.432282\pi$
$740$		−	15.7016i		−	0.577201i
$741$	−1.76067	+	15.0948i	−0.0646799	+	0.554520i
$742$	72.2063			2.65078
$743$	−7.35432	−	7.35432i	−0.269804	−	0.269804i	0.559217	−	0.829021i	$-0.311102\pi$
$743$	−7.35432	−	7.35432i	−0.269804	−	0.269804i	−0.829021	+	0.559217i	$0.811102\pi$
$744$			23.0669i			0.845672i
$745$	1.76636			0.0647145
$746$	−43.6382	+	43.6382i	−1.59771	+	1.59771i
$747$	−7.42906	−	7.42906i	−0.271815	−	0.271815i
$748$	−20.8779	+	27.7337i	−0.763370	+	1.01405i
$749$	−15.8801	−	15.8801i	−0.580245	−	0.580245i
$750$			13.8557i			0.505939i
$751$		−	12.2582i		−	0.447308i	−0.974669	−	0.223654i	$-0.928201\pi$
$751$		−	12.2582i		−	0.447308i	0.974669	−	0.223654i	$-0.0717986\pi$
$752$	0.932939	+	0.932939i	0.0340208	+	0.0340208i
$753$			11.6991i			0.426338i
$754$	37.6987	+	4.39722i	1.37290	+	0.160137i
$755$		−	2.50326i		−	0.0911029i
$756$	−9.12973	−	9.12973i	−0.332045	−	0.332045i
$757$	3.45084			0.125423			0.0627115	−	0.998032i	$-0.480025\pi$
$757$	3.45084			0.125423			0.0627115	+	0.998032i	$0.480025\pi$
$758$	67.7982			2.46254
$759$	12.5988	−	16.7360i	0.457309	−	0.607480i
$760$	5.83436	−	5.83436i	0.211635	−	0.211635i
$761$	15.4007	−	15.4007i	0.558275	−	0.558275i	−0.370541	−	0.928816i	$-0.620828\pi$
$761$	15.4007	−	15.4007i	0.558275	−	0.558275i	0.928816	+	0.370541i	$0.120828\pi$
$762$	−3.58118	−	3.58118i	−0.129733	−	0.129733i
$763$	−40.7031			−1.47355
$764$		−	40.1911i		−	1.45406i
$765$	1.37248	−	1.37248i	0.0496222	−	0.0496222i
$766$	19.6888			0.711387
$767$	−0.457337	+	3.92089i	−0.0165135	+	0.141575i
$768$	−19.4495			−0.701823
$769$	11.9936	+	11.9936i	0.432501	+	0.432501i	0.889478	−	0.456977i	$-0.151068\pi$
$769$	11.9936	+	11.9936i	0.432501	+	0.432501i	−0.456977	+	0.889478i	$0.651068\pi$
$770$	−18.2017	+	2.56705i	−0.655944	+	0.0925102i
$771$		−	15.6236i		−	0.562671i
$772$	−30.6158	−	30.6158i	−1.10189	−	1.10189i
$773$	−17.2109	+	17.2109i	−0.619033	+	0.619033i	−0.945283	−	0.326250i	$-0.894215\pi$
$773$	−17.2109	+	17.2109i	−0.619033	+	0.619033i	0.326250	+	0.945283i	$0.394215\pi$
$774$	17.8034	+	17.8034i	0.639929	+	0.639929i
$775$	23.9312	+	23.9312i	0.859635	+	0.859635i
$776$		−	42.7162i		−	1.53342i
$777$	28.8695			1.03569
$778$	30.8732	−	30.8732i	1.10686	−	1.10686i
$779$			47.5101i			1.70223i
$780$	0.873532	−	7.48904i	0.0312775	−	0.268151i
$781$	−31.9059	+	4.49981i	−1.14168	+	0.161016i
$782$	32.2223	−	32.2223i	1.15227	−	1.15227i
$783$			4.54764i			0.162519i
$784$			4.36156i			0.155770i
$785$	−5.30460	+	5.30460i	−0.189329	+	0.189329i
$786$	−11.9884	+	11.9884i	−0.427614	+	0.427614i
$787$	9.83332	−	9.83332i	0.350520	−	0.350520i	−0.509783	−	0.860303i	$-0.670274\pi$
$787$	9.83332	−	9.83332i	0.350520	−	0.350520i	0.860303	+	0.509783i	$0.170274\pi$
$788$	45.5136	−	45.5136i	1.62136	−	1.62136i
$789$		−	25.4067i		−	0.904504i
$790$		−	7.00143i		−	0.249100i
$791$	−3.58961	+	3.58961i	−0.127632	+	0.127632i
$792$	−10.3237	+	1.45599i	−0.366838	+	0.0517365i
$793$	27.3220	−	21.6140i	0.970231	−	0.767536i
$794$			16.7314i			0.593774i
$795$	−3.57251	+	3.57251i	−0.126704	+	0.126704i
$796$	−32.7279			−1.16001
$797$		−	40.8238i		−	1.44605i	−0.690821	−	0.723026i	$-0.742751\pi$
$797$		−	40.8238i		−	1.44605i	0.690821	−	0.723026i	$-0.257249\pi$
$798$	26.5255	+	26.5255i	0.938992	+	0.938992i
$799$	−5.18916	−	5.18916i	−0.183579	−	0.183579i
$800$	−16.2738	+	16.2738i	−0.575365	+	0.575365i
$801$	1.31899	+	1.31899i	0.0466043	+	0.0466043i
$802$			70.1490i			2.47705i
$803$	5.93233	−	0.836658i	0.209347	−	0.0295250i
$804$	27.2465	+	27.2465i	0.960908	+	0.960908i
$805$	15.1230			0.533017
$806$	−37.9957	−	48.0298i	−1.33834	−	1.69178i
$807$	−20.3398			−0.715996
$808$	6.83686	−	6.83686i	0.240520	−	0.240520i
$809$			5.72760i			0.201372i	0.994918	+	0.100686i	$0.0321037\pi$
$809$			5.72760i			0.201372i	−0.994918	+	0.100686i	$0.967896\pi$
$810$	1.44147			0.0506481
$811$	10.4897	+	10.4897i	0.368343	+	0.368343i	0.866873	−	0.498529i	$-0.166126\pi$
$811$	10.4897	+	10.4897i	0.368343	+	0.368343i	−0.498529	+	0.866873i	$0.666126\pi$
$812$	41.5187	−	41.5187i	1.45702	−	1.45702i
$813$	6.16624	−	6.16624i	0.216260	−	0.216260i
$814$	34.6687	−	46.0532i	1.21514	−	1.61416i
$815$	−11.2604			−0.394435
$816$	−1.74660			−0.0611434
$817$	−32.4181	−	32.4181i	−1.13417	−	1.13417i
$818$			11.4524i			0.400425i
$819$	13.7697	+	1.60611i	0.481151	+	0.0561221i
$820$		−	23.5714i		−	0.823151i
$821$	−36.1470	−	36.1470i	−1.26154	−	1.26154i	−0.950347	−	0.311192i	$-0.899272\pi$
$821$	−36.1470	−	36.1470i	−1.26154	−	1.26154i	−0.311192	−	0.950347i	$-0.600728\pi$
$822$			27.1527i			0.947059i
$823$			27.1045i			0.944805i	0.881383	+	0.472403i	$0.156613\pi$
$823$			27.1045i			0.944805i	−0.881383	+	0.472403i	$0.843387\pi$
$824$	−23.5854	−	23.5854i	−0.821636	−	0.821636i
$825$	−9.20002	+	12.2211i	−0.320304	+	0.425485i
$826$	6.89004	+	6.89004i	0.239735	+	0.239735i
$827$	−1.13811	+	1.13811i	−0.0395761	+	0.0395761i	−0.726618	−	0.687042i	$-0.758909\pi$
$827$	−1.13811	+	1.13811i	−0.0395761	+	0.0395761i	0.687042	+	0.726618i	$0.258909\pi$
$828$	21.2098			0.737091
$829$		−	5.71659i		−	0.198546i	−0.995060	−	0.0992728i	$-0.968348\pi$
$829$		−	5.71659i		−	0.198546i	0.995060	−	0.0992728i	$-0.0316516\pi$
$830$	−10.7088	−	10.7088i	−0.371707	−	0.371707i
$831$	13.4973			0.468215
$832$	35.8305	−	28.3450i	1.24220	−	0.982685i
$833$		−	24.2597i		−	0.840549i
$834$	24.1284	−	24.1284i	0.835498	−	0.835498i
$835$		−	2.62062i		−	0.0906903i
$836$	46.4831	−	6.55568i	1.60765	−	0.226733i
$837$	5.18868	−	5.18868i	0.179347	−	0.179347i
$838$	−3.57493	−	3.57493i	−0.123494	−	0.123494i
$839$	−28.2079	−	28.2079i	−0.973845	−	0.973845i	0.0258216	−	0.999667i	$-0.491780\pi$
$839$	−28.2079	−	28.2079i	−0.973845	−	0.973845i	−0.999667	+	0.0258216i	$0.991780\pi$
$840$	−5.32220	−	5.32220i	−0.183633	−	0.183633i
$841$	8.31901			0.286862
$842$	24.5147			0.844832
$843$	−21.7122	+	21.7122i	−0.747809	+	0.747809i
$844$	−1.01184			−0.0348289
$845$	4.25326	+	6.88822i	0.146317	+	0.236962i
$846$		−	5.45000i		−	0.187375i
$847$	−37.0110	−	20.4688i	−1.27171	−	0.703316i
$848$	4.54633			0.156122
$849$	23.5532			0.808344
$850$	−23.5296	+	23.5296i	−0.807060	+	0.807060i
$851$	−33.5342	+	33.5342i	−1.14954	+	1.14954i
$852$	−23.0687	−	23.0687i	−0.790321	−	0.790321i
$853$	−12.7144	+	12.7144i	−0.435334	+	0.435334i	−0.890438	−	0.455104i	$-0.849602\pi$
$853$	−12.7144	+	12.7144i	−0.435334	+	0.435334i	0.455104	+	0.890438i	$0.349602\pi$
$854$		−	85.9935i		−	2.94264i
$855$	−2.62477			−0.0897653
$856$	−12.9832	−	12.9832i	−0.443757	−	0.443757i
$857$	−31.5371			−1.07729			−0.538643	−	0.842534i	$-0.681063\pi$
$857$	−31.5371			−1.07729			−0.538643	+	0.842534i	$0.681063\pi$
$858$	19.0977	−	20.0369i	0.651986	−	0.684048i
$859$	6.52002			0.222460			0.111230	−	0.993795i	$-0.464521\pi$
$859$	6.52002			0.222460			0.111230	+	0.993795i	$0.464521\pi$
$860$	16.0838	+	16.0838i	0.548453	+	0.548453i
$861$	43.3395			1.47701
$862$		−	39.2677i		−	1.33746i
$863$	−17.0392	+	17.0392i	−0.580020	+	0.580020i	−0.934909	−	0.354889i	$-0.884519\pi$
$863$	−17.0392	+	17.0392i	−0.580020	+	0.580020i	0.354889	+	0.934909i	$0.384519\pi$
$864$	3.52842	+	3.52842i	0.120039	+	0.120039i
$865$	−1.49834	+	1.49834i	−0.0509450	+	0.0509450i
$866$	30.0050	−	30.0050i	1.01961	−	1.01961i
$867$	−7.28511			−0.247415
$868$	−94.7424			−3.21577
$869$	9.68861	−	12.8702i	0.328664	−	0.436590i
$870$			6.55529i			0.222245i
$871$	−41.0938	−	4.79323i	−1.39241	−	0.162412i
$872$	−33.2780			−1.12694
$873$	−9.60861	+	9.60861i	−0.325202	+	0.325202i
$874$	−61.6228			−2.08442
$875$	−23.0151			−0.778051
$876$	4.28921	+	4.28921i	0.144919	+	0.144919i
$877$	−6.55293	−	6.55293i	−0.221277	−	0.221277i	0.587759	−	0.809036i	$-0.300010\pi$
$877$	−6.55293	−	6.55293i	−0.221277	−	0.221277i	−0.809036	+	0.587759i	$0.800010\pi$
$878$	27.0266	+	27.0266i	0.912104	+	0.912104i
$879$	−4.64872	+	4.64872i	−0.156798	+	0.156798i
$880$	−1.14603	+	0.161630i	−0.0386328	+	0.00544853i
$881$		−	28.7393i		−	0.968252i	−0.874998	−	0.484126i	$-0.839138\pi$
$881$		−	28.7393i		−	0.968252i	0.874998	−	0.484126i	$-0.160862\pi$
$882$	12.7396	−	12.7396i	0.428964	−	0.428964i
$883$		−	27.1635i		−	0.914124i	−0.889435	−	0.457062i	$-0.848902\pi$
$883$		−	27.1635i		−	0.914124i	0.889435	−	0.457062i	$-0.151098\pi$
$884$	29.5966	−	23.4134i	0.995440	−	0.787478i
$885$	−0.681789			−0.0229181
$886$	48.9051	+	48.9051i	1.64300	+	1.64300i
$887$			5.92331i			0.198885i	0.995043	+	0.0994426i	$0.0317060\pi$
$887$			5.92331i			0.198885i	−0.995043	+	0.0994426i	$0.968294\pi$
$888$	23.6032			0.792071
$889$	5.94854	−	5.94854i	0.199507	−	0.199507i
$890$	1.90129	+	1.90129i	0.0637314	+	0.0637314i
$891$	2.64974	+	1.99471i	0.0887696	+	0.0668254i
$892$	2.86702	+	2.86702i	0.0959948	+	0.0959948i
$893$			9.92389i			0.332090i
$894$			6.56568i			0.219589i
$895$	10.3853	+	10.3853i	0.347143	+	0.347143i
$896$		−	74.4016i		−	2.48558i
$897$	−17.8602	+	14.1289i	−0.596334	+	0.471751i
$898$		−	63.5262i		−	2.11990i
$899$	23.5962	+	23.5962i	0.786978	+	0.786978i
$900$	−15.4880			−0.516266
$901$	−25.2874			−0.842446
$902$	52.0452	−	69.1359i	1.73292	−	2.30197i
$903$	−29.5723	+	29.5723i	−0.984106	+	0.984106i
$904$	−2.93479	+	2.93479i	−0.0976098	+	0.0976098i
$905$	−7.19714	−	7.19714i	−0.239241	−	0.239241i
$906$	9.30478			0.309131
$907$		−	47.0859i		−	1.56346i	−0.623617	−	0.781730i	$-0.714337\pi$
$907$		−	47.0859i		−	1.56346i	0.623617	−	0.781730i	$-0.285663\pi$
$908$	−10.5127	+	10.5127i	−0.348876	+	0.348876i
$909$	−3.07578			−0.102017
$910$	19.8486	+	2.31517i	0.657974	+	0.0767470i
$911$	2.90329			0.0961902			0.0480951	−	0.998843i	$-0.484685\pi$
$911$	2.90329			0.0961902			0.0480951	+	0.998843i	$0.484685\pi$
$912$	1.67013	+	1.67013i	0.0553034	+	0.0553034i
$913$	−4.86622	−	34.5039i	−0.161048	−	1.14191i
$914$		−	12.5715i		−	0.415827i
$915$	4.25465	+	4.25465i	0.140654	+	0.140654i
$916$	30.0698	−	30.0698i	0.993534	−	0.993534i
$917$	−19.9134	−	19.9134i	−0.657599	−	0.657599i
$918$	5.10161	+	5.10161i	0.168378	+	0.168378i
$919$		−	32.5707i		−	1.07441i	−0.843452	−	0.537204i	$-0.819481\pi$
$919$		−	32.5707i		−	1.07441i	0.843452	−	0.537204i	$-0.180519\pi$
$920$	12.3643			0.407639
$921$	8.38481	−	8.38481i	0.276289	−	0.276289i
$922$			82.3288i			2.71135i
$923$	34.7928	+	4.05827i	1.14522	+	0.133580i
$924$	−5.98020	−	42.4026i	−0.196734	−	1.39494i
$925$	24.4876	−	24.4876i	0.805148	−	0.805148i
$926$		−	14.6391i		−	0.481072i
$927$			10.6106i			0.348499i
$928$	−16.0460	+	16.0460i	−0.526734	+	0.526734i
$929$	10.6477	−	10.6477i	0.349339	−	0.349339i	−0.510524	−	0.859863i	$-0.670549\pi$
$929$	10.6477	−	10.6477i	0.349339	−	0.349339i	0.859863	+	0.510524i	$0.170549\pi$
$930$	7.47933	−	7.47933i	0.245257	−	0.245257i
$931$	−23.1975	+	23.1975i	−0.760266	+	0.760266i
$932$			40.0161i			1.31077i
$933$			3.95370i			0.129438i
$934$	−5.57614	+	5.57614i	−0.182457	+	0.182457i
$935$	6.37443	−	0.899010i	0.208466	−	0.0294008i
$936$	11.2578	+	1.31313i	0.367973	+	0.0429209i
$937$		−	4.52142i		−	0.147708i	−0.997269	−	0.0738542i	$-0.976470\pi$
$937$		−	4.52142i		−	0.147708i	0.997269	−	0.0738542i	$-0.0235300\pi$
$938$	−72.2126	+	72.2126i	−2.35783	+	2.35783i
$939$	29.7537			0.970975
$940$		−	4.92359i		−	0.160590i
$941$	−8.80672	−	8.80672i	−0.287091	−	0.287091i	0.548838	−	0.835929i	$-0.315070\pi$
$941$	−8.80672	−	8.80672i	−0.287091	−	0.287091i	−0.835929	+	0.548838i	$0.815070\pi$
$942$	−19.7175	−	19.7175i	−0.642432	−	0.642432i
$943$	−50.3422	+	50.3422i	−1.63937	+	1.63937i
$944$	0.433818	+	0.433818i	0.0141196	+	0.0141196i
$945$			2.39436i			0.0778885i
$946$	11.6617	+	82.6869i	0.379153	+	2.68838i
$947$	−19.6262	−	19.6262i	−0.637767	−	0.637767i	0.312237	−	0.950004i	$-0.398922\pi$
$947$	−19.6262	−	19.6262i	−0.637767	−	0.637767i	−0.950004	+	0.312237i	$0.898922\pi$
$948$	16.3105			0.529741
$949$	−6.46908	−	0.754562i	−0.209995	−	0.0244941i
$950$	44.9987			1.45995
$951$	1.56178	−	1.56178i	0.0506442	−	0.0506442i
$952$		−	37.6723i		−	1.22097i
$953$	−61.0383			−1.97722			−0.988612	−	0.150489i	$-0.951915\pi$
$953$	−61.0383			−1.97722			−0.988612	+	0.150489i	$0.951915\pi$
$954$	−13.2793	−	13.2793i	−0.429932	−	0.429932i
$955$	−5.27025	+	5.27025i	−0.170541	+	0.170541i
$956$	−3.91387	+	3.91387i	−0.126584	+	0.126584i
$957$	−9.07123	+	12.0500i	−0.293231	+	0.389523i
$958$	−13.3592			−0.431615
$959$	−45.1021			−1.45642
$960$	5.57962	+	5.57962i	0.180081	+	0.180081i
$961$		−	22.8448i		−	0.736928i
$962$	−49.1465	+	38.8791i	−1.58455	+	1.25351i
$963$			5.84091i			0.188221i
$964$	−13.7258	−	13.7258i	−0.442079	−	0.442079i
$965$			8.02930i			0.258472i
$966$			56.2133i			1.80863i
$967$	−32.1617	−	32.1617i	−1.03425	−	1.03425i	−0.999392	−	0.0348593i	$-0.988902\pi$
$967$	−32.1617	−	32.1617i	−1.03425	−	1.03425i	−0.0348593	−	0.999392i	$-0.511098\pi$
$968$	−30.2595	−	16.7349i	−0.972576	−	0.537879i
$969$	−9.28951	−	9.28951i	−0.298422	−	0.298422i
$970$	−13.8505	+	13.8505i	−0.444714	+	0.444714i
$971$	25.0196			0.802918			0.401459	−	0.915877i	$-0.368503\pi$
$971$	25.0196			0.802918			0.401459	+	0.915877i	$0.368503\pi$
$972$			3.35804i			0.107709i
$973$	40.0785	+	40.0785i	1.28486	+	1.28486i
$974$	4.68398			0.150084
$975$	13.0420	−	10.3173i	0.417678	−	0.330419i
$976$		−	5.41441i		−	0.173311i
$977$	26.1917	−	26.1917i	0.837946	−	0.837946i	−0.150642	−	0.988588i	$-0.548134\pi$
$977$	26.1917	−	26.1917i	0.837946	−	0.837946i	0.988588	+	0.150642i	$0.0481341\pi$
$978$		−	41.8557i		−	1.33840i
$979$	0.863973	+	6.12600i	0.0276127	+	0.195788i
$980$	11.5091	−	11.5091i	0.367644	−	0.367644i
$981$	7.48558	+	7.48558i	0.238996	+	0.238996i
$982$	64.7814	+	64.7814i	2.06726	+	2.06726i
$983$	−28.7977	−	28.7977i	−0.918504	−	0.918504i	0.0784164	−	0.996921i	$-0.475014\pi$
$983$	−28.7977	−	28.7977i	−0.918504	−	0.918504i	−0.996921	+	0.0784164i	$0.975014\pi$
$984$	35.4335			1.12958
$985$	−11.9364			−0.380325
$986$	−23.2003	+	23.2003i	−0.738847	+	0.738847i
$987$	9.05273			0.288152
$988$	−50.6889	−	5.91241i	−1.61263	−	0.188099i
$989$		−	68.7011i		−	2.18457i
$990$	3.81952	+	2.87532i	0.121392	+	0.0913838i
$991$	14.1917			0.450815			0.225408	−	0.974265i	$-0.427629\pi$
$991$	14.1917			0.450815			0.225408	+	0.974265i	$0.427629\pi$
$992$	36.6156			1.16255
$993$	−12.5690	+	12.5690i	−0.398866	+	0.398866i
$994$	61.1401	−	61.1401i	1.93925	−	1.93925i
$995$	4.29160	+	4.29160i	0.136053	+	0.136053i
$996$	24.9471	−	24.9471i	0.790480	−	0.790480i
$997$		−	38.5847i		−	1.22199i	−0.791635	−	0.610994i	$-0.790770\pi$
$997$		−	38.5847i		−	1.22199i	0.791635	−	0.610994i	$-0.209230\pi$
$998$	0.609934			0.0193071
$999$	−5.30931	−	5.30931i	−0.167979	−	0.167979i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.109.13	yes	28
11.10	odd	2	inner	429.2.m.b.109.2	✓	28
13.8	odd	4	inner	429.2.m.b.307.2	yes	28
143.21	even	4	inner	429.2.m.b.307.13	yes	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.2	✓	28	11.10	odd	2	inner
429.2.m.b.109.13	yes	28	1.1	even	1	trivial
429.2.m.b.307.2	yes	28	13.8	odd	4	inner
429.2.m.b.307.13	yes	28	143.21	even	4	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 429 = 3 \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	429.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.63677 + 1.63677i) q^{2} +1.00000 q^{3} +3.35804i q^{4} +(0.440340 - 0.440340i) q^{5} +(1.63677 + 1.63677i) q^{6} +(-2.71876 + 2.71876i) q^{7} +(-2.22281 + 2.22281i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(1.63677 + 1.63677i) q^{2} +1.00000 q^{3} +3.35804i q^{4} +(0.440340 - 0.440340i) q^{5} +(1.63677 + 1.63677i) q^{6} +(-2.71876 + 2.71876i) q^{7} +(-2.22281 + 2.22281i) q^{8} +1.00000 q^{9} +1.44147 q^{10} +(2.64974 + 1.99471i) q^{11} +3.35804i q^{12} +(-2.23697 - 2.82772i) q^{13} -8.89999 q^{14} +(0.440340 - 0.440340i) q^{15} -0.560371 q^{16} +3.11687 q^{17} +(1.63677 + 1.63677i) q^{18} +(-2.98040 - 2.98040i) q^{19} +(1.47868 + 1.47868i) q^{20} +(-2.71876 + 2.71876i) q^{21} +(1.07213 + 7.60191i) q^{22} -6.31611i q^{23} +(-2.22281 + 2.22281i) q^{24} +4.61220i q^{25} +(0.966925 - 8.28973i) q^{26} +1.00000 q^{27} +(-9.12973 - 9.12973i) q^{28} +4.54764i q^{29} +1.44147 q^{30} +(5.18868 - 5.18868i) q^{31} +(3.52842 + 3.52842i) q^{32} +(2.64974 + 1.99471i) q^{33} +(5.10161 + 5.10161i) q^{34} +2.39436i q^{35} +3.35804i q^{36} +(-5.30931 - 5.30931i) q^{37} -9.75645i q^{38} +(-2.23697 - 2.82772i) q^{39} +1.95758i q^{40} +(-7.97044 - 7.97044i) q^{41} -8.89999 q^{42} +10.8771 q^{43} +(-6.69834 + 8.89794i) q^{44} +(0.440340 - 0.440340i) q^{45} +(10.3380 - 10.3380i) q^{46} +(-1.66486 - 1.66486i) q^{47} -0.560371 q^{48} -7.78335i q^{49} +(-7.54912 + 7.54912i) q^{50} +3.11687 q^{51} +(9.49560 - 7.51183i) q^{52} -8.11308 q^{53} +(1.63677 + 1.63677i) q^{54} +(2.04514 - 0.288433i) q^{55} -12.0866i q^{56} +(-2.98040 - 2.98040i) q^{57} +(-7.44344 + 7.44344i) q^{58} +(-0.774163 - 0.774163i) q^{59} +(1.47868 + 1.47868i) q^{60} +9.66220i q^{61} +16.9854 q^{62} +(-2.71876 + 2.71876i) q^{63} +12.6712i q^{64} +(-2.23018 - 0.260131i) q^{65} +(1.07213 + 7.60191i) q^{66} +(8.11379 - 8.11379i) q^{67} +10.4666i q^{68} -6.31611i q^{69} +(-3.91902 + 3.91902i) q^{70} +(-6.86968 + 6.86968i) q^{71} +(-2.22281 + 2.22281i) q^{72} +(1.27729 - 1.27729i) q^{73} -17.3803i q^{74} +4.61220i q^{75} +(10.0083 - 10.0083i) q^{76} +(-12.6272 + 1.78086i) q^{77} +(0.966925 - 8.28973i) q^{78} -4.85714i q^{79} +(-0.246753 + 0.246753i) q^{80} +1.00000 q^{81} -26.0916i q^{82} +(-7.42906 - 7.42906i) q^{83} +(-9.12973 - 9.12973i) q^{84} +(1.37248 - 1.37248i) q^{85} +(17.8034 + 17.8034i) q^{86} +4.54764i q^{87} +(-10.3237 + 1.45599i) q^{88} +(1.31899 + 1.31899i) q^{89} +1.44147 q^{90} +(13.7697 + 1.60611i) q^{91} +21.2098 q^{92} +(5.18868 - 5.18868i) q^{93} -5.45000i q^{94} -2.62477 q^{95} +(3.52842 + 3.52842i) q^{96} +(-9.60861 + 9.60861i) q^{97} +(12.7396 - 12.7396i) q^{98} +(2.64974 + 1.99471i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9}+O(q^{10}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9	\( 28 q + 28 q^{3} - 4 q^{5} + 28 q^{9} - 4 q^{15} - 20 q^{16} - 16 q^{20} - 8 q^{22} + 12 q^{26} + 28 q^{27} + 8 q^{31} - 32 q^{34} - 12 q^{37} + 36 q^{44} - 4 q^{45} - 40 q^{47} - 20 q^{48} + 8 q^{53} - 16 q^{55} + 16 q^{58} - 44 q^{59} - 16 q^{60} - 8 q^{66} - 20 q^{67} - 36 q^{70} - 60 q^{71} + 12 q^{78} - 8 q^{80} + 28 q^{81} + 48 q^{86} + 32 q^{89} + 4 q^{91} + 64 q^{92} + 8 q^{93} + 8 q^{97}+O(q^{100}) \) 28 * q + 28 * q^3 - 4 * q^5 + 28 * q^9 - 4 * q^15 - 20 * q^16 - 16 * q^20 - 8 * q^22 + 12 * q^26 + 28 * q^27 + 8 * q^31 - 32 * q^34 - 12 * q^37 + 36 * q^44 - 4 * q^45 - 40 * q^47 - 20 * q^48 + 8 * q^53 - 16 * q^55 + 16 * q^58 - 44 * q^59 - 16 * q^60 - 8 * q^66 - 20 * q^67 - 36 * q^70 - 60 * q^71 + 12 * q^78 - 8 * q^80 + 28 * q^81 + 48 * q^86 + 32 * q^89 + 4 * q^91 + 64 * q^92 + 8 * q^93 + 8 * q^97

Introduction

L-functions

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