LMFDB - Embedded newform 429.2.m.b.307.3

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			307.3
Character	$\chi$	$=$	429.307
Dual form			429.2.m.b.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.43677 + 1.43677i) q^{2} +1.00000 q^{3} -2.12863i q^{4} +(-2.46780 - 2.46780i) q^{5} +(-1.43677 + 1.43677i) q^{6} +(0.806735 + 0.806735i) q^{7} +(0.184806 + 0.184806i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.43677 + 1.43677i) q^{2} +1.00000 q^{3} -2.12863i q^{4} +(-2.46780 - 2.46780i) q^{5} +(-1.43677 + 1.43677i) q^{6} +(0.806735 + 0.806735i) q^{7} +(0.184806 + 0.184806i) q^{8} +1.00000 q^{9} +7.09133 q^{10} +(0.500342 + 3.27867i) q^{11} -2.12863i q^{12} +(-0.994973 + 3.46555i) q^{13} -2.31819 q^{14} +(-2.46780 - 2.46780i) q^{15} +3.72620 q^{16} -1.84954 q^{17} +(-1.43677 + 1.43677i) q^{18} +(-5.23369 + 5.23369i) q^{19} +(-5.25303 + 5.25303i) q^{20} +(0.806735 + 0.806735i) q^{21} +(-5.42957 - 3.99182i) q^{22} +8.45113i q^{23} +(0.184806 + 0.184806i) q^{24} +7.18008i q^{25} +(-3.54965 - 6.40875i) q^{26} +1.00000 q^{27} +(1.71724 - 1.71724i) q^{28} -5.73560i q^{29} +7.09133 q^{30} +(4.19121 + 4.19121i) q^{31} +(-5.72332 + 5.72332i) q^{32} +(0.500342 + 3.27867i) q^{33} +(2.65736 - 2.65736i) q^{34} -3.98172i q^{35} -2.12863i q^{36} +(1.19044 - 1.19044i) q^{37} -15.0392i q^{38} +(-0.994973 + 3.46555i) q^{39} -0.912131i q^{40} +(-1.04443 + 1.04443i) q^{41} -2.31819 q^{42} +2.53246 q^{43} +(6.97906 - 1.06504i) q^{44} +(-2.46780 - 2.46780i) q^{45} +(-12.1423 - 12.1423i) q^{46} +(-2.58788 + 2.58788i) q^{47} +3.72620 q^{48} -5.69836i q^{49} +(-10.3161 - 10.3161i) q^{50} -1.84954 q^{51} +(7.37686 + 2.11792i) q^{52} +3.52260 q^{53} +(-1.43677 + 1.43677i) q^{54} +(6.85635 - 9.32584i) q^{55} +0.298180i q^{56} +(-5.23369 + 5.23369i) q^{57} +(8.24075 + 8.24075i) q^{58} +(-8.26157 + 8.26157i) q^{59} +(-5.25303 + 5.25303i) q^{60} +2.26751i q^{61} -12.0436 q^{62} +(0.806735 + 0.806735i) q^{63} -8.99379i q^{64} +(11.0077 - 6.09689i) q^{65} +(-5.42957 - 3.99182i) q^{66} +(-10.7166 - 10.7166i) q^{67} +3.93697i q^{68} +8.45113i q^{69} +(5.72083 + 5.72083i) q^{70} +(3.91665 + 3.91665i) q^{71} +(0.184806 + 0.184806i) q^{72} +(-7.89807 - 7.89807i) q^{73} +3.42079i q^{74} +7.18008i q^{75} +(11.1406 + 11.1406i) q^{76} +(-2.24137 + 3.04866i) q^{77} +(-3.54965 - 6.40875i) q^{78} +3.25730i q^{79} +(-9.19553 - 9.19553i) q^{80} +1.00000 q^{81} -3.00122i q^{82} +(-2.19244 + 2.19244i) q^{83} +(1.71724 - 1.71724i) q^{84} +(4.56429 + 4.56429i) q^{85} +(-3.63857 + 3.63857i) q^{86} -5.73560i q^{87} +(-0.513452 + 0.698385i) q^{88} +(11.1079 - 11.1079i) q^{89} +7.09133 q^{90} +(-3.59846 + 1.99310i) q^{91} +17.9893 q^{92} +(4.19121 + 4.19121i) q^{93} -7.43639i q^{94} +25.8314 q^{95} +(-5.72332 + 5.72332i) q^{96} +(2.64280 + 2.64280i) q^{97} +(8.18724 + 8.18724i) q^{98} +(0.500342 + 3.27867i) 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 $\left(\mathbb{Z}/429\mathbb{Z}\right)^\times$.

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

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 $

$2$	−1.43677	+	1.43677i	−1.01595	+	1.01595i	−0.0160804	+	0.999871i	$0.505119\pi$
$2$	−1.43677	+	1.43677i	−1.01595	+	1.01595i	−0.999871	+	0.0160804i	$0.994881\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$		−	2.12863i		−	1.06431i
$5$	−2.46780	−	2.46780i	−1.10363	−	1.10363i	−0.993969	−	0.109665i	$-0.965022\pi$
$5$	−2.46780	−	2.46780i	−1.10363	−	1.10363i	−0.109665	−	0.993969i	$-0.534978\pi$
$6$	−1.43677	+	1.43677i	−0.586560	+	0.586560i
$7$	0.806735	+	0.806735i	0.304917	+	0.304917i	0.842934	−	0.538017i	$-0.180826\pi$
$7$	0.806735	+	0.806735i	0.304917	+	0.304917i	−0.538017	+	0.842934i	$0.680826\pi$
$8$	0.184806	+	0.184806i	0.0653389	+	0.0653389i
$9$	1.00000			0.333333
$10$	7.09133			2.24248
$11$	0.500342	+	3.27867i	0.150859	+	0.988555i
$11$	0.500342	+	3.27867i	0.150859	+	0.988555i
$12$		−	2.12863i		−	0.614481i
$13$	−0.994973	+	3.46555i	−0.275956	+	0.961170i
$13$	−0.994973	+	3.46555i	−0.275956	+	0.961170i
$14$	−2.31819			−0.619562
$15$	−2.46780	−	2.46780i	−0.637183	−	0.637183i
$16$	3.72620			0.931551
$17$	−1.84954			−0.448579			−0.224289	−	0.974523i	$-0.572006\pi$
$17$	−1.84954			−0.448579			−0.224289	+	0.974523i	$0.572006\pi$
$18$	−1.43677	+	1.43677i	−0.338650	+	0.338650i
$19$	−5.23369	+	5.23369i	−1.20069	+	1.20069i	−0.226733	+	0.973957i	$0.572805\pi$
$19$	−5.23369	+	5.23369i	−1.20069	+	1.20069i	−0.973957	+	0.226733i	$0.927195\pi$
$20$	−5.25303	+	5.25303i	−1.17461	+	1.17461i
$21$	0.806735	+	0.806735i	0.176044	+	0.176044i
$22$	−5.42957	−	3.99182i	−1.15759	−	0.851059i
$23$			8.45113i			1.76218i	0.472946	+	0.881091i	$0.343191\pi$
$23$			8.45113i			1.76218i	−0.472946	+	0.881091i	$0.656809\pi$
$24$	0.184806	+	0.184806i	0.0377235	+	0.0377235i
$25$			7.18008i			1.43602i
$26$	−3.54965	−	6.40875i	−0.696144	−	1.25686i
$27$	1.00000			0.192450
$28$	1.71724	−	1.71724i	0.324527	−	0.324527i
$29$		−	5.73560i		−	1.06507i	−0.846407	−	0.532537i	$-0.821239\pi$
$29$		−	5.73560i		−	1.06507i	0.846407	−	0.532537i	$-0.178761\pi$
$30$	7.09133			1.29469
$31$	4.19121	+	4.19121i	0.752763	+	0.752763i	0.974994	−	0.222231i	$-0.0713339\pi$
$31$	4.19121	+	4.19121i	0.752763	+	0.752763i	−0.222231	+	0.974994i	$0.571334\pi$
$32$	−5.72332	+	5.72332i	−1.01175	+	1.01175i
$33$	0.500342	+	3.27867i	0.0870984	+	0.570743i
$34$	2.65736	−	2.65736i	0.455734	−	0.455734i
$35$		−	3.98172i		−	0.673034i
$36$		−	2.12863i		−	0.354771i
$37$	1.19044	−	1.19044i	0.195708	−	0.195708i	−0.602449	−	0.798157i	$-0.705808\pi$
$37$	1.19044	−	1.19044i	0.195708	−	0.195708i	0.798157	+	0.602449i	$0.205808\pi$
$38$		−	15.0392i		−	2.43969i
$39$	−0.994973	+	3.46555i	−0.159323	+	0.554932i
$40$		−	0.912131i		−	0.144221i
$41$	−1.04443	+	1.04443i	−0.163113	+	0.163113i	−0.783944	−	0.620831i	$-0.786795\pi$
$41$	−1.04443	+	1.04443i	−0.163113	+	0.163113i	0.620831	+	0.783944i	$0.286795\pi$
$42$	−2.31819			−0.357704
$43$	2.53246			0.386197			0.193099	−	0.981179i	$-0.438146\pi$
$43$	2.53246			0.386197			0.193099	+	0.981179i	$0.438146\pi$
$44$	6.97906	−	1.06504i	1.05213	−	0.160561i
$45$	−2.46780	−	2.46780i	−0.367878	−	0.367878i
$46$	−12.1423	−	12.1423i	−1.79029	−	1.79029i
$47$	−2.58788	+	2.58788i	−0.377481	+	0.377481i	−0.870193	−	0.492711i	$-0.836006\pi$
$47$	−2.58788	+	2.58788i	−0.377481	+	0.377481i	0.492711	+	0.870193i	$0.336006\pi$
$48$	3.72620			0.537831
$49$		−	5.69836i		−	0.814051i
$50$	−10.3161	−	10.3161i	−1.45892	−	1.45892i
$51$	−1.84954			−0.258987
$52$	7.37686	+	2.11792i	1.02299	+	0.293703i
$53$	3.52260			0.483866			0.241933	−	0.970293i	$-0.422219\pi$
$53$	3.52260			0.483866			0.241933	+	0.970293i	$0.422219\pi$
$54$	−1.43677	+	1.43677i	−0.195520	+	0.195520i
$55$	6.85635	−	9.32584i	0.924510	−	1.25750i
$56$			0.298180i			0.0398459i
$57$	−5.23369	+	5.23369i	−0.693219	+	0.693219i
$58$	8.24075	+	8.24075i	1.08206	+	1.08206i
$59$	−8.26157	+	8.26157i	−1.07556	+	1.07556i	−0.0786637	+	0.996901i	$0.525065\pi$
$59$	−8.26157	+	8.26157i	−1.07556	+	1.07556i	−0.996901	+	0.0786637i	$0.974935\pi$
$60$	−5.25303	+	5.25303i	−0.678163	+	0.678163i
$61$			2.26751i			0.290325i	0.989408	+	0.145162i	$0.0463705\pi$
$61$			2.26751i			0.290325i	−0.989408	+	0.145162i	$0.953630\pi$
$62$	−12.0436			−1.52954
$63$	0.806735	+	0.806735i	0.101639	+	0.101639i
$64$		−	8.99379i		−	1.12422i
$65$	11.0077	−	6.09689i	1.36533	−	0.756226i
$66$	−5.42957	−	3.99182i	−0.668334	−	0.491359i
$67$	−10.7166	−	10.7166i	−1.30924	−	1.30924i	−0.921963	−	0.387278i	$-0.873415\pi$
$67$	−10.7166	−	10.7166i	−1.30924	−	1.30924i	−0.387278	−	0.921963i	$-0.626585\pi$
$68$			3.93697i			0.477428i
$69$			8.45113i			1.01740i
$70$	5.72083	+	5.72083i	0.683769	+	0.683769i
$71$	3.91665	+	3.91665i	0.464820	+	0.464820i	0.900232	−	0.435411i	$-0.143397\pi$
$71$	3.91665	+	3.91665i	0.464820	+	0.464820i	−0.435411	+	0.900232i	$0.643397\pi$
$72$	0.184806	+	0.184806i	0.0217796	+	0.0217796i
$73$	−7.89807	−	7.89807i	−0.924399	−	0.924399i	0.0729376	−	0.997337i	$-0.476763\pi$
$73$	−7.89807	−	7.89807i	−0.924399	−	0.924399i	−0.997337	+	0.0729376i	$0.976763\pi$
$74$			3.42079i			0.397659i
$75$			7.18008i			0.829084i
$76$	11.1406	+	11.1406i	1.27791	+	1.27791i
$77$	−2.24137	+	3.04866i	−0.255428	+	0.347427i
$78$	−3.54965	−	6.40875i	−0.401919	−	0.725648i
$79$			3.25730i			0.366475i	0.983069	+	0.183237i	$0.0586577\pi$
$79$			3.25730i			0.366475i	−0.983069	+	0.183237i	$0.941342\pi$
$80$	−9.19553	−	9.19553i	−1.02809	−	1.02809i
$81$	1.00000			0.111111
$82$		−	3.00122i		−	0.331429i
$83$	−2.19244	+	2.19244i	−0.240652	+	0.240652i	−0.817120	−	0.576468i	$-0.804431\pi$
$83$	−2.19244	+	2.19244i	−0.240652	+	0.240652i	0.576468	+	0.817120i	$0.304431\pi$
$84$	1.71724	−	1.71724i	0.187366	−	0.187366i
$85$	4.56429	+	4.56429i	0.495067	+	0.495067i
$86$	−3.63857	+	3.63857i	−0.392357	+	0.392357i
$87$		−	5.73560i		−	0.614921i
$88$	−0.513452	+	0.698385i	−0.0547342	+	0.0744481i
$89$	11.1079	−	11.1079i	1.17743	−	1.17743i	0.197033	−	0.980397i	$-0.436869\pi$
$89$	11.1079	−	11.1079i	1.17743	−	1.17743i	0.980397	−	0.197033i	$-0.0631308\pi$
$90$	7.09133			0.747492
$91$	−3.59846	+	1.99310i	−0.377221	+	0.208934i
$92$	17.9893			1.87551
$93$	4.19121	+	4.19121i	0.434608	+	0.434608i
$94$		−	7.43639i		−	0.767005i
$95$	25.8314			2.65025
$96$	−5.72332	+	5.72332i	−0.584134	+	0.584134i
$97$	2.64280	+	2.64280i	0.268336	+	0.268336i	0.828429	−	0.560094i	$-0.189235\pi$
$97$	2.64280	+	2.64280i	0.268336	+	0.268336i	−0.560094	+	0.828429i	$0.689235\pi$
$98$	8.18724	+	8.18724i	0.827036	+	0.827036i
$99$	0.500342	+	3.27867i	0.0502863	+	0.329518i
$100$	15.2837			1.52837
$101$	9.47469			0.942767			0.471384	−	0.881928i	$-0.343755\pi$
$101$	9.47469			0.942767			0.471384	+	0.881928i	$0.343755\pi$
$102$	2.65736	−	2.65736i	0.263118	−	0.263118i
$103$			20.1541i			1.98584i	0.118793	+	0.992919i	$0.462098\pi$
$103$			20.1541i			1.98584i	−0.118793	+	0.992919i	$0.537902\pi$
$104$	−0.824333	+	0.456578i	−0.0808325	+	0.0447712i
$105$		−	3.98172i		−	0.388576i
$106$	−5.06117	+	5.06117i	−0.491584	+	0.491584i
$107$			13.4041i			1.29582i	0.761716	+	0.647911i	$0.224357\pi$
$107$			13.4041i			1.29582i	−0.761716	+	0.647911i	$0.775643\pi$
$108$		−	2.12863i		−	0.204827i
$109$	10.5424	−	10.5424i	1.00978	−	1.00978i	0.00982771	−	0.999952i	$-0.496872\pi$
$109$	10.5424	−	10.5424i	1.00978	−	1.00978i	0.999952	−	0.00982771i	$-0.00312831\pi$
$110$	3.54809	+	23.2501i	0.338297	+	2.21681i
$111$	1.19044	−	1.19044i	0.112992	−	0.112992i
$112$	3.00606	+	3.00606i	0.284046	+	0.284046i
$113$	−0.209399			−0.0196986			−0.00984928	−	0.999951i	$-0.503135\pi$
$113$	−0.209399			−0.0196986			−0.00984928	+	0.999951i	$0.503135\pi$
$114$		−	15.0392i		−	1.40855i
$115$	20.8557	−	20.8557i	1.94481	−	1.94481i
$116$	−12.2089			−1.13357
$117$	−0.994973	+	3.46555i	−0.0919853	+	0.320390i
$118$		−	23.7400i		−	2.18544i
$119$	−1.49209	−	1.49209i	−0.136779	−	0.136779i
$120$		−	0.912131i		−	0.0832658i
$121$	−10.4993	+	3.28091i	−0.954483	+	0.298265i
$122$	−3.25789	−	3.25789i	−0.294956	−	0.294956i
$123$	−1.04443	+	1.04443i	−0.0941732	+	0.0941732i
$124$	8.92151	−	8.92151i	0.801176	−	0.801176i
$125$	5.38001	−	5.38001i	0.481202	−	0.481202i
$126$	−2.31819			−0.206521
$127$	−3.63378			−0.322446			−0.161223	−	0.986918i	$-0.551544\pi$
$127$	−3.63378			−0.322446			−0.161223	+	0.986918i	$0.551544\pi$
$128$	1.47539	+	1.47539i	0.130408	+	0.130408i
$129$	2.53246			0.222971
$130$	−7.05568	+	24.5754i	−0.618824	+	2.15540i
$131$			12.7071i			1.11023i	0.831774	+	0.555114i	$0.187325\pi$
$131$			12.7071i			1.11023i	−0.831774	+	0.555114i	$0.812675\pi$
$132$	6.97906	−	1.06504i	0.607449	−	0.0927000i
$133$	−8.44440			−0.732222
$134$	30.7946			2.66025
$135$	−2.46780	−	2.46780i	−0.212394	−	0.212394i
$136$	−0.341806	−	0.341806i	−0.0293097	−	0.0293097i
$137$	−1.88272	+	1.88272i	−0.160851	+	0.160851i	−0.782944	−	0.622093i	$-0.786283\pi$
$137$	−1.88272	+	1.88272i	−0.160851	+	0.160851i	0.622093	+	0.782944i	$0.286283\pi$
$138$	−12.1423	−	12.1423i	−1.03363	−	1.03363i
$139$		−	16.7942i		−	1.42446i	−0.701945	−	0.712232i	$-0.747685\pi$
$139$		−	16.7942i		−	1.42446i	0.701945	−	0.712232i	$-0.252315\pi$
$140$	−8.47560			−0.716319
$141$	−2.58788	+	2.58788i	−0.217939	+	0.217939i
$142$	−11.2547			−0.944470
$143$	−11.8602	−	1.52822i	−0.991800	−	0.127796i
$144$	3.72620			0.310517
$145$	−14.1543	+	14.1543i	−1.17545	+	1.17545i
$146$	22.6954			1.87829
$147$		−	5.69836i		−	0.469993i
$148$	−2.53401	−	2.53401i	−0.208294	−	0.208294i
$149$	7.46175	−	7.46175i	0.611290	−	0.611290i	−0.331992	−	0.943282i	$-0.607721\pi$
$149$	7.46175	−	7.46175i	0.611290	−	0.611290i	0.943282	+	0.331992i	$0.107721\pi$
$150$	−10.3161	−	10.3161i	−0.842309	−	0.842309i
$151$	0.179599	+	0.179599i	0.0146156	+	0.0146156i	0.714377	−	0.699761i	$-0.246710\pi$
$151$	0.179599	+	0.179599i	0.0146156	+	0.0146156i	−0.699761	+	0.714377i	$0.746710\pi$
$152$	−1.93444			−0.156904
$153$	−1.84954			−0.149526
$154$	−1.15989	−	7.60057i	−0.0934664	−	0.612471i
$155$		−	20.6861i		−	1.66155i
$156$	7.37686	+	2.11792i	0.590621	+	0.169570i
$157$	−9.58339			−0.764838			−0.382419	−	0.923989i	$-0.624909\pi$
$157$	−9.58339			−0.764838			−0.382419	+	0.923989i	$0.624909\pi$
$158$	−4.68000	−	4.68000i	−0.372320	−	0.372320i
$159$	3.52260			0.279360
$160$	28.2480			2.23320
$161$	−6.81782	+	6.81782i	−0.537320	+	0.537320i
$162$	−1.43677	+	1.43677i	−0.112883	+	0.112883i
$163$	0.610390	−	0.610390i	0.0478095	−	0.0478095i	−0.682798	−	0.730607i	$-0.739237\pi$
$163$	0.610390	−	0.610390i	0.0478095	−	0.0478095i	0.730607	+	0.682798i	$0.239237\pi$
$164$	2.22320	+	2.22320i	0.173603	+	0.173603i
$165$	6.85635	−	9.32584i	0.533766	−	0.726016i
$166$		−	6.30008i		−	0.488981i
$167$	4.01508	+	4.01508i	0.310696	+	0.310696i	0.845179	−	0.534483i	$-0.179494\pi$
$167$	4.01508	+	4.01508i	0.310696	+	0.310696i	−0.534483	+	0.845179i	$0.679494\pi$
$168$			0.298180i			0.0230051i
$169$	−11.0201	−	6.89625i	−0.847697	−	0.530481i
$170$	−13.1157			−1.00593
$171$	−5.23369	+	5.23369i	−0.400230	+	0.400230i
$172$		−	5.39067i		−	0.411035i
$173$	−12.4826			−0.949034			−0.474517	−	0.880246i	$-0.657377\pi$
$173$	−12.4826			−0.949034			−0.474517	+	0.880246i	$0.657377\pi$
$174$	8.24075	+	8.24075i	0.624730	+	0.624730i
$175$	−5.79242	+	5.79242i	−0.437866	+	0.437866i
$176$	1.86438	+	12.2170i	0.140533	+	0.920889i
$177$	−8.26157	+	8.26157i	−0.620978	+	0.620978i
$178$			31.9189i			2.39242i
$179$		−	13.0366i		−	0.974402i	−0.873290	−	0.487201i	$-0.838018\pi$
$179$		−	13.0366i		−	0.974402i	0.873290	−	0.487201i	$-0.161982\pi$
$180$	−5.25303	+	5.25303i	−0.391537	+	0.391537i
$181$		−	3.27418i		−	0.243368i	−0.992569	−	0.121684i	$-0.961171\pi$
$181$		−	3.27418i		−	0.243368i	0.992569	−	0.121684i	$-0.0388295\pi$
$182$	2.30653	−	8.03379i	0.170972	−	0.595504i
$183$			2.26751i			0.167619i
$184$	−1.56182	+	1.56182i	−0.115139	+	0.115139i
$185$	−5.87556			−0.431979
$186$	−12.0436			−0.883081
$187$	−0.925402	−	6.06402i	−0.0676721	−	0.443445i
$188$	5.50863	+	5.50863i	0.401758	+	0.401758i
$189$	0.806735	+	0.806735i	0.0586813	+	0.0586813i
$190$	−37.1138	+	37.1138i	−2.69252	+	2.69252i
$191$	1.34725			0.0974837			0.0487418	−	0.998811i	$-0.484479\pi$
$191$	1.34725			0.0974837			0.0487418	+	0.998811i	$0.484479\pi$
$192$		−	8.99379i		−	0.649071i
$193$	11.1141	+	11.1141i	0.800011	+	0.800011i	0.983097	−	0.183086i	$-0.0586087\pi$
$193$	11.1141	+	11.1141i	0.800011	+	0.800011i	−0.183086	+	0.983097i	$0.558609\pi$
$194$	−7.59420			−0.545232
$195$	11.0077	−	6.09689i	0.788276	−	0.436607i
$196$	−12.1297			−0.866405
$197$	−12.2514	+	12.2514i	−0.872875	+	0.872875i	−0.992785	−	0.119910i	$-0.961739\pi$
$197$	−12.2514	+	12.2514i	−0.872875	+	0.872875i	0.119910	+	0.992785i	$0.461739\pi$
$198$	−5.42957	−	3.99182i	−0.385863	−	0.283686i
$199$			17.0285i			1.20712i	0.797319	+	0.603558i	$0.206251\pi$
$199$			17.0285i			1.20712i	−0.797319	+	0.603558i	$0.793749\pi$
$200$	−1.32693	+	1.32693i	−0.0938278	+	0.0938278i
$201$	−10.7166	−	10.7166i	−0.755891	−	0.755891i
$202$	−13.6130	+	13.6130i	−0.957805	+	0.957805i
$203$	4.62711	−	4.62711i	0.324759	−	0.324759i
$204$			3.93697i			0.275643i
$205$	5.15489			0.360033
$206$	−28.9568	−	28.9568i	−2.01751	−	2.01751i
$207$			8.45113i			0.587394i
$208$	−3.70747	+	12.9133i	−0.257067	+	0.895379i
$209$	−19.7782	−	14.5409i	−1.36808	−	1.00581i
$210$	5.72083	+	5.72083i	0.394774	+	0.394774i
$211$		−	24.6882i		−	1.69961i	−0.527100	−	0.849803i	$-0.676721\pi$
$211$		−	24.6882i		−	1.69961i	0.527100	−	0.849803i	$-0.323279\pi$
$212$		−	7.49829i		−	0.514985i
$213$	3.91665	+	3.91665i	0.268364	+	0.268364i
$214$	−19.2586	−	19.2586i	−1.31649	−	1.31649i
$215$	−6.24961	−	6.24961i	−0.426220	−	0.426220i
$216$	0.184806	+	0.184806i	0.0125745	+	0.0125745i
$217$			6.76239i			0.459061i
$218$			30.2941i			2.05177i
$219$	−7.89807	−	7.89807i	−0.533702	−	0.533702i
$220$	−19.8512	−	14.5946i	−1.33837	−	0.983968i
$221$	1.84024	−	6.40966i	0.123788	−	0.431160i
$222$			3.42079i			0.229588i
$223$	7.74609	+	7.74609i	0.518716	+	0.518716i	0.917183	−	0.398466i	$-0.130457\pi$
$223$	7.74609	+	7.74609i	0.518716	+	0.518716i	−0.398466	+	0.917183i	$0.630457\pi$
$224$	−9.23440			−0.616999
$225$			7.18008i			0.478672i
$226$	0.300858	−	0.300858i	0.0200128	−	0.0200128i
$227$	13.9087	−	13.9087i	0.923152	−	0.923152i	−0.0740984	−	0.997251i	$-0.523608\pi$
$227$	13.9087	−	13.9087i	0.923152	−	0.923152i	0.997251	+	0.0740984i	$0.0236079\pi$
$228$	11.1406	+	11.1406i	0.737802	+	0.737802i
$229$	6.81839	−	6.81839i	0.450572	−	0.450572i	−0.444972	−	0.895544i	$-0.646787\pi$
$229$	6.81839	−	6.81839i	0.450572	−	0.450572i	0.895544	+	0.444972i	$0.146787\pi$
$230$			59.9298i			3.95165i
$231$	−2.24137	+	3.04866i	−0.147471	+	0.200587i
$232$	1.05998	−	1.05998i	0.0695908	−	0.0695908i
$233$	18.4834			1.21089			0.605443	−	0.795888i	$-0.292996\pi$
$233$	18.4834			1.21089			0.605443	+	0.795888i	$0.292996\pi$
$234$	−3.54965	−	6.40875i	−0.232048	−	0.418953i
$235$	12.7728			0.833202
$236$	17.5858	+	17.5858i	1.14474	+	1.14474i
$237$			3.25730i			0.211584i
$238$	4.28757			0.277922
$239$	16.1828	−	16.1828i	1.04678	−	1.04678i	0.0479252	−	0.998851i	$-0.484739\pi$
$239$	16.1828	−	16.1828i	1.04678	−	1.04678i	0.998851	−	0.0479252i	$-0.0152609\pi$
$240$	−9.19553	−	9.19553i	−0.593569	−	0.593569i
$241$	11.6741	+	11.6741i	0.751996	+	0.751996i	0.974851	−	0.222856i	$-0.0715378\pi$
$241$	11.6741	+	11.6741i	0.751996	+	0.751996i	−0.222856	+	0.974851i	$0.571538\pi$
$242$	10.3712	−	19.7990i	0.666686	−	1.27273i
$243$	1.00000			0.0641500
$244$	4.82668			0.308996
$245$	−14.0624	+	14.0624i	−0.898414	+	0.898414i
$246$		−	3.00122i		−	0.191351i
$247$	−12.9302	−	23.3450i	−0.822730	−	1.48541i
$248$			1.54912i			0.0983695i
$249$	−2.19244	+	2.19244i	−0.138940	+	0.138940i
$250$			15.4597i			0.977756i
$251$			6.21499i			0.392287i	0.980575	+	0.196143i	$0.0628418\pi$
$251$			6.21499i			0.392287i	−0.980575	+	0.196143i	$0.937158\pi$
$252$	1.71724	−	1.71724i	0.108176	−	0.108176i
$253$	−27.7085	+	4.22846i	−1.74202	+	0.265841i
$254$	5.22091	−	5.22091i	0.327589	−	0.327589i
$255$	4.56429	+	4.56429i	0.285827	+	0.285827i
$256$	13.7480			0.859248
$257$		−	2.89104i		−	0.180338i	−0.995926	−	0.0901690i	$-0.971259\pi$
$257$		−	2.89104i		−	0.180338i	0.995926	−	0.0901690i	$-0.0287407\pi$
$258$	−3.63857	+	3.63857i	−0.226528	+	0.226528i
$259$	1.92074			0.119349
$260$	−12.9780	−	23.4312i	−0.804861	−	1.45314i
$261$		−	5.73560i		−	0.355025i
$262$	−18.2573	−	18.2573i	−1.12794	−	1.12794i
$263$		−	17.8849i		−	1.10283i	−0.834232	−	0.551414i	$-0.814089\pi$
$263$		−	17.8849i		−	1.10283i	0.834232	−	0.551414i	$-0.185911\pi$
$264$	−0.513452	+	0.698385i	−0.0316008	+	0.0429826i
$265$	−8.69306	−	8.69306i	−0.534011	−	0.534011i
$266$	12.1327	−	12.1327i	0.743902	−	0.743902i
$267$	11.1079	−	11.1079i	0.679790	−	0.679790i
$268$	−22.8116	+	22.8116i	−1.39344	+	1.39344i
$269$	−2.24160			−0.136673			−0.0683363	−	0.997662i	$-0.521769\pi$
$269$	−2.24160			−0.136673			−0.0683363	+	0.997662i	$0.521769\pi$
$270$	7.09133			0.431565
$271$	0.322684	+	0.322684i	0.0196017	+	0.0196017i	0.716840	−	0.697238i	$-0.245588\pi$
$271$	0.322684	+	0.322684i	0.0196017	+	0.0196017i	−0.697238	+	0.716840i	$0.745588\pi$
$272$	−6.89175			−0.417874
$273$	−3.59846	+	1.99310i	−0.217789	+	0.120628i
$274$		−	5.41006i		−	0.326834i
$275$	−23.5411	+	3.59250i	−1.41958	+	0.216636i
$276$	17.9893			1.08283
$277$	4.38638			0.263552			0.131776	−	0.991280i	$-0.457932\pi$
$277$	4.38638			0.263552			0.131776	+	0.991280i	$0.457932\pi$
$278$	24.1294	+	24.1294i	1.44718	+	1.44718i
$279$	4.19121	+	4.19121i	0.250921	+	0.250921i
$280$	0.735848	−	0.735848i	0.0439753	−	0.0439753i
$281$	1.87584	+	1.87584i	0.111903	+	0.111903i	0.760841	−	0.648938i	$-0.224787\pi$
$281$	1.87584	+	1.87584i	0.111903	+	0.111903i	−0.648938	+	0.760841i	$0.724787\pi$
$282$		−	7.43639i		−	0.442831i
$283$	−18.1094			−1.07649			−0.538246	−	0.842788i	$-0.680913\pi$
$283$	−18.1094			−1.07649			−0.538246	+	0.842788i	$0.680913\pi$
$284$	8.33708	−	8.33708i	0.494714	−	0.494714i
$285$	25.8314			1.53012
$286$	19.2361	−	14.8447i	1.13746	−	0.877786i
$287$	−1.68516			−0.0994717
$288$	−5.72332	+	5.72332i	−0.337250	+	0.337250i
$289$	−13.5792			−0.798777
$290$		−	40.6731i		−	2.38840i
$291$	2.64280	+	2.64280i	0.154924	+	0.154924i
$292$	−16.8120	+	16.8120i	−0.983850	+	0.983850i
$293$	−1.26575	−	1.26575i	−0.0739461	−	0.0739461i	0.669166	−	0.743113i	$-0.266651\pi$
$293$	−1.26575	−	1.26575i	−0.0739461	−	0.0739461i	−0.743113	+	0.669166i	$0.766651\pi$
$294$	8.18724	+	8.18724i	0.477489	+	0.477489i
$295$	40.7758			2.37406
$296$	0.440003			0.0255747
$297$	0.500342	+	3.27867i	0.0290328	+	0.190248i
$298$			21.4417i			1.24208i
$299$	−29.2878	−	8.40865i	−1.69376	−	0.486285i
$300$	15.2837			0.882405
$301$	2.04303	+	2.04303i	0.117758	+	0.117758i
$302$	−0.516087			−0.0296975
$303$	9.47469			0.544307
$304$	−19.5018	+	19.5018i	−1.11850	+	1.11850i
$305$	5.59576	−	5.59576i	0.320412	−	0.320412i
$306$	2.65736	−	2.65736i	0.151911	−	0.151911i
$307$	−9.58923	−	9.58923i	−0.547286	−	0.547286i	0.378369	−	0.925655i	$-0.376485\pi$
$307$	−9.58923	−	9.58923i	−0.547286	−	0.547286i	−0.925655	+	0.378369i	$0.876485\pi$
$308$	6.48946	+	4.77104i	0.369771	+	0.271855i
$309$			20.1541i			1.14652i
$310$	29.7212	+	29.7212i	1.68805	+	1.68805i
$311$		−	14.5052i		−	0.822514i	−0.911519	−	0.411257i	$-0.865090\pi$
$311$		−	14.5052i		−	0.822514i	0.911519	−	0.411257i	$-0.134910\pi$
$312$	−0.824333	+	0.456578i	−0.0466687	+	0.0258487i
$313$	−15.4280			−0.872042			−0.436021	−	0.899937i	$-0.643613\pi$
$313$	−15.4280			−0.872042			−0.436021	+	0.899937i	$0.643613\pi$
$314$	13.7691	−	13.7691i	0.777038	−	0.777038i
$315$		−	3.98172i		−	0.224345i
$316$	6.93357			0.390044
$317$	14.6252	+	14.6252i	0.821431	+	0.821431i	0.986313	−	0.164883i	$-0.0527245\pi$
$317$	14.6252	+	14.6252i	0.821431	+	0.821431i	−0.164883	+	0.986313i	$0.552725\pi$
$318$	−5.06117	+	5.06117i	−0.283816	+	0.283816i
$319$	18.8051	−	2.86976i	1.05288	−	0.160676i
$320$	−22.1949	+	22.1949i	−1.24073	+	1.24073i
$321$			13.4041i			0.748143i
$322$		−	19.5913i		−	1.09178i
$323$	9.67990	−	9.67990i	0.538604	−	0.538604i
$324$		−	2.12863i		−	0.118257i
$325$	−24.8829	−	7.14398i	−1.38026	−	0.396277i
$326$			1.75398i			0.0971442i
$327$	10.5424	−	10.5424i	0.582996	−	0.582996i
$328$	−0.386035			−0.0213152
$329$	−4.17547			−0.230201
$330$	3.54809	+	23.2501i	0.195316	+	1.27988i
$331$	3.21850	+	3.21850i	0.176905	+	0.176905i	0.790005	−	0.613100i	$-0.210078\pi$
$331$	3.21850	+	3.21850i	0.176905	+	0.176905i	−0.613100	+	0.790005i	$0.710078\pi$
$332$	4.66689	+	4.66689i	0.256129	+	0.256129i
$333$	1.19044	−	1.19044i	0.0652359	−	0.0652359i
$334$	−11.5375			−0.631304
$335$			52.8929i			2.88985i
$336$	3.00606	+	3.00606i	0.163994	+	0.163994i
$337$	−12.3662			−0.673631			−0.336815	−	0.941571i	$-0.609350\pi$
$337$	−12.3662			−0.673631			−0.336815	+	0.941571i	$0.609350\pi$
$338$	25.7417	−	5.92497i	1.40016	−	0.322276i
$339$	−0.209399			−0.0113730
$340$	9.71566	−	9.71566i	0.526906	−	0.526906i
$341$	−11.6445	+	15.8386i	−0.630587	+	0.857709i
$342$		−	15.0392i		−	0.813228i
$343$	10.2442	−	10.2442i	0.553135	−	0.553135i
$344$	0.468016	+	0.468016i	0.0252337	+	0.0252337i
$345$	20.8557	−	20.8557i	1.12283	−	1.12283i
$346$	17.9346	−	17.9346i	0.964172	−	0.964172i
$347$			3.76086i			0.201893i	0.994892	+	0.100947i	$0.0321872\pi$
$347$			3.76086i			0.201893i	−0.994892	+	0.100947i	$0.967813\pi$
$348$	−12.2089			−0.654468
$349$	23.0160	+	23.0160i	1.23202	+	1.23202i	0.963188	+	0.268829i	$0.0866367\pi$
$349$	23.0160	+	23.0160i	1.23202	+	1.23202i	0.268829	+	0.963188i	$0.413363\pi$
$350$		−	16.6448i		−	0.889701i
$351$	−0.994973	+	3.46555i	−0.0531077	+	0.184977i
$352$	−21.6285	−	15.9012i	−1.15280	−	0.847538i
$353$	2.37821	+	2.37821i	0.126580	+	0.126580i	0.767558	−	0.640979i	$-0.221471\pi$
$353$	2.37821	+	2.37821i	0.126580	+	0.126580i	−0.640979	+	0.767558i	$0.721471\pi$
$354$		−	23.7400i		−	1.26177i
$355$		−	19.3310i		−	1.02598i
$356$	−23.6445	−	23.6445i	−1.25315	−	1.25315i
$357$	−1.49209	−	1.49209i	−0.0789696	−	0.0789696i
$358$	18.7306	+	18.7306i	0.989945	+	0.989945i
$359$	−3.50128	−	3.50128i	−0.184790	−	0.184790i	0.608649	−	0.793439i	$-0.291712\pi$
$359$	−3.50128	−	3.50128i	−0.184790	−	0.184790i	−0.793439	+	0.608649i	$0.791712\pi$
$360$		−	0.912131i		−	0.0480735i
$361$		−	35.7830i		−	1.88331i
$362$	4.70425	+	4.70425i	0.247250	+	0.247250i
$363$	−10.4993	+	3.28091i	−0.551071	+	0.172203i
$364$	4.24257	+	7.65977i	0.222371	+	0.401481i
$365$			38.9817i			2.04040i
$366$	−3.25789	−	3.25789i	−0.170293	−	0.170293i
$367$	31.9029			1.66532			0.832659	−	0.553786i	$-0.186817\pi$
$367$	31.9029			1.66532			0.832659	+	0.553786i	$0.186817\pi$
$368$			31.4906i			1.64156i
$369$	−1.04443	+	1.04443i	−0.0543709	+	0.0543709i
$370$	8.44183	−	8.44183i	0.438870	−	0.438870i
$371$	2.84180	+	2.84180i	0.147539	+	0.147539i
$372$	8.92151	−	8.92151i	0.462559	−	0.462559i
$373$			9.79286i			0.507055i	0.967328	+	0.253528i	$0.0815909\pi$
$373$			9.79286i			0.507055i	−0.967328	+	0.253528i	$0.918409\pi$
$374$	10.0422	+	7.38302i	0.519270	+	0.381767i
$375$	5.38001	−	5.38001i	0.277822	−	0.277822i
$376$	−0.956514			−0.0493285
$377$	19.8770	+	5.70677i	1.02372	+	0.293913i
$378$	−2.31819			−0.119235
$379$	22.1448	+	22.1448i	1.13750	+	1.13750i	0.988897	+	0.148605i	$0.0474782\pi$
$379$	22.1448	+	22.1448i	1.13750	+	1.13750i	0.148605	+	0.988897i	$0.452522\pi$
$380$		−	54.9854i		−	2.82069i
$381$	−3.63378			−0.186164
$382$	−1.93569	+	1.93569i	−0.0990386	+	0.0990386i
$383$	6.75039	+	6.75039i	0.344929	+	0.344929i	0.858217	−	0.513288i	$-0.171573\pi$
$383$	6.75039	+	6.75039i	0.344929	+	0.344929i	−0.513288	+	0.858217i	$0.671573\pi$
$384$	1.47539	+	1.47539i	0.0752909	+	0.0752909i
$385$	13.0547	−	1.99222i	0.665331	−	0.101533i
$386$	−31.9369			−1.62554
$387$	2.53246			0.128732
$388$	5.62553	−	5.62553i	0.285593	−	0.285593i
$389$			0.190919i			0.00967996i	0.999988	+	0.00483998i	$0.00154062\pi$
$389$			0.190919i			0.00967996i	−0.999988	+	0.00483998i	$0.998459\pi$
$390$	−7.05568	+	24.5754i	−0.357278	+	1.24442i
$391$		−	15.6307i		−	0.790478i
$392$	1.05309	−	1.05309i	0.0531892	−	0.0531892i
$393$			12.7071i			0.640990i
$394$		−	35.2049i		−	1.77360i
$395$	8.03836	−	8.03836i	0.404454	−	0.404454i
$396$	6.97906	−	1.06504i	0.350711	−	0.0535204i
$397$	−13.8046	+	13.8046i	−0.692831	+	0.692831i	−0.962854	−	0.270023i	$-0.912969\pi$
$397$	−13.8046	+	13.8046i	−0.692831	+	0.692831i	0.270023	+	0.962854i	$0.412969\pi$
$398$	−24.4660	−	24.4660i	−1.22637	−	1.22637i
$399$	−8.44440			−0.422749
$400$			26.7544i			1.33772i
$401$	1.89078	−	1.89078i	0.0944212	−	0.0944212i	−0.658318	−	0.752740i	$-0.728732\pi$
$401$	1.89078	−	1.89078i	0.0944212	−	0.0944212i	0.752740	+	0.658318i	$0.228732\pi$
$402$	30.7946			1.53590
$403$	−18.6950	+	10.3547i	−0.931263	+	0.515804i
$404$		−	20.1681i		−	1.00340i
$405$	−2.46780	−	2.46780i	−0.122626	−	0.122626i
$406$			13.2962i			0.659879i
$407$	4.49870	+	3.30744i	0.222992	+	0.163944i
$408$	−0.341806	−	0.341806i	−0.0169219	−	0.0169219i
$409$	−0.356625	+	0.356625i	−0.0176340	+	0.0176340i	−0.715869	−	0.698235i	$-0.753969\pi$
$409$	−0.356625	+	0.356625i	−0.0176340	+	0.0176340i	0.698235	+	0.715869i	$0.253969\pi$
$410$	−7.40641	+	7.40641i	−0.365776	+	0.365776i
$411$	−1.88272	+	1.88272i	−0.0928675	+	0.0928675i
$412$	42.9004			2.11355
$413$	−13.3298			−0.655916
$414$	−12.1423	−	12.1423i	−0.596764	−	0.596764i
$415$	10.8210			0.531183
$416$	−14.1399	−	25.5290i	−0.693265	−	1.25166i
$417$		−	16.7942i		−	0.822414i
$418$	49.3086	−	7.52476i	2.41176	−	0.368048i
$419$	−12.7447			−0.622621			−0.311311	−	0.950308i	$-0.600768\pi$
$419$	−12.7447			−0.622621			−0.311311	+	0.950308i	$0.600768\pi$
$420$	−8.47560			−0.413567
$421$	−1.76178	−	1.76178i	−0.0858639	−	0.0858639i	0.662870	−	0.748734i	$-0.269338\pi$
$421$	−1.76178	−	1.76178i	−0.0858639	−	0.0858639i	−0.748734	+	0.662870i	$0.769338\pi$
$422$	35.4713	+	35.4713i	1.72672	+	1.72672i
$423$	−2.58788	+	2.58788i	−0.125827	+	0.125827i
$424$	0.650998	+	0.650998i	0.0316153	+	0.0316153i
$425$		−	13.2798i		−	0.644166i
$426$	−11.2547			−0.545290
$427$	−1.82928	+	1.82928i	−0.0885250	+	0.0885250i
$428$	28.5323			1.37916
$429$	−11.8602	−	1.52822i	−0.572616	−	0.0737833i
$430$	17.9585			0.866038
$431$	−17.0697	+	17.0697i	−0.822220	+	0.822220i	−0.986426	−	0.164206i	$-0.947494\pi$
$431$	−17.0697	+	17.0697i	−0.822220	+	0.822220i	0.164206	+	0.986426i	$0.447494\pi$
$432$	3.72620			0.179277
$433$			25.0380i			1.20325i	0.798779	+	0.601625i	$0.205480\pi$
$433$			25.0380i			1.20325i	−0.798779	+	0.601625i	$0.794520\pi$
$434$	−9.71601	−	9.71601i	−0.466383	−	0.466383i
$435$	−14.1543	+	14.1543i	−0.678648	+	0.678648i
$436$	−22.4408	−	22.4408i	−1.07472	−	1.07472i
$437$	−44.2306	−	44.2306i	−2.11584	−	2.11584i
$438$	22.6954			1.08443
$439$	−11.6640			−0.556692			−0.278346	−	0.960481i	$-0.589786\pi$
$439$	−11.6640			−0.556692			−0.278346	+	0.960481i	$0.589786\pi$
$440$	2.99057	−	0.456378i	0.142570	−	0.0217570i
$441$		−	5.69836i		−	0.271350i
$442$	6.56522	+	11.8532i	0.312276	+	0.563800i
$443$	14.4010			0.684214			0.342107	−	0.939661i	$-0.388859\pi$
$443$	14.4010			0.684214			0.342107	+	0.939661i	$0.388859\pi$
$444$	−2.53401	−	2.53401i	−0.120259	−	0.120259i
$445$	−54.8239			−2.59890
$446$	−22.2587			−1.05398
$447$	7.46175	−	7.46175i	0.352928	−	0.352928i
$448$	7.25561	−	7.25561i	0.342795	−	0.342795i
$449$	1.40102	−	1.40102i	0.0661182	−	0.0661182i	−0.673274	−	0.739393i	$-0.735113\pi$
$449$	1.40102	−	1.40102i	0.0661182	−	0.0661182i	0.739393	+	0.673274i	$0.235113\pi$
$450$	−10.3161	−	10.3161i	−0.486307	−	0.486307i
$451$	−3.94691	−	2.90177i	−0.185853	−	0.136639i
$452$			0.445731i			0.0209654i
$453$	0.179599	+	0.179599i	0.00843832	+	0.00843832i
$454$			39.9672i			1.87576i
$455$	13.7989	+	3.96170i	0.646900	+	0.185728i
$456$	−1.93444			−0.0905884
$457$	2.77667	−	2.77667i	0.129887	−	0.129887i	−0.639174	−	0.769062i	$-0.720724\pi$
$457$	2.77667	−	2.77667i	0.129887	−	0.129887i	0.769062	+	0.639174i	$0.220724\pi$
$458$			19.5929i			0.915518i
$459$	−1.84954			−0.0863290
$460$	−44.3940	−	44.3940i	−2.06988	−	2.06988i
$461$	−4.82833	+	4.82833i	−0.224878	+	0.224878i	−0.810549	−	0.585671i	$-0.800831\pi$
$461$	−4.82833	+	4.82833i	−0.224878	+	0.224878i	0.585671	+	0.810549i	$0.300831\pi$
$462$	−1.15989	−	7.60057i	−0.0539628	−	0.353610i
$463$	12.1947	−	12.1947i	0.566735	−	0.566735i	−0.364477	−	0.931212i	$-0.618752\pi$
$463$	12.1947	−	12.1947i	0.566735	−	0.566735i	0.931212	+	0.364477i	$0.118752\pi$
$464$		−	21.3720i		−	0.992171i
$465$		−	20.6861i		−	0.959296i
$466$	−26.5564	+	26.5564i	−1.23020	+	1.23020i
$467$			21.7196i			1.00507i	0.864558	+	0.502533i	$0.167598\pi$
$467$			21.7196i			1.00507i	−0.864558	+	0.502533i	$0.832402\pi$
$468$	7.37686	+	2.11792i	0.340995	+	0.0979011i
$469$		−	17.2909i		−	0.798420i
$470$	−18.3515	+	18.3515i	−0.846493	+	0.846493i
$471$	−9.58339			−0.441579
$472$	−3.05358			−0.140553
$473$	1.26710	+	8.30310i	0.0582613	+	0.381777i
$474$	−4.68000	−	4.68000i	−0.214959	−	0.214959i
$475$	−37.5783	−	37.5783i	−1.72421	−	1.72421i
$476$	−3.17609	+	3.17609i	−0.145576	+	0.145576i
$477$	3.52260			0.161289
$478$			46.5019i			2.12695i
$479$	27.0506	+	27.0506i	1.23598	+	1.23598i	0.961632	+	0.274344i	$0.0884607\pi$
$479$	27.0506	+	27.0506i	1.23598	+	1.23598i	0.274344	+	0.961632i	$0.411539\pi$
$480$	28.2480			1.28934
$481$	2.94108	+	5.31000i	0.134102	+	0.242115i
$482$	−33.5461			−1.52798
$483$	−6.81782	+	6.81782i	−0.310222	+	0.310222i
$484$	6.98383	+	22.3491i	0.317447	+	1.01587i
$485$		−	13.0438i		−	0.592289i
$486$	−1.43677	+	1.43677i	−0.0651733	+	0.0651733i
$487$	7.83176	+	7.83176i	0.354891	+	0.354891i	0.861926	−	0.507035i	$-0.169258\pi$
$487$	7.83176	+	7.83176i	0.354891	+	0.354891i	−0.507035	+	0.861926i	$0.669258\pi$
$488$	−0.419050	+	0.419050i	−0.0189695	+	0.0189695i
$489$	0.610390	−	0.610390i	0.0276028	−	0.0276028i
$490$		−	40.4089i		−	1.82549i
$491$	−11.1179			−0.501745			−0.250873	−	0.968020i	$-0.580718\pi$
$491$	−11.1179			−0.501745			−0.250873	+	0.968020i	$0.580718\pi$
$492$	2.22320	+	2.22320i	0.100230	+	0.100230i
$493$			10.6082i			0.477770i
$494$	52.1192	+	14.9636i	2.34495	+	0.673245i
$495$	6.85635	−	9.32584i	0.308170	−	0.419165i
$496$	15.6173	+	15.6173i	0.701237	+	0.701237i
$497$			6.31939i			0.283463i
$498$		−	6.30008i		−	0.282313i
$499$	−17.9331	−	17.9331i	−0.802798	−	0.802798i	0.180734	−	0.983532i	$-0.442153\pi$
$499$	−17.9331	−	17.9331i	−0.802798	−	0.802798i	−0.983532	+	0.180734i	$0.942153\pi$
$500$	−11.4520	−	11.4520i	−0.512150	−	0.512150i
$501$	4.01508	+	4.01508i	0.179380	+	0.179380i
$502$	−8.92952	−	8.92952i	−0.398544	−	0.398544i
$503$			7.08080i			0.315717i	0.987462	+	0.157859i	$0.0504590\pi$
$503$			7.08080i			0.315717i	−0.987462	+	0.157859i	$0.949541\pi$
$504$			0.298180i			0.0132820i
$505$	−23.3817	−	23.3817i	−1.04047	−	1.04047i
$506$	33.7354	−	45.8860i	1.49972	−	2.03988i
$507$	−11.0201	−	6.89625i	−0.489418	−	0.306273i
$508$			7.73496i			0.343183i
$509$	−18.6114	−	18.6114i	−0.824938	−	0.824938i	0.161874	−	0.986811i	$-0.448246\pi$
$509$	−18.6114	−	18.6114i	−0.824938	−	0.824938i	−0.986811	+	0.161874i	$0.948246\pi$
$510$	−13.1157			−0.580772
$511$		−	12.7433i		−	0.563730i
$512$	−22.7035	+	22.7035i	−1.00336	+	1.00336i
$513$	−5.23369	+	5.23369i	−0.231073	+	0.231073i
$514$	4.15376	+	4.15376i	0.183215	+	0.183215i
$515$	49.7362	−	49.7362i	2.19164	−	2.19164i
$516$		−	5.39067i		−	0.237311i
$517$	−9.77963	−	7.18997i	−0.430108	−	0.316215i
$518$	−2.75967	+	2.75967i	−0.121253	+	0.121253i
$519$	−12.4826			−0.547925
$520$	3.16103	+	0.907545i	0.138621	+	0.0397985i
$521$	27.7135			1.21415			0.607076	−	0.794644i	$-0.292342\pi$
$521$	27.7135			1.21415			0.607076	+	0.794644i	$0.292342\pi$
$522$	8.24075	+	8.24075i	0.360688	+	0.360688i
$523$			39.6665i			1.73450i	0.497876	+	0.867248i	$0.334114\pi$
$523$			39.6665i			1.73450i	−0.497876	+	0.867248i	$0.665886\pi$
$524$	27.0487			1.18163
$525$	−5.79242	+	5.79242i	−0.252802	+	0.252802i
$526$	25.6965	+	25.6965i	1.12042	+	1.12042i
$527$	−7.75179	−	7.75179i	−0.337673	−	0.337673i
$528$	1.86438	+	12.2170i	0.0811366	+	0.531676i
$529$	−48.4216			−2.10529
$530$	24.9799			1.08506
$531$	−8.26157	+	8.26157i	−0.358522	+	0.358522i
$532$			17.9750i			0.779314i
$533$	−2.58035	−	4.65871i	−0.111767	−	0.201791i
$534$			31.9189i			1.38127i
$535$	33.0786	−	33.0786i	1.43011	−	1.43011i
$536$		−	3.96099i		−	0.171089i
$537$		−	13.0366i		−	0.562571i
$538$	3.22066	−	3.22066i	0.138853	−	0.138853i
$539$	18.6830	−	2.85113i	0.804735	−	0.122807i
$540$	−5.25303	+	5.25303i	−0.226054	+	0.226054i
$541$	5.36868	+	5.36868i	0.230817	+	0.230817i	0.813034	−	0.582216i	$-0.197814\pi$
$541$	5.36868	+	5.36868i	0.230817	+	0.230817i	−0.582216	+	0.813034i	$0.697814\pi$
$542$	−0.927248			−0.0398287
$543$		−	3.27418i		−	0.140509i
$544$	10.5855	−	10.5855i	0.453849	−	0.453849i
$545$	−52.0331			−2.22885
$546$	2.30653	−	8.03379i	0.0987105	−	0.343815i
$547$		−	14.2020i		−	0.607232i	−0.952794	−	0.303616i	$-0.901806\pi$
$547$		−	14.2020i		−	0.607232i	0.952794	−	0.303616i	$-0.0981941\pi$
$548$	4.00760	+	4.00760i	0.171196	+	0.171196i
$549$			2.26751i			0.0967749i
$550$	28.6616	−	38.9848i	1.22213	−	1.66232i
$551$	30.0183	+	30.0183i	1.27882	+	1.27882i
$552$	−1.56182	+	1.56182i	−0.0664756	+	0.0664756i
$553$	−2.62778	+	2.62778i	−0.111744	+	0.111744i
$554$	−6.30222	+	6.30222i	−0.267756	+	0.267756i
$555$	−5.87556			−0.249403
$556$	−35.7485			−1.51607
$557$	8.68613	+	8.68613i	0.368043	+	0.368043i	0.866763	−	0.498720i	$-0.166196\pi$
$557$	8.68613	+	8.68613i	0.368043	+	0.368043i	−0.498720	+	0.866763i	$0.666196\pi$
$558$	−12.0436			−0.509847
$559$	−2.51973	+	8.77638i	−0.106573	+	0.371201i
$560$		−	14.8367i		−	0.626965i
$561$	−0.925402	−	6.06402i	−0.0390705	−	0.256023i
$562$	−5.39032			−0.227377
$563$	−35.2328			−1.48488			−0.742442	−	0.669911i	$-0.766332\pi$
$563$	−35.2328			−1.48488			−0.742442	+	0.669911i	$0.766332\pi$
$564$	5.50863	+	5.50863i	0.231955	+	0.231955i
$565$	0.516754	+	0.516754i	0.0217400	+	0.0217400i
$566$	26.0191	−	26.0191i	1.09366	−	1.09366i
$567$	0.806735	+	0.806735i	0.0338797	+	0.0338797i
$568$			1.44764i			0.0607418i
$569$	19.4480			0.815301			0.407651	−	0.913138i	$-0.366348\pi$
$569$	19.4480			0.815301			0.407651	+	0.913138i	$0.366348\pi$
$570$	−37.1138	+	37.1138i	−1.55453	+	1.55453i
$571$	24.7198			1.03449			0.517246	−	0.855837i	$-0.326957\pi$
$571$	24.7198			1.03449			0.517246	+	0.855837i	$0.326957\pi$
$572$	−3.25302	+	25.2459i	−0.136015	+	1.05559i
$573$	1.34725			0.0562822
$574$	2.42119	−	2.42119i	0.101058	−	0.101058i
$575$	−60.6798			−2.53052
$576$		−	8.99379i		−	0.374741i
$577$	12.7206	+	12.7206i	0.529567	+	0.529567i	0.920443	−	0.390876i	$-0.127828\pi$
$577$	12.7206	+	12.7206i	0.529567	+	0.529567i	−0.390876	+	0.920443i	$0.627828\pi$
$578$	19.5102	−	19.5102i	0.811519	−	0.811519i
$579$	11.1141	+	11.1141i	0.461886	+	0.461886i
$580$	30.1293	+	30.1293i	1.25105	+	1.25105i
$581$	−3.53744			−0.146758
$582$	−7.59420			−0.314790
$583$	1.76250	+	11.5494i	0.0729954	+	0.478328i
$584$		−	2.91923i		−	0.120799i
$585$	11.0077	−	6.09689i	0.455111	−	0.252075i
$586$	3.63720			0.150251
$587$	−5.89486	−	5.89486i	−0.243307	−	0.243307i	0.574910	−	0.818217i	$-0.305037\pi$
$587$	−5.89486	−	5.89486i	−0.243307	−	0.243307i	−0.818217	+	0.574910i	$0.805037\pi$
$588$	−12.1297			−0.500219
$589$	−43.8709			−1.80767
$590$	−58.5855	+	58.5855i	−2.41193	+	2.41193i
$591$	−12.2514	+	12.2514i	−0.503955	+	0.503955i
$592$	4.43583	−	4.43583i	0.182312	−	0.182312i
$593$	25.2854	+	25.2854i	1.03835	+	1.03835i	0.999235	+	0.0391135i	$0.0124534\pi$
$593$	25.2854	+	25.2854i	1.03835	+	1.03835i	0.0391135	+	0.999235i	$0.487547\pi$
$594$	−5.42957	−	3.99182i	−0.222778	−	0.163786i
$595$			7.36434i			0.301909i
$596$	−15.8833	−	15.8833i	−0.650604	−	0.650604i
$597$			17.0285i			0.696929i
$598$	54.1612	−	29.9986i	2.21482	−	1.22673i
$599$	4.61398			0.188522			0.0942611	−	0.995548i	$-0.469951\pi$
$599$	4.61398			0.188522			0.0942611	+	0.995548i	$0.469951\pi$
$600$	−1.32693	+	1.32693i	−0.0541715	+	0.0541715i
$601$			11.4964i			0.468947i	0.972123	+	0.234473i	$0.0753366\pi$
$601$			11.4964i			0.468947i	−0.972123	+	0.234473i	$0.924663\pi$
$602$	−5.87073			−0.239273
$603$	−10.7166	−	10.7166i	−0.436414	−	0.436414i
$604$	0.382300	−	0.382300i	0.0155556	−	0.0155556i
$605$	34.0069	+	17.8136i	1.38258	+	0.724225i
$606$	−13.6130	+	13.6130i	−0.552989	+	0.552989i
$607$			27.2383i			1.10557i	0.833324	+	0.552784i	$0.186435\pi$
$607$			27.2383i			1.10557i	−0.833324	+	0.552784i	$0.813565\pi$
$608$		−	59.9081i		−	2.42959i
$609$	4.62711	−	4.62711i	0.187500	−	0.187500i
$610$			16.0797i			0.651047i
$611$	−6.39356	−	11.5433i	−0.258656	−	0.466992i
$612$			3.93697i			0.159143i
$613$	12.7736	−	12.7736i	0.515919	−	0.515919i	−0.400415	−	0.916334i	$-0.631134\pi$
$613$	12.7736	−	12.7736i	0.515919	−	0.515919i	0.916334	+	0.400415i	$0.131134\pi$
$614$	27.5551			1.11203
$615$	5.15489			0.207865
$616$	−0.977632	+	0.149192i	−0.0393899	+	0.00601111i
$617$	26.7508	+	26.7508i	1.07695	+	1.07695i	0.996782	+	0.0801644i	$0.0255445\pi$
$617$	26.7508	+	26.7508i	1.07695	+	1.07695i	0.0801644	+	0.996782i	$0.474455\pi$
$618$	−28.9568	−	28.9568i	−1.16481	−	1.16481i
$619$	7.99442	−	7.99442i	0.321323	−	0.321323i	−0.527952	−	0.849274i	$-0.677040\pi$
$619$	7.99442	−	7.99442i	0.321323	−	0.321323i	0.849274	+	0.527952i	$0.177040\pi$
$620$	−44.0330			−1.76841
$621$			8.45113i			0.339132i
$622$	20.8407	+	20.8407i	0.835634	+	0.835634i
$623$	17.9222			0.718037
$624$	−3.70747	+	12.9133i	−0.148418	+	0.516947i
$625$	9.34684			0.373874
$626$	22.1665	−	22.1665i	0.885952	−	0.885952i
$627$	−19.7782	−	14.5409i	−0.789863	−	0.580707i
$628$			20.3995i			0.814027i
$629$	−2.20177	+	2.20177i	−0.0877903	+	0.0877903i
$630$	5.72083	+	5.72083i	0.227923	+	0.227923i
$631$	1.17766	−	1.17766i	0.0468821	−	0.0468821i	−0.683277	−	0.730159i	$-0.739446\pi$
$631$	1.17766	−	1.17766i	0.0468821	−	0.0468821i	0.730159	+	0.683277i	$0.239446\pi$
$632$	−0.601970	+	0.601970i	−0.0239451	+	0.0239451i
$633$		−	24.6882i		−	0.981269i
$634$	−42.0260			−1.66907
$635$	8.96744	+	8.96744i	0.355862	+	0.355862i
$636$		−	7.49829i		−	0.297326i
$637$	19.7479	+	5.66971i	0.782442	+	0.224642i
$638$	−22.8955	+	31.1419i	−0.906441	+	1.23292i
$639$	3.91665	+	3.91665i	0.154940	+	0.154940i
$640$		−	7.28196i		−	0.287845i
$641$		−	17.0637i		−	0.673977i	−0.941509	−	0.336988i	$-0.890592\pi$
$641$		−	17.0637i		−	0.673977i	0.941509	−	0.336988i	$-0.109408\pi$
$642$	−19.2586	−	19.2586i	−0.760076	−	0.760076i
$643$	−24.7856	−	24.7856i	−0.977447	−	0.977447i	0.0223038	−	0.999751i	$-0.492900\pi$
$643$	−24.7856	−	24.7856i	−0.977447	−	0.977447i	−0.999751	+	0.0223038i	$0.992900\pi$
$644$	14.5126	+	14.5126i	0.571877	+	0.571877i
$645$	−6.24961	−	6.24961i	−0.246078	−	0.246078i
$646$			27.8156i			1.09439i
$647$		−	15.4495i		−	0.607384i	−0.952770	−	0.303692i	$-0.901781\pi$
$647$		−	15.4495i		−	0.607384i	0.952770	−	0.303692i	$-0.0982194\pi$
$648$	0.184806	+	0.184806i	0.00725988	+	0.00725988i
$649$	−31.2206	−	22.9533i	−1.22551	−	0.900997i
$650$	46.0154	−	25.4868i	1.80487	−	0.999675i
$651$			6.76239i			0.265039i
$652$	−1.29929	−	1.29929i	−0.0508842	−	0.0508842i
$653$	−38.5327			−1.50790			−0.753951	−	0.656930i	$-0.771855\pi$
$653$	−38.5327			−1.50790			−0.753951	+	0.656930i	$0.771855\pi$
$654$			30.2941i			1.18459i
$655$	31.3587	−	31.3587i	1.22528	−	1.22528i
$656$	−3.89176	+	3.89176i	−0.151948	+	0.151948i
$657$	−7.89807	−	7.89807i	−0.308133	−	0.308133i
$658$	5.99919	−	5.99919i	0.233873	−	0.233873i
$659$			33.1420i			1.29103i	0.763748	+	0.645515i	$0.223357\pi$
$659$			33.1420i			1.29103i	−0.763748	+	0.645515i	$0.776643\pi$
$660$	−19.8512	−	14.5946i	−0.772708	−	0.568094i
$661$	29.3873	−	29.3873i	1.14303	−	1.14303i	0.155141	−	0.987892i	$-0.450417\pi$
$661$	29.3873	−	29.3873i	1.14303	−	1.14303i	0.987892	−	0.155141i	$-0.0495831\pi$
$662$	−9.24850			−0.359453
$663$	1.84024	−	6.40966i	0.0714689	−	0.248931i
$664$	−0.810355			−0.0314479
$665$	20.8391	+	20.8391i	0.808105	+	0.808105i
$666$			3.42079i			0.132553i
$667$	48.4723			1.87686
$668$	8.54660	−	8.54660i	0.330678	−	0.330678i
$669$	7.74609	+	7.74609i	0.299481	+	0.299481i
$670$	−75.9950	−	75.9950i	−2.93594	−	2.93594i
$671$	−7.43441	+	1.13453i	−0.287002	+	0.0437981i
$672$	−9.23440			−0.356225
$673$	48.5415			1.87114			0.935568	−	0.353146i	$-0.114888\pi$
$673$	48.5415			1.87114			0.935568	+	0.353146i	$0.114888\pi$
$674$	17.7674	−	17.7674i	0.684376	−	0.684376i
$675$			7.18008i			0.276361i
$676$	−14.6795	+	23.4576i	−0.564598	+	0.902215i
$677$			17.7276i			0.681327i	0.940185	+	0.340664i	$0.110652\pi$
$677$			17.7276i			0.681327i	−0.940185	+	0.340664i	$0.889348\pi$
$678$	0.300858	−	0.300858i	0.0115544	−	0.0115544i
$679$			4.26408i			0.163640i
$680$			1.68702i			0.0646943i
$681$	13.9087	−	13.9087i	0.532982	−	0.532982i
$682$	−6.02593	−	39.4870i	−0.230745	−	1.51204i
$683$	−27.9977	+	27.9977i	−1.07130	+	1.07130i	−0.0740483	+	0.997255i	$0.523592\pi$
$683$	−27.9977	+	27.9977i	−1.07130	+	1.07130i	−0.997255	+	0.0740483i	$0.976408\pi$
$684$	11.1406	+	11.1406i	0.425970	+	0.425970i
$685$	9.29233			0.355042
$686$			29.4372i			1.12392i
$687$	6.81839	−	6.81839i	0.260138	−	0.260138i
$688$	9.43647			0.359762
$689$	−3.50489	+	12.2077i	−0.133526	+	0.465077i
$690$			59.9298i			2.28149i
$691$	15.0897	+	15.0897i	0.574041	+	0.574041i	0.933255	−	0.359214i	$-0.116955\pi$
$691$	15.0897	+	15.0897i	0.574041	+	0.574041i	−0.359214	+	0.933255i	$0.616955\pi$
$692$			26.5708i			1.01007i
$693$	−2.24137	+	3.04866i	−0.0851427	+	0.115809i
$694$	−5.40349	−	5.40349i	−0.205114	−	0.205114i
$695$	−41.4447	+	41.4447i	−1.57209	+	1.57209i
$696$	1.05998	−	1.05998i	0.0401783	−	0.0401783i
$697$	1.93171	−	1.93171i	0.0731689	−	0.0731689i
$698$	−66.1374			−2.50334
$699$	18.4834			0.699106
$700$	12.3299	+	12.3299i	0.466026	+	0.466026i
$701$	31.3880			1.18551			0.592754	−	0.805384i	$-0.298041\pi$
$701$	31.3880			1.18551			0.592754	+	0.805384i	$0.298041\pi$
$702$	−3.54965	−	6.40875i	−0.133973	−	0.241883i
$703$			12.4608i			0.469969i
$704$	29.4876	−	4.49997i	1.11136	−	0.169599i
$705$	12.7728			0.481050
$706$	−6.83390			−0.257197
$707$	7.64357	+	7.64357i	0.287466	+	0.287466i
$708$	17.5858	+	17.5858i	0.660915	+	0.660915i
$709$	9.02612	−	9.02612i	0.338983	−	0.338983i	−0.517001	−	0.855985i	$-0.672952\pi$
$709$	9.02612	−	9.02612i	0.338983	−	0.338983i	0.855985	+	0.517001i	$0.172952\pi$
$710$	27.7742	+	27.7742i	1.04235	+	1.04235i
$711$			3.25730i			0.122158i
$712$	4.10561			0.153864
$713$	−35.4205	+	35.4205i	−1.32651	+	1.32651i
$714$	4.28757			0.160458
$715$	25.4973	+	33.0400i	0.953544	+	1.23563i
$716$	−27.7501			−1.03707
$717$	16.1828	−	16.1828i	0.604356	−	0.604356i
$718$	10.0611			0.375476
$719$		−	11.2711i		−	0.420342i	−0.977665	−	0.210171i	$-0.932598\pi$
$719$		−	11.2711i		−	0.420342i	0.977665	−	0.210171i	$-0.0674021\pi$
$720$	−9.19553	−	9.19553i	−0.342697	−	0.342697i
$721$	−16.2590	+	16.2590i	−0.605516	+	0.605516i
$722$	51.4120	+	51.4120i	1.91336	+	1.91336i
$723$	11.6741	+	11.6741i	0.434165	+	0.434165i
$724$	−6.96951			−0.259020
$725$	41.1821			1.52946
$726$	10.3712	−	19.7990i	0.384911	−	0.734811i
$727$			29.3858i			1.08986i	0.838482	+	0.544929i	$0.183443\pi$
$727$			29.3858i			1.08986i	−0.838482	+	0.544929i	$0.816557\pi$
$728$	−1.03336	−	0.296681i	−0.0382987	−	0.0109957i
$729$	1.00000			0.0370370
$730$	−56.0078	−	56.0078i	−2.07294	−	2.07294i
$731$	−4.68388			−0.173240
$732$	4.82668			0.178399
$733$	13.4027	−	13.4027i	0.495041	−	0.495041i	−0.414849	−	0.909890i	$-0.636166\pi$
$733$	13.4027	−	13.4027i	0.495041	−	0.495041i	0.909890	+	0.414849i	$0.136166\pi$
$734$	−45.8372	+	45.8372i	−1.69188	+	1.69188i
$735$	−14.0624	+	14.0624i	−0.518700	+	0.518700i
$736$	−48.3685	−	48.3685i	−1.78289	−	1.78289i
$737$	29.7742	−	40.4981i	1.09675	−	1.49177i
$738$		−	3.00122i		−	0.110476i
$739$	−23.0478	−	23.0478i	−0.847827	−	0.847827i	0.142034	−	0.989862i	$-0.454636\pi$
$739$	−23.0478	−	23.0478i	−0.847827	−	0.847827i	−0.989862	+	0.142034i	$0.954636\pi$
$740$			12.5069i			0.459761i
$741$	−12.9302	−	23.3450i	−0.475004	−	0.857599i
$742$	−8.16604			−0.299785
$743$	35.2058	−	35.2058i	1.29158	−	1.29158i	0.357763	−	0.933812i	$-0.383540\pi$
$743$	35.2058	−	35.2058i	1.29158	−	1.29158i	0.933812	−	0.357763i	$-0.116460\pi$
$744$			1.54912i			0.0567937i
$745$	−36.8282			−1.34928
$746$	−14.0701	−	14.0701i	−0.515143	−	0.515143i
$747$	−2.19244	+	2.19244i	−0.0802173	+	0.0802173i
$748$	−12.9080	+	1.96983i	−0.471964	+	0.0720243i
$749$	−10.8135	+	10.8135i	−0.395118	+	0.395118i
$750$			15.4597i			0.564508i
$751$			3.34633i			0.122109i	0.998134	+	0.0610547i	$0.0194464\pi$
$751$			3.34633i			0.122109i	−0.998134	+	0.0610547i	$0.980554\pi$
$752$	−9.64297	+	9.64297i	−0.351643	+	0.351643i
$753$			6.21499i			0.226487i
$754$	−36.7580	+	20.3594i	−1.33865	+	0.741446i
$755$		−	0.886431i		−	0.0322605i
$756$	1.71724	−	1.71724i	0.0624553	−	0.0624553i
$757$	31.7572			1.15424			0.577118	−	0.816661i	$-0.304177\pi$
$757$	31.7572			1.15424			0.577118	+	0.816661i	$0.304177\pi$
$758$	−63.6340			−2.31129
$759$	−27.7085	+	4.22846i	−1.00575	+	0.153483i
$760$	4.77381	+	4.77381i	0.173164	+	0.173164i
$761$	9.87418	+	9.87418i	0.357939	+	0.357939i	0.863053	−	0.505114i	$-0.168550\pi$
$761$	9.87418	+	9.87418i	0.357939	+	0.357939i	−0.505114	+	0.863053i	$0.668550\pi$
$762$	5.22091	−	5.22091i	0.189134	−	0.189134i
$763$	17.0099			0.615798
$764$		−	2.86779i		−	0.103753i
$765$	4.56429	+	4.56429i	0.165022	+	0.165022i
$766$	−19.3975			−0.700862
$767$	−20.4108	−	36.8509i	−0.736993	−	1.33061i
$768$	13.7480			0.496087
$769$	−20.3212	+	20.3212i	−0.732800	+	0.732800i	−0.971174	−	0.238374i	$-0.923386\pi$
$769$	−20.3212	+	20.3212i	−0.732800	+	0.732800i	0.238374	+	0.971174i	$0.423386\pi$
$770$	−15.8943	+	21.6191i	−0.572791	+	0.779097i
$771$		−	2.89104i		−	0.104118i
$772$	23.6578	−	23.6578i	0.851462	−	0.851462i
$773$	−21.3311	−	21.3311i	−0.767225	−	0.767225i	0.210392	−	0.977617i	$-0.432526\pi$
$773$	−21.3311	−	21.3311i	−0.767225	−	0.767225i	−0.977617	+	0.210392i	$0.932526\pi$
$774$	−3.63857	+	3.63857i	−0.130786	+	0.130786i
$775$	−30.0932	+	30.0932i	−1.08098	+	1.08098i
$776$			0.976813i			0.0350655i
$777$	1.92074			0.0689063
$778$	−0.274306	−	0.274306i	−0.00983436	−	0.00983436i
$779$		−	10.9324i		−	0.391696i
$780$	−12.9780	−	23.4312i	−0.464687	−	0.838973i
$781$	−10.8817	+	14.8010i	−0.389378	+	0.529623i
$782$	22.4577	+	22.4577i	0.803087	+	0.803087i
$783$		−	5.73560i		−	0.204974i
$784$		−	21.2332i		−	0.758330i
$785$	23.6499	+	23.6499i	0.844101	+	0.844101i
$786$	−18.2573	−	18.2573i	−0.651215	−	0.651215i
$787$	−16.4657	−	16.4657i	−0.586939	−	0.586939i	0.349862	−	0.936801i	$-0.386228\pi$
$787$	−16.4657	−	16.4657i	−0.586939	−	0.586939i	−0.936801	+	0.349862i	$0.886228\pi$
$788$	26.0786	+	26.0786i	0.929012	+	0.929012i
$789$		−	17.8849i		−	0.636718i
$790$			23.0986i			0.821811i
$791$	−0.168929	−	0.168929i	−0.00600643	−	0.00600643i
$792$	−0.513452	+	0.698385i	−0.0182447	+	0.0248160i
$793$	−7.85816	−	2.25611i	−0.279052	−	0.0801168i
$794$		−	39.6680i		−	1.40777i
$795$	−8.69306	−	8.69306i	−0.308311	−	0.308311i
$796$	36.2473			1.28475
$797$		−	16.6430i		−	0.589527i	−0.955570	−	0.294763i	$-0.904759\pi$
$797$		−	16.6430i		−	0.589527i	0.955570	−	0.294763i	$-0.0952408\pi$
$798$	12.1327	−	12.1327i	0.429492	−	0.429492i
$799$	4.78638	−	4.78638i	0.169330	−	0.169330i
$800$	−41.0939	−	41.0939i	−1.45289	−	1.45289i
$801$	11.1079	−	11.1079i	0.392477	−	0.392477i
$802$			5.43325i			0.191855i
$803$	21.9434	−	29.8469i	0.774366	−	1.05327i
$804$	−22.8116	+	22.8116i	−0.804504	+	0.804504i
$805$	33.6501			1.18601
$806$	11.9831	−	41.7377i	0.422086	−	1.47015i
$807$	−2.24160			−0.0789079
$808$	1.75098	+	1.75098i	0.0615994	+	0.0615994i
$809$		−	39.0144i		−	1.37167i	−0.727756	−	0.685836i	$-0.759437\pi$
$809$		−	39.0144i		−	1.37167i	0.727756	−	0.685836i	$-0.240563\pi$
$810$	7.09133			0.249164
$811$	3.16389	−	3.16389i	0.111099	−	0.111099i	−0.649372	−	0.760471i	$-0.724968\pi$
$811$	3.16389	−	3.16389i	0.111099	−	0.111099i	0.760471	+	0.649372i	$0.224968\pi$
$812$	−9.84939	−	9.84939i	−0.345646	−	0.345646i
$813$	0.322684	+	0.322684i	0.0113170	+	0.0113170i
$814$	−11.2156	+	1.71157i	−0.393108	+	0.0599904i
$815$	−3.01264			−0.105528
$816$	−6.89175			−0.241260
$817$	−13.2541	+	13.2541i	−0.463703	+	0.463703i
$818$		−	1.02478i		−	0.0358305i
$819$	−3.59846	+	1.99310i	−0.125740	+	0.0696446i
$820$		−	10.9728i		−	0.383188i
$821$	15.4509	−	15.4509i	0.539240	−	0.539240i	−0.384066	−	0.923306i	$-0.625476\pi$
$821$	15.4509	−	15.4509i	0.539240	−	0.539240i	0.923306	+	0.384066i	$0.125476\pi$
$822$		−	5.41006i		−	0.188698i
$823$			10.8572i			0.378459i	0.981933	+	0.189230i	$0.0605991\pi$
$823$			10.8572i			0.378459i	−0.981933	+	0.189230i	$0.939401\pi$
$824$	−3.72460	+	3.72460i	−0.129753	+	0.129753i
$825$	−23.5411	+	3.59250i	−0.819596	+	0.125075i
$826$	19.1519	−	19.1519i	0.666379	−	0.666379i
$827$	−37.6510	−	37.6510i	−1.30925	−	1.30925i	−0.921954	−	0.387300i	$-0.873408\pi$
$827$	−37.6510	−	37.6510i	−1.30925	−	1.30925i	−0.387300	−	0.921954i	$-0.626592\pi$
$828$	17.9893			0.625171
$829$			23.8056i			0.826804i	0.910549	+	0.413402i	$0.135660\pi$
$829$			23.8056i			0.826804i	−0.910549	+	0.413402i	$0.864340\pi$
$830$	−15.5473	+	15.5473i	−0.539656	+	0.539656i
$831$	4.38638			0.152162
$832$	31.1684	+	8.94858i	1.08057	+	0.310236i
$833$			10.5393i			0.365166i
$834$	24.1294	+	24.1294i	0.835532	+	0.835532i
$835$		−	19.8168i		−	0.685789i
$836$	−30.9521	+	42.1003i	−1.07050	+	1.45607i
$837$	4.19121	+	4.19121i	0.144869	+	0.144869i
$838$	18.3113	−	18.3113i	0.632553	−	0.632553i
$839$	−23.5223	+	23.5223i	−0.812080	+	0.812080i	−0.984945	−	0.172866i	$-0.944697\pi$
$839$	−23.5223	+	23.5223i	−0.812080	+	0.812080i	0.172866	+	0.984945i	$0.444697\pi$
$840$	0.735848	−	0.735848i	0.0253892	−	0.0253892i
$841$	−3.89711			−0.134383
$842$	5.06255			0.174467
$843$	1.87584	+	1.87584i	0.0646075	+	0.0646075i
$844$	−52.5520			−1.80891
$845$	10.1767	+	44.2139i	0.350090	+	1.52100i
$846$		−	7.43639i		−	0.255668i
$847$	−11.1170	−	5.82334i	−0.381984	−	0.200092i
$848$	13.1259			0.450745
$849$	−18.1094			−0.621513
$850$	19.0801	+	19.0801i	0.654441	+	0.654441i
$851$	10.0606	+	10.0606i	0.344873	+	0.344873i
$852$	8.33708	−	8.33708i	0.285624	−	0.285624i
$853$	−10.5053	−	10.5053i	−0.359694	−	0.359694i	0.504006	−	0.863700i	$-0.331859\pi$
$853$	−10.5053	−	10.5053i	−0.359694	−	0.359694i	−0.863700	+	0.504006i	$0.831859\pi$
$854$		−	5.25651i		−	0.179874i
$855$	25.8314			0.883415
$856$	−2.47716	+	2.47716i	−0.0846676	+	0.0846676i
$857$	−25.9215			−0.885463			−0.442731	−	0.896654i	$-0.645990\pi$
$857$	−25.9215			−0.885463			−0.442731	+	0.896654i	$0.645990\pi$
$858$	19.2361	−	14.8447i	0.656710	−	0.506790i
$859$	3.11975			0.106444			0.0532222	−	0.998583i	$-0.483051\pi$
$859$	3.11975			0.106444			0.0532222	+	0.998583i	$0.483051\pi$
$860$	−13.3031	+	13.3031i	−0.453632	+	0.453632i
$861$	−1.68516			−0.0574300
$862$		−	49.0506i		−	1.67067i
$863$	−35.8583	−	35.8583i	−1.22063	−	1.22063i	−0.967408	−	0.253222i	$-0.918510\pi$
$863$	−35.8583	−	35.8583i	−1.22063	−	1.22063i	−0.253222	−	0.967408i	$-0.581490\pi$
$864$	−5.72332	+	5.72332i	−0.194711	+	0.194711i
$865$	30.8046	+	30.8046i	1.04739	+	1.04739i
$866$	−35.9739	−	35.9739i	−1.22244	−	1.22244i
$867$	−13.5792			−0.461174
$868$	14.3946			0.488584
$869$	−10.6796	+	1.62976i	−0.362281	+	0.0552860i
$870$		−	40.6731i		−	1.37895i
$871$	47.8016	−	26.4762i	1.61970	−	0.897111i
$872$	3.89661			0.131956
$873$	2.64280	+	2.64280i	0.0894452	+	0.0894452i
$874$	127.099			4.29917
$875$	8.68048			0.293454
$876$	−16.8120	+	16.8120i	−0.568026	+	0.568026i
$877$	26.7951	−	26.7951i	0.904806	−	0.904806i	−0.0910412	−	0.995847i	$-0.529019\pi$
$877$	26.7951	−	26.7951i	0.904806	−	0.904806i	0.995847	+	0.0910412i	$0.0290195\pi$
$878$	16.7585	−	16.7585i	0.565572	−	0.565572i
$879$	−1.26575	−	1.26575i	−0.0426928	−	0.0426928i
$880$	25.5482	−	34.7500i	0.861228	−	1.17142i
$881$		−	43.6508i		−	1.47063i	−0.677725	−	0.735316i	$-0.737034\pi$
$881$		−	43.6508i		−	1.47063i	0.677725	−	0.735316i	$-0.262966\pi$
$882$	8.18724	+	8.18724i	0.275679	+	0.275679i
$883$			34.4945i			1.16083i	0.814320	+	0.580416i	$0.197110\pi$
$883$			34.4945i			1.16083i	−0.814320	+	0.580416i	$0.802890\pi$
$884$	−13.6438	−	3.91718i	−0.458890	−	0.131749i
$885$	40.7758			1.37066
$886$	−20.6910	+	20.6910i	−0.695128	+	0.695128i
$887$			34.1259i			1.14583i	0.819613	+	0.572917i	$0.194188\pi$
$887$			34.1259i			1.14583i	−0.819613	+	0.572917i	$0.805812\pi$
$888$	0.440003			0.0147655
$889$	−2.93150	−	2.93150i	−0.0983193	−	0.0983193i
$890$	78.7695	−	78.7695i	2.64036	−	2.64036i
$891$	0.500342	+	3.27867i	0.0167621	+	0.109839i
$892$	16.4885	−	16.4885i	0.552077	−	0.552077i
$893$		−	27.0883i		−	0.906476i
$894$			21.4417i			0.717116i
$895$	−32.1718	+	32.1718i	−1.07538	+	1.07538i
$896$			2.38050i			0.0795271i
$897$	−29.2878	−	8.40865i	−0.977892	−	0.280757i
$898$			4.02589i			0.134346i
$899$	24.0391	−	24.0391i	0.801749	−	0.801749i
$900$	15.2837			0.509457
$901$	−6.51517			−0.217052
$902$	9.83999	−	1.50164i	0.327636	−	0.0499990i
$903$	2.04303	+	2.04303i	0.0679877	+	0.0679877i
$904$	−0.0386982	−	0.0386982i	−0.00128708	−	0.00128708i
$905$	−8.08003	+	8.08003i	−0.268589	+	0.268589i
$906$	−0.516087			−0.0171458
$907$			18.7633i			0.623027i	0.950242	+	0.311513i	$0.100836\pi$
$907$			18.7633i			0.623027i	−0.950242	+	0.311513i	$0.899164\pi$
$908$	−29.6064	−	29.6064i	−0.982523	−	0.982523i
$909$	9.47469			0.314256
$910$	−25.5179	+	14.1337i	−0.845909	+	0.468529i
$911$	−33.4630			−1.10868			−0.554339	−	0.832291i	$-0.687029\pi$
$911$	−33.4630			−1.10868			−0.554339	+	0.832291i	$0.687029\pi$
$912$	−19.5018	+	19.5018i	−0.645769	+	0.645769i
$913$	−8.28526	−	6.09132i	−0.274202	−	0.201593i
$914$			7.97889i			0.263918i
$915$	5.59576	−	5.59576i	0.184990	−	0.184990i
$916$	−14.5138	−	14.5138i	−0.479550	−	0.479550i
$917$	−10.2513	+	10.2513i	−0.338527	+	0.338527i
$918$	2.65736	−	2.65736i	0.0877060	−	0.0877060i
$919$			48.2550i			1.59178i	0.605438	+	0.795892i	$0.292998\pi$
$919$			48.2550i			1.59178i	−0.605438	+	0.795892i	$0.707002\pi$
$920$	7.70854			0.254143
$921$	−9.58923	−	9.58923i	−0.315976	−	0.315976i
$922$		−	13.8744i		−	0.456929i
$923$	−17.4703	+	9.67637i	−0.575041	+	0.318502i
$924$	6.48946	+	4.77104i	0.213487	+	0.156956i
$925$	8.54748	+	8.54748i	0.281039	+	0.281039i
$926$			35.0420i			1.15155i
$927$			20.1541i			0.661946i
$928$	32.8267	+	32.8267i	1.07759	+	1.07759i
$929$	11.8711	+	11.8711i	0.389479	+	0.389479i	0.874501	−	0.485023i	$-0.161189\pi$
$929$	11.8711	+	11.8711i	0.389479	+	0.389479i	−0.485023	+	0.874501i	$0.661189\pi$
$930$	29.7212	+	29.7212i	0.974598	+	0.974598i
$931$	29.8234	+	29.8234i	0.977423	+	0.977423i
$932$		−	39.3442i		−	1.28876i
$933$		−	14.5052i		−	0.474879i
$934$	−31.2062	−	31.2062i	−1.02110	−	1.02110i
$935$	−12.6811	+	17.2485i	−0.414716	+	0.564086i
$936$	−0.824333	+	0.456578i	−0.0269442	+	0.0149237i
$937$		−	5.86594i		−	0.191632i	−0.995399	−	0.0958159i	$-0.969454\pi$
$937$		−	5.86594i		−	0.191632i	0.995399	−	0.0958159i	$-0.0305460\pi$
$938$	24.8431	+	24.8431i	0.811156	+	0.811156i
$939$	−15.4280			−0.503473
$940$		−	27.1884i		−	0.886788i
$941$	−34.4772	+	34.4772i	−1.12392	+	1.12392i	−0.132778	+	0.991146i	$0.542390\pi$
$941$	−34.4772	+	34.4772i	−1.12392	+	1.12392i	−0.991146	+	0.132778i	$0.957610\pi$
$942$	13.7691	−	13.7691i	0.448623	−	0.448623i
$943$	−8.82662	−	8.82662i	−0.287434	−	0.287434i
$944$	−30.7843	+	30.7843i	−1.00194	+	1.00194i
$945$		−	3.98172i		−	0.129525i
$946$	−13.7502	−	10.1091i	−0.447057	−	0.328676i
$947$	10.4611	−	10.4611i	0.339941	−	0.339941i	−0.516404	−	0.856345i	$-0.672730\pi$
$947$	10.4611	−	10.4611i	0.339941	−	0.339941i	0.856345	+	0.516404i	$0.172730\pi$
$948$	6.93357			0.225192
$949$	35.2295	−	19.5128i	1.14360	−	0.633412i
$950$	107.983			3.50343
$951$	14.6252	+	14.6252i	0.474253	+	0.474253i
$952$		−	0.551494i		−	0.0178740i
$953$	7.22162			0.233931			0.116966	−	0.993136i	$-0.462683\pi$
$953$	7.22162			0.233931			0.116966	+	0.993136i	$0.462683\pi$
$954$	−5.06117	+	5.06117i	−0.163861	+	0.163861i
$955$	−3.32475	−	3.32475i	−0.107586	−	0.107586i
$956$	−34.4471	−	34.4471i	−1.11410	−	1.11410i
$957$	18.8051	−	2.86976i	0.607883	−	0.0927663i
$958$	−77.7312			−2.51138
$959$	−3.03770			−0.0980926
$960$	−22.1949	+	22.1949i	−0.716337	+	0.716337i
$961$			4.13245i			0.133305i
$962$	−11.8549	−	3.40359i	−0.382218	−	0.109736i
$963$			13.4041i			0.431940i
$964$	24.8498	−	24.8498i	0.800359	−	0.800359i
$965$		−	54.8548i		−	1.76584i
$966$		−	19.5913i		−	0.630340i
$967$	35.5858	−	35.5858i	1.14436	−	1.14436i	0.156720	−	0.987643i	$-0.449908\pi$
$967$	35.5858	−	35.5858i	1.14436	−	1.14436i	0.987643	−	0.156720i	$-0.0500922\pi$
$968$	−2.54667	−	1.33401i	−0.0818532	−	0.0428766i
$969$	9.67990	−	9.67990i	0.310963	−	0.310963i
$970$	18.7410	+	18.7410i	0.601736	+	0.601736i
$971$	23.6070			0.757585			0.378793	−	0.925482i	$-0.376339\pi$
$971$	23.6070			0.757585			0.378793	+	0.925482i	$0.376339\pi$
$972$		−	2.12863i		−	0.0682757i
$973$	13.5484	−	13.5484i	0.434343	−	0.434343i
$974$	−22.5049			−0.721103
$975$	−24.8829	−	7.14398i	−0.796891	−	0.228791i
$976$			8.44920i			0.270452i
$977$	−25.6179	−	25.6179i	−0.819590	−	0.819590i	0.166459	−	0.986048i	$-0.446767\pi$
$977$	−25.6179	−	25.6179i	−0.819590	−	0.819590i	−0.986048	+	0.166459i	$0.946767\pi$
$978$			1.75398i			0.0560862i
$979$	41.9767	+	30.8612i	1.34158	+	0.986329i
$980$	29.9336	+	29.9336i	0.956194	+	0.956194i
$981$	10.5424	−	10.5424i	0.336593	−	0.336593i
$982$	15.9739	−	15.9739i	0.509748	−	0.509748i
$983$	3.30596	−	3.30596i	0.105444	−	0.105444i	−0.652417	−	0.757861i	$-0.726245\pi$
$983$	3.30596	−	3.30596i	0.105444	−	0.105444i	0.757861	+	0.652417i	$0.226245\pi$
$984$	−0.386035			−0.0123063
$985$	60.4680			1.92667
$986$	−15.2416	−	15.2416i	−0.485390	−	0.485390i
$987$	−4.17547			−0.132907
$988$	−49.6927	+	27.5236i	−1.58094	+	0.875643i
$989$			21.4022i			0.680550i
$990$	3.54809	+	23.2501i	0.112766	+	0.738937i
$991$	−33.8865			−1.07644			−0.538220	−	0.842804i	$-0.680903\pi$
$991$	−33.8865			−1.07644			−0.538220	+	0.842804i	$0.680903\pi$
$992$	−47.9752			−1.52321
$993$	3.21850	+	3.21850i	0.102136	+	0.102136i
$994$	−9.07952	−	9.07952i	−0.287985	−	0.287985i
$995$	42.0229	−	42.0229i	1.33221	−	1.33221i
$996$	4.66689	+	4.66689i	0.147876	+	0.147876i
$997$		−	15.7695i		−	0.499424i	−0.968320	−	0.249712i	$-0.919664\pi$
$997$		−	15.7695i		−	0.499424i	0.968320	−	0.249712i	$-0.0803359\pi$
$998$	51.5317			1.63121
$999$	1.19044	−	1.19044i	0.0376640	−	0.0376640i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	429.2.m.b.307.3	yes	28
11.10	odd	2	inner	429.2.m.b.307.12	yes	28
13.5	odd	4	inner	429.2.m.b.109.12	yes	28
143.109	even	4	inner	429.2.m.b.109.3	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
429.2.m.b.109.3	✓	28	143.109	even	4	inner
429.2.m.b.109.12	yes	28	13.5	odd	4	inner
429.2.m.b.307.3	yes	28	1.1	even	1	trivial
429.2.m.b.307.12	yes	28	11.10	odd	2	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)

\(f(q)\)	\(=\)	\(q+(-1.43677 + 1.43677i) q^{2} +1.00000 q^{3} -2.12863i q^{4} +(-2.46780 - 2.46780i) q^{5} +(-1.43677 + 1.43677i) q^{6} +(0.806735 + 0.806735i) q^{7} +(0.184806 + 0.184806i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.43677 + 1.43677i) q^{2} +1.00000 q^{3} -2.12863i q^{4} +(-2.46780 - 2.46780i) q^{5} +(-1.43677 + 1.43677i) q^{6} +(0.806735 + 0.806735i) q^{7} +(0.184806 + 0.184806i) q^{8} +1.00000 q^{9} +7.09133 q^{10} +(0.500342 + 3.27867i) q^{11} -2.12863i q^{12} +(-0.994973 + 3.46555i) q^{13} -2.31819 q^{14} +(-2.46780 - 2.46780i) q^{15} +3.72620 q^{16} -1.84954 q^{17} +(-1.43677 + 1.43677i) q^{18} +(-5.23369 + 5.23369i) q^{19} +(-5.25303 + 5.25303i) q^{20} +(0.806735 + 0.806735i) q^{21} +(-5.42957 - 3.99182i) q^{22} +8.45113i q^{23} +(0.184806 + 0.184806i) q^{24} +7.18008i q^{25} +(-3.54965 - 6.40875i) q^{26} +1.00000 q^{27} +(1.71724 - 1.71724i) q^{28} -5.73560i q^{29} +7.09133 q^{30} +(4.19121 + 4.19121i) q^{31} +(-5.72332 + 5.72332i) q^{32} +(0.500342 + 3.27867i) q^{33} +(2.65736 - 2.65736i) q^{34} -3.98172i q^{35} -2.12863i q^{36} +(1.19044 - 1.19044i) q^{37} -15.0392i q^{38} +(-0.994973 + 3.46555i) q^{39} -0.912131i q^{40} +(-1.04443 + 1.04443i) q^{41} -2.31819 q^{42} +2.53246 q^{43} +(6.97906 - 1.06504i) q^{44} +(-2.46780 - 2.46780i) q^{45} +(-12.1423 - 12.1423i) q^{46} +(-2.58788 + 2.58788i) q^{47} +3.72620 q^{48} -5.69836i q^{49} +(-10.3161 - 10.3161i) q^{50} -1.84954 q^{51} +(7.37686 + 2.11792i) q^{52} +3.52260 q^{53} +(-1.43677 + 1.43677i) q^{54} +(6.85635 - 9.32584i) q^{55} +0.298180i q^{56} +(-5.23369 + 5.23369i) q^{57} +(8.24075 + 8.24075i) q^{58} +(-8.26157 + 8.26157i) q^{59} +(-5.25303 + 5.25303i) q^{60} +2.26751i q^{61} -12.0436 q^{62} +(0.806735 + 0.806735i) q^{63} -8.99379i q^{64} +(11.0077 - 6.09689i) q^{65} +(-5.42957 - 3.99182i) q^{66} +(-10.7166 - 10.7166i) q^{67} +3.93697i q^{68} +8.45113i q^{69} +(5.72083 + 5.72083i) q^{70} +(3.91665 + 3.91665i) q^{71} +(0.184806 + 0.184806i) q^{72} +(-7.89807 - 7.89807i) q^{73} +3.42079i q^{74} +7.18008i q^{75} +(11.1406 + 11.1406i) q^{76} +(-2.24137 + 3.04866i) q^{77} +(-3.54965 - 6.40875i) q^{78} +3.25730i q^{79} +(-9.19553 - 9.19553i) q^{80} +1.00000 q^{81} -3.00122i q^{82} +(-2.19244 + 2.19244i) q^{83} +(1.71724 - 1.71724i) q^{84} +(4.56429 + 4.56429i) q^{85} +(-3.63857 + 3.63857i) q^{86} -5.73560i q^{87} +(-0.513452 + 0.698385i) q^{88} +(11.1079 - 11.1079i) q^{89} +7.09133 q^{90} +(-3.59846 + 1.99310i) q^{91} +17.9893 q^{92} +(4.19121 + 4.19121i) q^{93} -7.43639i q^{94} +25.8314 q^{95} +(-5.72332 + 5.72332i) q^{96} +(2.64280 + 2.64280i) q^{97} +(8.18724 + 8.18724i) q^{98} +(0.500342 + 3.27867i) 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

Modular forms

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