LMFDB - Embedded newform 429.2.m.a.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.a.109.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.12106 + 1.12106i) q^{2} -1.00000 q^{3} -0.513571i q^{4} +(0.850971 + 0.850971i) q^{5} +(1.12106 - 1.12106i) q^{6} +(-0.675060 - 0.675060i) q^{7} +(-1.66638 - 1.66638i) q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+(-1.12106 + 1.12106i) q^{2} -1.00000 q^{3} -0.513571i q^{4} +(0.850971 + 0.850971i) q^{5} +(1.12106 - 1.12106i) q^{6} +(-0.675060 - 0.675060i) q^{7} +(-1.66638 - 1.66638i) q^{8} +1.00000 q^{9} -1.90799 q^{10} +(-0.299521 + 3.30307i) q^{11} +0.513571i q^{12} +(-3.60528 - 0.0438666i) q^{13} +1.51357 q^{14} +(-0.850971 - 0.850971i) q^{15} +4.76339 q^{16} -7.43124 q^{17} +(-1.12106 + 1.12106i) q^{18} +(2.00891 - 2.00891i) q^{19} +(0.437034 - 0.437034i) q^{20} +(0.675060 + 0.675060i) q^{21} +(-3.36717 - 4.03874i) q^{22} +3.77898i q^{23} +(1.66638 + 1.66638i) q^{24} -3.55170i q^{25} +(4.09093 - 3.99258i) q^{26} -1.00000 q^{27} +(-0.346691 + 0.346691i) q^{28} +0.246409i q^{29} +1.90799 q^{30} +(-7.23254 - 7.23254i) q^{31} +(-2.00730 + 2.00730i) q^{32} +(0.299521 - 3.30307i) q^{33} +(8.33090 - 8.33090i) q^{34} -1.14891i q^{35} -0.513571i q^{36} +(0.872788 - 0.872788i) q^{37} +4.50424i q^{38} +(3.60528 + 0.0438666i) q^{39} -2.83609i q^{40} +(2.78745 - 2.78745i) q^{41} -1.51357 q^{42} -4.52405 q^{43} +(1.69636 + 0.153826i) q^{44} +(0.850971 + 0.850971i) q^{45} +(-4.23648 - 4.23648i) q^{46} +(2.70266 - 2.70266i) q^{47} -4.76339 q^{48} -6.08859i q^{49} +(3.98168 + 3.98168i) q^{50} +7.43124 q^{51} +(-0.0225286 + 1.85157i) q^{52} -12.4473 q^{53} +(1.12106 - 1.12106i) q^{54} +(-3.06570 + 2.55593i) q^{55} +2.24982i q^{56} +(-2.00891 + 2.00891i) q^{57} +(-0.276241 - 0.276241i) q^{58} +(-6.27696 + 6.27696i) q^{59} +(-0.437034 + 0.437034i) q^{60} -3.96296i q^{61} +16.2163 q^{62} +(-0.675060 - 0.675060i) q^{63} +5.02615i q^{64} +(-3.03066 - 3.10532i) q^{65} +(3.36717 + 4.03874i) q^{66} +(6.55818 + 6.55818i) q^{67} +3.81647i q^{68} -3.77898i q^{69} +(1.28801 + 1.28801i) q^{70} +(2.41976 + 2.41976i) q^{71} +(-1.66638 - 1.66638i) q^{72} +(5.88991 + 5.88991i) q^{73} +1.95690i q^{74} +3.55170i q^{75} +(-1.03172 - 1.03172i) q^{76} +(2.43197 - 2.02758i) q^{77} +(-4.09093 + 3.99258i) q^{78} +11.3349i q^{79} +(4.05350 + 4.05350i) q^{80} +1.00000 q^{81} +6.24982i q^{82} +(2.61335 - 2.61335i) q^{83} +(0.346691 - 0.346691i) q^{84} +(-6.32377 - 6.32377i) q^{85} +(5.07175 - 5.07175i) q^{86} -0.246409i q^{87} +(6.00330 - 5.00506i) q^{88} +(-5.39241 + 5.39241i) q^{89} -1.90799 q^{90} +(2.40417 + 2.46340i) q^{91} +1.94077 q^{92} +(7.23254 + 7.23254i) q^{93} +6.05972i q^{94} +3.41905 q^{95} +(2.00730 - 2.00730i) q^{96} +(-10.7087 - 10.7087i) q^{97} +(6.82570 + 6.82570i) q^{98} +(-0.299521 + 3.30307i) 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^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) $ 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

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 $

$2$	−1.12106	+	1.12106i	−0.792712	+	0.792712i	−0.981934	−	0.189222i	$-0.939403\pi$
$2$	−1.12106	+	1.12106i	−0.792712	+	0.792712i	0.189222	+	0.981934i	$0.439403\pi$
$3$	−1.00000			−0.577350
$3$	−1.00000			−0.577350
$4$		−	0.513571i		−	0.256786i
$5$	0.850971	+	0.850971i	0.380566	+	0.380566i	0.871306	−	0.490740i	$-0.163274\pi$
$5$	0.850971	+	0.850971i	0.380566	+	0.380566i	−0.490740	+	0.871306i	$0.663274\pi$
$6$	1.12106	−	1.12106i	0.457673	−	0.457673i
$7$	−0.675060	−	0.675060i	−0.255149	−	0.255149i	0.567929	−	0.823078i	$-0.307745\pi$
$7$	−0.675060	−	0.675060i	−0.255149	−	0.255149i	−0.823078	+	0.567929i	$0.807745\pi$
$8$	−1.66638	−	1.66638i	−0.589155	−	0.589155i
$9$	1.00000			0.333333
$10$	−1.90799			−0.603358
$11$	−0.299521	+	3.30307i	−0.0903091	+	0.995914i
$11$	−0.299521	+	3.30307i	−0.0903091	+	0.995914i
$12$			0.513571i			0.148255i
$13$	−3.60528	−	0.0438666i	−0.999926	−	0.0121664i
$13$	−3.60528	−	0.0438666i	−0.999926	−	0.0121664i
$14$	1.51357			0.404519
$15$	−0.850971	−	0.850971i	−0.219720	−	0.219720i
$16$	4.76339			1.19085
$17$	−7.43124			−1.80234			−0.901170	−	0.433466i	$-0.857290\pi$
$17$	−7.43124			−1.80234			−0.901170	+	0.433466i	$0.857290\pi$
$18$	−1.12106	+	1.12106i	−0.264237	+	0.264237i
$19$	2.00891	−	2.00891i	0.460876	−	0.460876i	−0.438067	−	0.898943i	$-0.644337\pi$
$19$	2.00891	−	2.00891i	0.460876	−	0.460876i	0.898943	+	0.438067i	$0.144337\pi$
$20$	0.437034	−	0.437034i	0.0977239	−	0.0977239i
$21$	0.675060	+	0.675060i	0.147310	+	0.147310i
$22$	−3.36717	−	4.03874i	−0.717884	−	0.861062i
$23$			3.77898i			0.787971i	0.919117	+	0.393986i	$0.128904\pi$
$23$			3.77898i			0.787971i	−0.919117	+	0.393986i	$0.871096\pi$
$24$	1.66638	+	1.66638i	0.340149	+	0.340149i
$25$		−	3.55170i		−	0.710339i
$26$	4.09093	−	3.99258i	0.802298	−	0.783009i
$27$	−1.00000			−0.192450
$28$	−0.346691	+	0.346691i	−0.0655185	+	0.0655185i
$29$			0.246409i			0.0457571i	0.999738	+	0.0228785i	$0.00728310\pi$
$29$			0.246409i			0.0457571i	−0.999738	+	0.0228785i	$0.992717\pi$
$30$	1.90799			0.348349
$31$	−7.23254	−	7.23254i	−1.29900	−	1.29900i	−0.929051	−	0.369952i	$-0.879374\pi$
$31$	−7.23254	−	7.23254i	−1.29900	−	1.29900i	−0.369952	−	0.929051i	$-0.620626\pi$
$32$	−2.00730	+	2.00730i	−0.354844	+	0.354844i
$33$	0.299521	−	3.30307i	0.0521400	−	0.574991i
$34$	8.33090	−	8.33090i	1.42874	−	1.42874i
$35$		−	1.14891i		−	0.194202i
$36$		−	0.513571i		−	0.0855952i
$37$	0.872788	−	0.872788i	0.143486	−	0.143486i	−0.631715	−	0.775201i	$-0.717649\pi$
$37$	0.872788	−	0.872788i	0.143486	−	0.143486i	0.775201	+	0.631715i	$0.217649\pi$
$38$			4.50424i			0.730684i
$39$	3.60528	+	0.0438666i	0.577308	+	0.00702427i
$40$		−	2.83609i		−	0.448425i
$41$	2.78745	−	2.78745i	0.435326	−	0.435326i	−0.455109	−	0.890436i	$-0.650400\pi$
$41$	2.78745	−	2.78745i	0.435326	−	0.435326i	0.890436	+	0.455109i	$0.150400\pi$
$42$	−1.51357			−0.233549
$43$	−4.52405			−0.689911			−0.344955	−	0.938619i	$-0.612106\pi$
$43$	−4.52405			−0.689911			−0.344955	+	0.938619i	$0.612106\pi$
$44$	1.69636	+	0.153826i	0.255736	+	0.0231901i
$45$	0.850971	+	0.850971i	0.126855	+	0.126855i
$46$	−4.23648	−	4.23648i	−0.624635	−	0.624635i
$47$	2.70266	−	2.70266i	0.394224	−	0.394224i	−0.481966	−	0.876190i	$-0.660077\pi$
$47$	2.70266	−	2.70266i	0.394224	−	0.394224i	0.876190	+	0.481966i	$0.160077\pi$
$48$	−4.76339			−0.687536
$49$		−	6.08859i		−	0.869798i
$50$	3.98168	+	3.98168i	0.563095	+	0.563095i
$51$	7.43124			1.04058
$52$	−0.0225286	+	1.85157i	−0.00312416	+	0.256767i
$53$	−12.4473			−1.70976			−0.854882	−	0.518822i	$-0.826371\pi$
$53$	−12.4473			−1.70976			−0.854882	+	0.518822i	$0.826371\pi$
$54$	1.12106	−	1.12106i	0.152558	−	0.152558i
$55$	−3.06570	+	2.55593i	−0.413379	+	0.344642i
$56$			2.24982i			0.300644i
$57$	−2.00891	+	2.00891i	−0.266087	+	0.266087i
$58$	−0.276241	−	0.276241i	−0.0362722	−	0.0362722i
$59$	−6.27696	+	6.27696i	−0.817190	+	0.817190i	−0.985700	−	0.168510i	$-0.946105\pi$
$59$	−6.27696	+	6.27696i	−0.817190	+	0.817190i	0.168510	+	0.985700i	$0.446105\pi$
$60$	−0.437034	+	0.437034i	−0.0564209	+	0.0564209i
$61$		−	3.96296i		−	0.507405i	−0.967282	−	0.253702i	$-0.918352\pi$
$61$		−	3.96296i		−	0.507405i	0.967282	−	0.253702i	$-0.0816484\pi$
$62$	16.2163			2.05947
$63$	−0.675060	−	0.675060i	−0.0850496	−	0.0850496i
$64$			5.02615i			0.628269i
$65$	−3.03066	−	3.10532i	−0.375907	−	0.385168i
$66$	3.36717	+	4.03874i	0.414471	+	0.497135i
$67$	6.55818	+	6.55818i	0.801209	+	0.801209i	0.983285	−	0.182076i	$-0.0582816\pi$
$67$	6.55818	+	6.55818i	0.801209	+	0.801209i	−0.182076	+	0.983285i	$0.558282\pi$
$68$			3.81647i			0.462815i
$69$		−	3.77898i		−	0.454935i
$70$	1.28801	+	1.28801i	0.153946	+	0.153946i
$71$	2.41976	+	2.41976i	0.287173	+	0.287173i	0.835961	−	0.548788i	$-0.184911\pi$
$71$	2.41976	+	2.41976i	0.287173	+	0.287173i	−0.548788	+	0.835961i	$0.684911\pi$
$72$	−1.66638	−	1.66638i	−0.196385	−	0.196385i
$73$	5.88991	+	5.88991i	0.689362	+	0.689362i	0.962091	−	0.272729i	$-0.0879263\pi$
$73$	5.88991	+	5.88991i	0.689362	+	0.689362i	−0.272729	+	0.962091i	$0.587926\pi$
$74$			1.95690i			0.227485i
$75$			3.55170i			0.410115i
$76$	−1.03172	−	1.03172i	−0.118346	−	0.118346i
$77$	2.43197	−	2.02758i	0.277148	−	0.231064i
$78$	−4.09093	+	3.99258i	−0.463207	+	0.452071i
$79$			11.3349i			1.27528i	0.770334	+	0.637640i	$0.220089\pi$
$79$			11.3349i			1.27528i	−0.770334	+	0.637640i	$0.779911\pi$
$80$	4.05350	+	4.05350i	0.453196	+	0.453196i
$81$	1.00000			0.111111
$82$			6.24982i			0.690177i
$83$	2.61335	−	2.61335i	0.286853	−	0.286853i	−0.548982	−	0.835834i	$-0.684984\pi$
$83$	2.61335	−	2.61335i	0.286853	−	0.286853i	0.835834	+	0.548982i	$0.184984\pi$
$84$	0.346691	−	0.346691i	0.0378271	−	0.0378271i
$85$	−6.32377	−	6.32377i	−0.685909	−	0.685909i
$86$	5.07175	−	5.07175i	0.546901	−	0.546901i
$87$		−	0.246409i		−	0.0264179i
$88$	6.00330	−	5.00506i	0.639954	−	0.533542i
$89$	−5.39241	+	5.39241i	−0.571594	+	0.571594i	−0.932574	−	0.360980i	$-0.882442\pi$
$89$	−5.39241	+	5.39241i	−0.571594	+	0.571594i	0.360980	+	0.932574i	$0.382442\pi$
$90$	−1.90799			−0.201119
$91$	2.40417	+	2.46340i	0.252026	+	0.258234i
$92$	1.94077			0.202340
$93$	7.23254	+	7.23254i	0.749980	+	0.749980i
$94$			6.05972i			0.625012i
$95$	3.41905			0.350787
$96$	2.00730	−	2.00730i	0.204869	−	0.204869i
$97$	−10.7087	−	10.7087i	−1.08730	−	1.08730i	−0.995805	−	0.0914992i	$-0.970834\pi$
$97$	−10.7087	−	10.7087i	−1.08730	−	1.08730i	−0.0914992	−	0.995805i	$-0.529166\pi$
$98$	6.82570	+	6.82570i	0.689500	+	0.689500i
$99$	−0.299521	+	3.30307i	−0.0301030	+	0.331971i
$100$	−1.82405			−0.182405
$101$	−2.29024			−0.227888			−0.113944	−	0.993487i	$-0.536348\pi$
$101$	−2.29024			−0.227888			−0.113944	+	0.993487i	$0.536348\pi$
$102$	−8.33090	+	8.33090i	−0.824882	+	0.824882i
$103$			11.4308i			1.12631i	0.826352	+	0.563154i	$0.190412\pi$
$103$			11.4308i			1.12631i	−0.826352	+	0.563154i	$0.809588\pi$
$104$	5.93468	+	6.08088i	0.581944	+	0.596279i
$105$			1.14891i			0.112122i
$106$	13.9542	−	13.9542i	1.35535	−	1.35535i
$107$			19.5035i			1.88548i	0.333533	+	0.942738i	$0.391759\pi$
$107$			19.5035i			1.88548i	−0.333533	+	0.942738i	$0.608241\pi$
$108$			0.513571i			0.0494184i
$109$	−12.9767	+	12.9767i	−1.24294	+	1.24294i	−0.284164	+	0.958776i	$0.591716\pi$
$109$	−12.9767	+	12.9767i	−1.24294	+	1.24294i	−0.958776	+	0.284164i	$0.908284\pi$
$110$	0.571483	−	6.30222i	0.0544887	−	0.600893i
$111$	−0.872788	+	0.872788i	−0.0828414	+	0.0828414i
$112$	−3.21557	−	3.21557i	−0.303843	−	0.303843i
$113$	−18.4795			−1.73840			−0.869201	−	0.494459i	$-0.835366\pi$
$113$	−18.4795			−1.73840			−0.869201	+	0.494459i	$0.835366\pi$
$114$		−	4.50424i		−	0.421861i
$115$	−3.21580	+	3.21580i	−0.299875	+	0.299875i
$116$	0.126549			0.0117498
$117$	−3.60528	−	0.0438666i	−0.333309	−	0.00405546i
$118$		−	14.0738i		−	1.29559i
$119$	5.01653	+	5.01653i	0.459865	+	0.459865i
$120$			2.83609i			0.258898i
$121$	−10.8206	−	1.97868i	−0.983689	−	0.179880i
$122$	4.44273	+	4.44273i	0.402226	+	0.402226i
$123$	−2.78745	+	2.78745i	−0.251336	+	0.251336i
$124$	−3.71443	+	3.71443i	−0.333565	+	0.333565i
$125$	7.27725	−	7.27725i	0.650897	−	0.650897i
$126$	1.51357			0.134840
$127$	−4.89459			−0.434324			−0.217162	−	0.976136i	$-0.569680\pi$
$127$	−4.89459			−0.434324			−0.217162	+	0.976136i	$0.569680\pi$
$128$	−9.64924	−	9.64924i	−0.852880	−	0.852880i
$129$	4.52405			0.398320
$130$	6.87883	+	0.0836968i	0.603314	+	0.00734069i
$131$		−	1.84165i		−	0.160906i	−0.996758	−	0.0804530i	$-0.974363\pi$
$131$		−	1.84165i		−	0.160906i	0.996758	−	0.0804530i	$-0.0256367\pi$
$132$	−1.69636	−	0.153826i	−0.147649	−	0.0133888i
$133$	−2.71227			−0.235184
$134$	−14.7043			−1.27026
$135$	−0.850971	−	0.850971i	−0.0732399	−	0.0732399i
$136$	12.3833	+	12.3833i	1.06186	+	1.06186i
$137$	12.4192	−	12.4192i	1.06104	−	1.06104i	0.0630322	−	0.998011i	$-0.479923\pi$
$137$	12.4192	−	12.4192i	1.06104	−	1.06104i	0.998011	−	0.0630322i	$-0.0200771\pi$
$138$	4.23648	+	4.23648i	0.360633	+	0.360633i
$139$			11.7143i			0.993593i	0.867867	+	0.496796i	$0.165490\pi$
$139$			11.7143i			0.993593i	−0.867867	+	0.496796i	$0.834510\pi$
$140$	−0.590049			−0.0498682
$141$	−2.70266	+	2.70266i	−0.227605	+	0.227605i
$142$	−5.42542			−0.455291
$143$	1.22475	−	11.8954i	0.102419	−	0.994741i
$144$	4.76339			0.396949
$145$	−0.209687	+	0.209687i	−0.0174136	+	0.0174136i
$146$	−13.2059			−1.09293
$147$			6.08859i			0.502178i
$148$	−0.448239	−	0.448239i	−0.0368450	−	0.0368450i
$149$	13.0754	−	13.0754i	1.07118	−	1.07118i	0.0739121	−	0.997265i	$-0.476452\pi$
$149$	13.0754	−	13.0754i	1.07118	−	1.07118i	0.997265	−	0.0739121i	$-0.0235484\pi$
$150$	−3.98168	−	3.98168i	−0.325103	−	0.325103i
$151$	9.57308	+	9.57308i	0.779047	+	0.779047i	0.979669	−	0.200622i	$-0.0642963\pi$
$151$	9.57308	+	9.57308i	0.779047	+	0.779047i	−0.200622	+	0.979669i	$0.564296\pi$
$152$	−6.69523			−0.543055
$153$	−7.43124			−0.600780
$154$	−0.453347	+	4.99944i	−0.0365317	+	0.402866i
$155$		−	12.3094i		−	0.988712i
$156$	0.0225286	−	1.85157i	0.00180373	−	0.148244i
$157$	8.15572			0.650897			0.325449	−	0.945560i	$-0.394485\pi$
$157$	8.15572			0.650897			0.325449	+	0.945560i	$0.394485\pi$
$158$	−12.7072	−	12.7072i	−1.01093	−	1.01093i
$159$	12.4473			0.987133
$160$	−3.41631			−0.270083
$161$	2.55104	−	2.55104i	0.201050	−	0.201050i
$162$	−1.12106	+	1.12106i	−0.0880791	+	0.0880791i
$163$	5.54165	−	5.54165i	0.434055	−	0.434055i	−0.455950	−	0.890005i	$-0.650700\pi$
$163$	5.54165	−	5.54165i	0.434055	−	0.434055i	0.890005	+	0.455950i	$0.150700\pi$
$164$	−1.43155	−	1.43155i	−0.111786	−	0.111786i
$165$	3.06570	−	2.55593i	0.238665	−	0.198979i
$166$			5.85947i			0.454783i
$167$	−0.229296	−	0.229296i	−0.0177435	−	0.0177435i	0.698179	−	0.715923i	$-0.253994\pi$
$167$	−0.229296	−	0.229296i	−0.0177435	−	0.0177435i	−0.715923	+	0.698179i	$0.753994\pi$
$168$		−	2.24982i		−	0.173577i
$169$	12.9962	+	0.316303i	0.999704	+	0.0243310i
$170$	14.1787			1.08746
$171$	2.00891	−	2.00891i	0.153625	−	0.153625i
$172$			2.32342i			0.177159i
$173$	−10.9234			−0.830491			−0.415245	−	0.909709i	$-0.636304\pi$
$173$	−10.9234			−0.830491			−0.415245	+	0.909709i	$0.636304\pi$
$174$	0.276241	+	0.276241i	0.0209418	+	0.0209418i
$175$	−2.39761	+	2.39761i	−0.181242	+	0.181242i
$176$	−1.42674	+	15.7338i	−0.107544	+	1.18598i
$177$	6.27696	−	6.27696i	0.471805	−	0.471805i
$178$		−	12.0905i		−	0.906219i
$179$		−	10.3266i		−	0.771847i	−0.922531	−	0.385923i	$-0.873883\pi$
$179$		−	10.3266i		−	0.771847i	0.922531	−	0.385923i	$-0.126117\pi$
$180$	0.437034	−	0.437034i	0.0325746	−	0.0325746i
$181$			11.0278i			0.819690i	0.912155	+	0.409845i	$0.134417\pi$
$181$			11.0278i			0.819690i	−0.912155	+	0.409845i	$0.865583\pi$
$182$	−5.45686	−	0.0663952i	−0.404489	−	0.00492154i
$183$			3.96296i			0.292950i
$184$	6.29722	−	6.29722i	0.464237	−	0.464237i
$185$	1.48543			0.109211
$186$	−16.2163			−1.18904
$187$	2.22581	−	24.5459i	0.162768	−	1.79498i
$188$	−1.38801	−	1.38801i	−0.101231	−	0.101231i
$189$	0.675060	+	0.675060i	0.0491034	+	0.0491034i
$190$	−3.83298	+	3.83298i	−0.278073	+	0.278073i
$191$	−13.1251			−0.949697			−0.474849	−	0.880067i	$-0.657497\pi$
$191$	−13.1251			−0.949697			−0.474849	+	0.880067i	$0.657497\pi$
$192$		−	5.02615i		−	0.362731i
$193$	14.4855	+	14.4855i	1.04269	+	1.04269i	0.999047	+	0.0436394i	$0.0138953\pi$
$193$	14.4855	+	14.4855i	1.04269	+	1.04269i	0.0436394	+	0.999047i	$0.486105\pi$
$194$	24.0103			1.72384
$195$	3.03066	+	3.10532i	0.217030	+	0.222377i
$196$	−3.12692			−0.223352
$197$	1.33757	−	1.33757i	0.0952980	−	0.0952980i	−0.657851	−	0.753149i	$-0.728534\pi$
$197$	1.33757	−	1.33757i	0.0952980	−	0.0952980i	0.753149	+	0.657851i	$0.228534\pi$
$198$	−3.36717	−	4.03874i	−0.239295	−	0.287021i
$199$		−	5.28728i		−	0.374806i	−0.982283	−	0.187403i	$-0.939993\pi$
$199$		−	5.28728i		−	0.374806i	0.982283	−	0.187403i	$-0.0600070\pi$
$200$	−5.91849	+	5.91849i	−0.418500	+	0.418500i
$201$	−6.55818	−	6.55818i	−0.462578	−	0.462578i
$202$	2.56751	−	2.56751i	0.180649	−	0.180649i
$203$	0.166341	−	0.166341i	0.0116749	−	0.0116749i
$204$		−	3.81647i		−	0.267206i
$205$	4.74407			0.331340
$206$	−12.8146	−	12.8146i	−0.892839	−	0.892839i
$207$			3.77898i			0.262657i
$208$	−17.1734	−	0.208953i	−1.19076	−	0.0144883i
$209$	6.03387	+	7.23729i	0.417371	+	0.500614i
$210$	−1.28801	−	1.28801i	−0.0888808	−	0.0888808i
$211$		−	1.85803i		−	0.127912i	−0.997953	−	0.0639562i	$-0.979628\pi$
$211$		−	1.85803i		−	0.127912i	0.997953	−	0.0639562i	$-0.0203718\pi$
$212$			6.39256i			0.439043i
$213$	−2.41976	−	2.41976i	−0.165799	−	0.165799i
$214$	−21.8647	−	21.8647i	−1.49464	−	1.49464i
$215$	−3.84983	−	3.84983i	−0.262556	−	0.262556i
$216$	1.66638	+	1.66638i	0.113383	+	0.113383i
$217$			9.76480i			0.662878i
$218$		−	29.0954i		−	1.97059i
$219$	−5.88991	−	5.88991i	−0.398003	−	0.398003i
$220$	1.31265	+	1.57446i	0.0884992	+	0.106150i
$221$	26.7917	+	0.325983i	1.80221	+	0.0219280i
$222$		−	1.95690i		−	0.131339i
$223$	−2.11012	−	2.11012i	−0.141304	−	0.141304i	0.632916	−	0.774220i	$-0.281858\pi$
$223$	−2.11012	−	2.11012i	−0.141304	−	0.141304i	−0.774220	+	0.632916i	$0.781858\pi$
$224$	2.71010			0.181076
$225$		−	3.55170i		−	0.236780i
$226$	20.7167	−	20.7167i	1.37805	−	1.37805i
$227$	20.5713	−	20.5713i	1.36537	−	1.36537i	0.498448	−	0.866920i	$-0.333904\pi$
$227$	20.5713	−	20.5713i	1.36537	−	1.36537i	0.866920	−	0.498448i	$-0.166096\pi$
$228$	1.03172	+	1.03172i	0.0683273	+	0.0683273i
$229$	−7.75638	+	7.75638i	−0.512556	+	0.512556i	−0.915309	−	0.402753i	$-0.868053\pi$
$229$	−7.75638	+	7.75638i	−0.512556	+	0.512556i	0.402753	+	0.915309i	$0.368053\pi$
$230$		−	7.21024i		−	0.475429i
$231$	−2.43197	+	2.02758i	−0.160012	+	0.133405i
$232$	0.410612	−	0.410612i	0.0269580	−	0.0269580i
$233$	−20.1032			−1.31701			−0.658503	−	0.752578i	$-0.728810\pi$
$233$	−20.1032			−1.31701			−0.658503	+	0.752578i	$0.728810\pi$
$234$	4.09093	−	3.99258i	0.267433	−	0.261003i
$235$	4.59977			0.300056
$236$	3.22367	+	3.22367i	0.209843	+	0.209843i
$237$		−	11.3349i		−	0.736284i
$238$	−11.2477			−0.729081
$239$	−10.8128	+	10.8128i	−0.699423	+	0.699423i	−0.964286	−	0.264863i	$-0.914673\pi$
$239$	−10.8128	+	10.8128i	−0.699423	+	0.699423i	0.264863	+	0.964286i	$0.414673\pi$
$240$	−4.05350	−	4.05350i	−0.261653	−	0.261653i
$241$	−8.92902	−	8.92902i	−0.575169	−	0.575169i	0.358399	−	0.933568i	$-0.383323\pi$
$241$	−8.92902	−	8.92902i	−0.575169	−	0.575169i	−0.933568	+	0.358399i	$0.883323\pi$
$242$	14.3488	−	9.91233i	0.922375	−	0.637189i
$243$	−1.00000			−0.0641500
$244$	−2.03526			−0.130294
$245$	5.18121	−	5.18121i	0.331015	−	0.331015i
$246$		−	6.24982i		−	0.398474i
$247$	−7.33082	+	7.15457i	−0.466449	+	0.455235i
$248$			24.1044i			1.53063i
$249$	−2.61335	+	2.61335i	−0.165614	+	0.165614i
$250$			16.3165i			1.03195i
$251$			23.1015i			1.45816i	0.684430	+	0.729078i	$0.260051\pi$
$251$			23.1015i			1.45816i	−0.684430	+	0.729078i	$0.739949\pi$
$252$	−0.346691	+	0.346691i	−0.0218395	+	0.0218395i
$253$	−12.4822	−	1.13188i	−0.784751	−	0.0711610i
$254$	5.48715	−	5.48715i	0.344294	−	0.344294i
$255$	6.32377	+	6.32377i	0.396010	+	0.396010i
$256$	11.5825			0.723909
$257$			11.2666i			0.702793i	0.936227	+	0.351397i	$0.114293\pi$
$257$			11.2666i			0.702793i	−0.936227	+	0.351397i	$0.885707\pi$
$258$	−5.07175	+	5.07175i	−0.315753	+	0.315753i
$259$	−1.17837			−0.0732203
$260$	−1.59480	+	1.55646i	−0.0989056	+	0.0965277i
$261$			0.246409i			0.0152524i
$262$	2.06461	+	2.06461i	0.127552	+	0.127552i
$263$			6.58637i			0.406133i	0.979165	+	0.203066i	$0.0650907\pi$
$263$			6.58637i			0.406133i	−0.979165	+	0.203066i	$0.934909\pi$
$264$	−6.00330	+	5.00506i	−0.369477	+	0.308040i
$265$	−10.5923	−	10.5923i	−0.650678	−	0.650678i
$266$	3.04063	−	3.04063i	0.186433	−	0.186433i
$267$	5.39241	−	5.39241i	0.330010	−	0.330010i
$268$	3.36809	−	3.36809i	0.205739	−	0.205739i
$269$	8.85053			0.539627			0.269813	−	0.962913i	$-0.413038\pi$
$269$	8.85053			0.539627			0.269813	+	0.962913i	$0.413038\pi$
$270$	1.90799			0.116116
$271$	−9.40355	−	9.40355i	−0.571225	−	0.571225i	0.361246	−	0.932471i	$-0.382352\pi$
$271$	−9.40355	−	9.40355i	−0.571225	−	0.571225i	−0.932471	+	0.361246i	$0.882352\pi$
$272$	−35.3979			−2.14631
$273$	−2.40417	−	2.46340i	−0.145507	−	0.149091i
$274$			27.8454i			1.68220i
$275$	11.7315	+	1.06381i	0.707437	+	0.0641501i
$276$	−1.94077			−0.116821
$277$	11.5221			0.692296			0.346148	−	0.938180i	$-0.387489\pi$
$277$	11.5221			0.692296			0.346148	+	0.938180i	$0.387489\pi$
$278$	−13.1325	−	13.1325i	−0.787633	−	0.787633i
$279$	−7.23254	−	7.23254i	−0.433001	−	0.433001i
$280$	−1.91453	+	1.91453i	−0.114415	+	0.114415i
$281$	−15.2681	−	15.2681i	−0.910819	−	0.910819i	0.0855176	−	0.996337i	$-0.472746\pi$
$281$	−15.2681	−	15.2681i	−0.910819	−	0.910819i	−0.996337	+	0.0855176i	$0.972746\pi$
$282$		−	6.05972i		−	0.360851i
$283$	1.21751			0.0723737			0.0361869	−	0.999345i	$-0.488479\pi$
$283$	1.21751			0.0723737			0.0361869	+	0.999345i	$0.488479\pi$
$284$	1.24272	−	1.24272i	0.0737419	−	0.0737419i
$285$	−3.41905			−0.202527
$286$	11.9625	+	14.7085i	0.707355	+	0.869733i
$287$	−3.76339			−0.222146
$288$	−2.00730	+	2.00730i	−0.118281	+	0.118281i
$289$	38.2233			2.24843
$290$		−	0.470146i		−	0.0276079i
$291$	10.7087	+	10.7087i	0.627755	+	0.627755i
$292$	3.02489	−	3.02489i	0.177018	−	0.177018i
$293$	−8.56257	−	8.56257i	−0.500231	−	0.500231i	0.411279	−	0.911510i	$-0.365082\pi$
$293$	−8.56257	−	8.56257i	−0.500231	−	0.500231i	−0.911510	+	0.411279i	$0.865082\pi$
$294$	−6.82570	−	6.82570i	−0.398083	−	0.398083i
$295$	−10.6830			−0.621989
$296$	−2.90880			−0.169070
$297$	0.299521	−	3.30307i	0.0173800	−	0.191664i
$298$			29.3167i			1.69827i
$299$	0.165771	−	13.6243i	0.00958677	−	0.787913i
$300$	1.82405			0.105312
$301$	3.05400	+	3.05400i	0.176030	+	0.176030i
$302$	−21.4641			−1.23512
$303$	2.29024			0.131571
$304$	9.56922	−	9.56922i	0.548833	−	0.548833i
$305$	3.37236	−	3.37236i	0.193101	−	0.193101i
$306$	8.33090	−	8.33090i	0.476246	−	0.476246i
$307$	3.18728	+	3.18728i	0.181908	+	0.181908i	0.792187	−	0.610279i	$-0.208943\pi$
$307$	3.18728	+	3.18728i	0.181908	+	0.181908i	−0.610279	+	0.792187i	$0.708943\pi$
$308$	−1.04131	−	1.24899i	−0.0593339	−	0.0711677i
$309$		−	11.4308i		−	0.650274i
$310$	13.7996	+	13.7996i	0.783764	+	0.783764i
$311$			6.59476i			0.373954i	0.982364	+	0.186977i	$0.0598691\pi$
$311$			6.59476i			0.373954i	−0.982364	+	0.186977i	$0.940131\pi$
$312$	−5.93468	−	6.08088i	−0.335985	−	0.344262i
$313$	−24.4375			−1.38129			−0.690644	−	0.723195i	$-0.742673\pi$
$313$	−24.4375			−1.38129			−0.690644	+	0.723195i	$0.742673\pi$
$314$	−9.14309	+	9.14309i	−0.515974	+	0.515974i
$315$		−	1.14891i		−	0.0647339i
$316$	5.82130			0.327474
$317$	21.5305	+	21.5305i	1.20928	+	1.20928i	0.971262	+	0.238014i	$0.0764963\pi$
$317$	21.5305	+	21.5305i	1.20928	+	1.20928i	0.238014	+	0.971262i	$0.423504\pi$
$318$	−13.9542	+	13.9542i	−0.782513	+	0.782513i
$319$	−0.813908	−	0.0738049i	−0.0455701	−	0.00413228i
$320$	−4.27711	+	4.27711i	−0.239098	+	0.239098i
$321$		−	19.5035i		−	1.08858i
$322$			5.71975i			0.318749i
$323$	−14.9287	+	14.9287i	−0.830655	+	0.830655i
$324$		−	0.513571i		−	0.0285317i
$325$	−0.155801	+	12.8049i	−0.00864227	+	0.710287i
$326$			12.4251i			0.688162i
$327$	12.9767	−	12.9767i	0.717612	−	0.717612i
$328$	−9.28990			−0.512949
$329$	−3.64892			−0.201171
$330$	−0.571483	+	6.30222i	−0.0314591	+	0.346926i
$331$	5.84499	+	5.84499i	0.321270	+	0.321270i	0.849254	−	0.527984i	$-0.177052\pi$
$331$	5.84499	+	5.84499i	0.321270	+	0.321270i	−0.527984	+	0.849254i	$0.677052\pi$
$332$	−1.34214	−	1.34214i	−0.0736597	−	0.0736597i
$333$	0.872788	−	0.872788i	0.0478285	−	0.0478285i
$334$	0.514111			0.0281309
$335$			11.1616i			0.609825i
$336$	3.21557	+	3.21557i	0.175424	+	0.175424i
$337$	4.57368			0.249144			0.124572	−	0.992211i	$-0.460244\pi$
$337$	4.57368			0.249144			0.124572	+	0.992211i	$0.460244\pi$
$338$	−14.9241	+	14.2149i	−0.811765	+	0.773190i
$339$	18.4795			1.00367
$340$	−3.24771	+	3.24771i	−0.176132	+	0.176132i
$341$	26.0559	−	21.7233i	1.41101	−	1.17638i
$342$			4.50424i			0.243561i
$343$	−8.83558	+	8.83558i	−0.477077	+	0.477077i
$344$	7.53879	+	7.53879i	0.406464	+	0.406464i
$345$	3.21580	−	3.21580i	0.173133	−	0.173133i
$346$	12.2458	−	12.2458i	0.658340	−	0.658340i
$347$			7.58514i			0.407191i	0.979055	+	0.203596i	$0.0652628\pi$
$347$			7.58514i			0.407191i	−0.979055	+	0.203596i	$0.934737\pi$
$348$	−0.126549			−0.00678373
$349$	6.09310	+	6.09310i	0.326156	+	0.326156i	0.851123	−	0.524967i	$-0.175922\pi$
$349$	6.09310	+	6.09310i	0.326156	+	0.326156i	−0.524967	+	0.851123i	$0.675922\pi$
$350$		−	5.37575i		−	0.287346i
$351$	3.60528	+	0.0438666i	0.192436	+	0.00234142i
$352$	−6.02903	−	7.23149i	−0.321348	−	0.385439i
$353$	−9.88986	−	9.88986i	−0.526384	−	0.526384i	0.393108	−	0.919492i	$-0.371400\pi$
$353$	−9.88986	−	9.88986i	−0.526384	−	0.526384i	−0.919492	+	0.393108i	$0.871400\pi$
$354$			14.0738i			0.748011i
$355$			4.11829i			0.218576i
$356$	2.76939	+	2.76939i	0.146777	+	0.146777i
$357$	−5.01653	−	5.01653i	−0.265503	−	0.265503i
$358$	11.5768	+	11.5768i	0.611852	+	0.611852i
$359$	1.75029	+	1.75029i	0.0923766	+	0.0923766i	0.751785	−	0.659408i	$-0.229193\pi$
$359$	1.75029	+	1.75029i	0.0923766	+	0.0923766i	−0.659408	+	0.751785i	$0.729193\pi$
$360$		−	2.83609i		−	0.149475i
$361$			10.9285i			0.575187i
$362$	−12.3629	−	12.3629i	−0.649778	−	0.649778i
$363$	10.8206	+	1.97868i	0.567933	+	0.103854i
$364$	1.26513	−	1.23471i	0.0663108	−	0.0647166i
$365$			10.0243i			0.524695i
$366$	−4.44273	−	4.44273i	−0.232225	−	0.232225i
$367$	4.27025			0.222905			0.111453	−	0.993770i	$-0.464450\pi$
$367$	4.27025			0.222905			0.111453	+	0.993770i	$0.464450\pi$
$368$			18.0007i			0.938353i
$369$	2.78745	−	2.78745i	0.145109	−	0.145109i
$370$	−1.66527	+	1.66527i	−0.0865732	+	0.0865732i
$371$	8.40266	+	8.40266i	0.436244	+	0.436244i
$372$	3.71443	−	3.71443i	0.192584	−	0.192584i
$373$		−	25.9516i		−	1.34372i	−0.740676	−	0.671862i	$-0.765495\pi$
$373$		−	25.9516i		−	1.34372i	0.740676	−	0.671862i	$-0.234505\pi$
$374$	25.0223	+	30.0128i	1.29387	+	1.55193i
$375$	−7.27725	+	7.27725i	−0.375795	+	0.375795i
$376$	−9.00734			−0.464518
$377$	0.0108091	−	0.888376i	0.000556698	−	0.0457537i
$378$	−1.51357			−0.0778497
$379$	−14.4270	−	14.4270i	−0.741066	−	0.741066i	0.231717	−	0.972783i	$-0.425566\pi$
$379$	−14.4270	−	14.4270i	−0.741066	−	0.741066i	−0.972783	+	0.231717i	$0.925566\pi$
$380$		−	1.75593i		−	0.0900771i
$381$	4.89459			0.250757
$382$	14.7141	−	14.7141i	0.752837	−	0.752837i
$383$	3.27449	+	3.27449i	0.167319	+	0.167319i	0.785800	−	0.618481i	$-0.212252\pi$
$383$	3.27449	+	3.27449i	0.167319	+	0.167319i	−0.618481	+	0.785800i	$0.712252\pi$
$384$	9.64924	+	9.64924i	0.492411	+	0.492411i
$385$	3.79494	+	0.344124i	0.193408	+	0.0175382i
$386$	−32.4783			−1.65310
$387$	−4.52405			−0.229970
$388$	−5.49969	+	5.49969i	−0.279204	+	0.279204i
$389$		−	34.6092i		−	1.75475i	−0.479802	−	0.877377i	$-0.659291\pi$
$389$		−	34.6092i		−	1.75475i	0.479802	−	0.877377i	$-0.340709\pi$
$390$	−6.87883	−	0.0836968i	−0.348323	−	0.00423815i
$391$		−	28.0825i		−	1.42019i
$392$	−10.1459	+	10.1459i	−0.512446	+	0.512446i
$393$			1.84165i			0.0928991i
$394$			2.99901i			0.151088i
$395$	−9.64571	+	9.64571i	−0.485328	+	0.485328i
$396$	1.69636	+	0.153826i	0.0852455	+	0.00773003i
$397$	−18.8071	+	18.8071i	−0.943899	+	0.943899i	−0.998508	−	0.0546085i	$-0.982609\pi$
$397$	−18.8071	+	18.8071i	−0.943899	+	0.943899i	0.0546085	+	0.998508i	$0.482609\pi$
$398$	5.92739	+	5.92739i	0.297113	+	0.297113i
$399$	2.71227			0.135783
$400$		−	16.9181i		−	0.845905i
$401$	−10.3747	+	10.3747i	−0.518086	+	0.518086i	−0.916992	−	0.398906i	$-0.869390\pi$
$401$	−10.3747	+	10.3747i	−0.518086	+	0.518086i	0.398906	+	0.916992i	$0.369390\pi$
$402$	14.7043			0.733383
$403$	25.7581	+	26.3926i	1.28310	+	1.31471i
$404$			1.17620i			0.0585183i
$405$	0.850971	+	0.850971i	0.0422851	+	0.0422851i
$406$			0.372958i			0.0185096i
$407$	2.62146	+	3.14430i	0.129941	+	0.155857i
$408$	−12.3833	−	12.3833i	−0.613064	−	0.613064i
$409$	12.5400	−	12.5400i	0.620065	−	0.620065i	−0.325483	−	0.945548i	$-0.605527\pi$
$409$	12.5400	−	12.5400i	0.620065	−	0.620065i	0.945548	+	0.325483i	$0.105527\pi$
$410$	−5.31841	+	5.31841i	−0.262658	+	0.262658i
$411$	−12.4192	+	12.4192i	−0.612594	+	0.612594i
$412$	5.87052			0.289220
$413$	8.47465			0.417010
$414$	−4.23648	−	4.23648i	−0.208212	−	0.208212i
$415$	4.44777			0.218333
$416$	7.32494	−	7.14883i	0.359135	−	0.350500i
$417$		−	11.7143i		−	0.573651i
$418$	−14.8778	−	1.34912i	−0.727698	−	0.0659874i
$419$	−0.0491403			−0.00240066			−0.00120033	−	0.999999i	$-0.500382\pi$
$419$	−0.0491403			−0.00240066			−0.00120033	+	0.999999i	$0.500382\pi$
$420$	0.590049			0.0287914
$421$	−7.93330	−	7.93330i	−0.386646	−	0.386646i	0.486844	−	0.873489i	$-0.338148\pi$
$421$	−7.93330	−	7.93330i	−0.386646	−	0.386646i	−0.873489	+	0.486844i	$0.838148\pi$
$422$	2.08298	+	2.08298i	0.101398	+	0.101398i
$423$	2.70266	−	2.70266i	0.131408	−	0.131408i
$424$	20.7419	+	20.7419i	1.00732	+	1.00732i
$425$			26.3935i			1.28027i
$426$	5.42542			0.262862
$427$	−2.67523	+	2.67523i	−0.129464	+	0.129464i
$428$	10.0165			0.484164
$429$	−1.22475	+	11.8954i	−0.0591317	+	0.574314i
$430$	8.63182			0.416263
$431$	−4.16310	+	4.16310i	−0.200530	+	0.200530i	−0.800227	−	0.599697i	$-0.795288\pi$
$431$	−4.16310	+	4.16310i	−0.200530	+	0.200530i	0.599697	+	0.800227i	$0.295288\pi$
$432$	−4.76339			−0.229179
$433$			29.3722i			1.41154i	0.708442	+	0.705769i	$0.249398\pi$
$433$			29.3722i			1.41154i	−0.708442	+	0.705769i	$0.750602\pi$
$434$	−10.9470	−	10.9470i	−0.525471	−	0.525471i
$435$	0.209687	−	0.209687i	0.0100537	−	0.0100537i
$436$	6.66445	+	6.66445i	0.319169	+	0.319169i
$437$	7.59163	+	7.59163i	0.363157	+	0.363157i
$438$	13.2059			0.631004
$439$	−11.4725			−0.547551			−0.273776	−	0.961794i	$-0.588273\pi$
$439$	−11.4725			−0.547551			−0.273776	+	0.961794i	$0.588273\pi$
$440$	9.36780	+	0.849468i	0.446592	+	0.0404968i
$441$		−	6.08859i		−	0.289933i
$442$	−30.4007	+	29.6698i	−1.44601	+	1.41125i
$443$	22.7420			1.08051			0.540253	−	0.841502i	$-0.318328\pi$
$443$	22.7420			1.08051			0.540253	+	0.841502i	$0.318328\pi$
$444$	0.448239	+	0.448239i	0.0212725	+	0.0212725i
$445$	−9.17756			−0.435058
$446$	4.73116			0.224027
$447$	−13.0754	+	13.0754i	−0.618444	+	0.618444i
$448$	3.39295	−	3.39295i	0.160302	−	0.160302i
$449$	−5.03844	+	5.03844i	−0.237779	+	0.237779i	−0.815930	−	0.578151i	$-0.803774\pi$
$449$	−5.03844	+	5.03844i	−0.237779	+	0.237779i	0.578151	+	0.815930i	$0.303774\pi$
$450$	3.98168	+	3.98168i	0.187698	+	0.187698i
$451$	8.37224	+	10.0420i	0.394233	+	0.472861i
$452$			9.49053i			0.446397i
$453$	−9.57308	−	9.57308i	−0.449783	−	0.449783i
$454$			46.1236i			2.16469i
$455$	−0.0503988	+	4.14216i	−0.00236273	+	0.194187i
$456$	6.69523			0.313533
$457$	24.1395	−	24.1395i	1.12920	−	1.12920i	0.138892	−	0.990308i	$-0.455646\pi$
$457$	24.1395	−	24.1395i	1.12920	−	1.12920i	0.990308	−	0.138892i	$-0.0443541\pi$
$458$		−	17.3908i		−	0.812619i
$459$	7.43124			0.346860
$460$	1.65154	+	1.65154i	0.0770036	+	0.0770036i
$461$	19.5166	−	19.5166i	0.908977	−	0.908977i	−0.0872123	−	0.996190i	$-0.527796\pi$
$461$	19.5166	−	19.5166i	0.908977	−	0.908977i	0.996190	+	0.0872123i	$0.0277959\pi$
$462$	0.453347	−	4.99944i	0.0210916	−	0.232595i
$463$	1.92897	−	1.92897i	0.0896469	−	0.0896469i	−0.660861	−	0.750508i	$-0.729809\pi$
$463$	1.92897	−	1.92897i	0.0896469	−	0.0896469i	0.750508	+	0.660861i	$0.229809\pi$
$464$			1.17374i			0.0544897i
$465$			12.3094i			0.570833i
$466$	22.5370	−	22.5370i	1.04401	−	1.04401i
$467$		−	31.1406i		−	1.44102i	−0.693447	−	0.720508i	$-0.743909\pi$
$467$		−	31.1406i		−	1.44102i	0.693447	−	0.720508i	$-0.256091\pi$
$468$	−0.0225286	+	1.85157i	−0.00104139	+	0.0855889i
$469$		−	8.85432i		−	0.408855i
$470$	−5.15664	+	5.15664i	−0.237858	+	0.237858i
$471$	−8.15572			−0.375796
$472$	20.9196			0.962904
$473$	1.35505	−	14.9433i	0.0623052	−	0.687092i
$474$	12.7072	+	12.7072i	0.583661	+	0.583661i
$475$	−7.13505	−	7.13505i	−0.327378	−	0.327378i
$476$	2.57635	−	2.57635i	0.118087	−	0.118087i
$477$	−12.4473			−0.569922
$478$		−	24.2437i		−	1.10888i
$479$	−12.5135	−	12.5135i	−0.571756	−	0.571756i	0.360863	−	0.932619i	$-0.382482\pi$
$479$	−12.5135	−	12.5135i	−0.571756	−	0.571756i	−0.932619	+	0.360863i	$0.882482\pi$
$480$	3.41631			0.155932
$481$	−3.18494	+	3.10836i	−0.145221	+	0.141729i
$482$	20.0200			0.911887
$483$	−2.55104	+	2.55104i	−0.116076	+	0.116076i
$484$	−1.01619	+	5.55714i	−0.0461906	+	0.252597i
$485$		−	18.2256i		−	0.827582i
$486$	1.12106	−	1.12106i	0.0508525	−	0.0508525i
$487$	−11.2499	−	11.2499i	−0.509781	−	0.509781i	0.404678	−	0.914459i	$-0.367384\pi$
$487$	−11.2499	−	11.2499i	−0.509781	−	0.509781i	−0.914459	+	0.404678i	$0.867384\pi$
$488$	−6.60380	+	6.60380i	−0.298940	+	0.298940i
$489$	−5.54165	+	5.54165i	−0.250602	+	0.250602i
$490$			11.6169i			0.524800i
$491$	2.39305			0.107997			0.0539985	−	0.998541i	$-0.482803\pi$
$491$	2.39305			0.107997			0.0539985	+	0.998541i	$0.482803\pi$
$492$	1.43155	+	1.43155i	0.0645394	+	0.0645394i
$493$		−	1.83113i		−	0.0824698i
$494$	0.197585	−	16.2391i	0.00888979	−	0.730630i
$495$	−3.06570	+	2.55593i	−0.137793	+	0.114881i
$496$	−34.4514	−	34.4514i	−1.54691	−	1.54691i
$497$		−	3.26697i		−	0.146543i
$498$		−	5.85947i		−	0.262569i
$499$	12.0345	+	12.0345i	0.538739	+	0.538739i	0.923158	−	0.384420i	$-0.125598\pi$
$499$	12.0345	+	12.0345i	0.538739	+	0.538739i	−0.384420	+	0.923158i	$0.625598\pi$
$500$	−3.73739	−	3.73739i	−0.167141	−	0.167141i
$501$	0.229296	+	0.229296i	0.0102442	+	0.0102442i
$502$	−25.8983	−	25.8983i	−1.15590	−	1.15590i
$503$		−	4.93436i		−	0.220012i	−0.993931	−	0.110006i	$-0.964913\pi$
$503$		−	4.93436i		−	0.220012i	0.993931	−	0.110006i	$-0.0350870\pi$
$504$			2.24982i			0.100215i
$505$	−1.94893	−	1.94893i	−0.0867262	−	0.0867262i
$506$	15.2623	−	12.7245i	0.678492	−	0.565672i
$507$	−12.9962	−	0.316303i	−0.577179	−	0.0140475i
$508$			2.51372i			0.111528i
$509$	−14.6289	−	14.6289i	−0.648413	−	0.648413i	0.304197	−	0.952609i	$-0.401612\pi$
$509$	−14.6289	−	14.6289i	−0.648413	−	0.648413i	−0.952609	+	0.304197i	$0.901612\pi$
$510$	−14.1787			−0.627843
$511$		−	7.95208i		−	0.351779i
$512$	6.31370	−	6.31370i	0.279029	−	0.279029i
$513$	−2.00891	+	2.00891i	−0.0886956	+	0.0886956i
$514$	−12.6306	−	12.6306i	−0.557113	−	0.557113i
$515$	−9.72726	+	9.72726i	−0.428634	+	0.428634i
$516$		−	2.32342i		−	0.102283i
$517$	8.11758	+	9.73659i	0.357011	+	0.428215i
$518$	1.32103	−	1.32103i	0.0580426	−	0.0580426i
$519$	10.9234			0.479484
$520$	−0.124409	+	10.2249i	−0.00545571	+	0.448391i
$521$	5.03014			0.220375			0.110187	−	0.993911i	$-0.464855\pi$
$521$	5.03014			0.220375			0.110187	+	0.993911i	$0.464855\pi$
$522$	−0.276241	−	0.276241i	−0.0120907	−	0.0120907i
$523$		−	28.7479i		−	1.25706i	−0.777786	−	0.628529i	$-0.783657\pi$
$523$		−	28.7479i		−	1.25706i	0.777786	−	0.628529i	$-0.216343\pi$
$524$	−0.945820			−0.0413183
$525$	2.39761	−	2.39761i	0.104640	−	0.104640i
$526$	−7.38374	−	7.38374i	−0.321947	−	0.321947i
$527$	53.7467	+	53.7467i	2.34124	+	2.34124i
$528$	1.42674	−	15.7338i	0.0620907	−	0.684726i
$529$	8.71933			0.379101
$530$	23.7492			1.03160
$531$	−6.27696	+	6.27696i	−0.272397	+	0.272397i
$532$			1.39295i			0.0603918i
$533$	−10.1718	+	9.92726i	−0.440590	+	0.429998i
$534$			12.0905i			0.523206i
$535$	−16.5969	+	16.5969i	−0.717548	+	0.717548i
$536$		−	21.8569i		−	0.944073i
$537$			10.3266i			0.445626i
$538$	−9.92202	+	9.92202i	−0.427769	+	0.427769i
$539$	20.1110	+	1.82366i	0.866244	+	0.0785507i
$540$	−0.437034	+	0.437034i	−0.0188070	+	0.0188070i
$541$	4.07167	+	4.07167i	0.175055	+	0.175055i	0.789196	−	0.614141i	$-0.210498\pi$
$541$	4.07167	+	4.07167i	0.175055	+	0.175055i	−0.614141	+	0.789196i	$0.710498\pi$
$542$	21.0840			0.905635
$543$		−	11.0278i		−	0.473248i
$544$	14.9167	−	14.9167i	0.639549	−	0.639549i
$545$	−22.0855			−0.946041
$546$	5.45686	+	0.0663952i	0.233532	+	0.00284145i
$547$		−	31.7760i		−	1.35864i	−0.733840	−	0.679322i	$-0.762274\pi$
$547$		−	31.7760i		−	1.35864i	0.733840	−	0.679322i	$-0.237726\pi$
$548$	−6.37815	−	6.37815i	−0.272461	−	0.272461i
$549$		−	3.96296i		−	0.169135i
$550$	−14.3444	+	11.9592i	−0.611646	+	0.509941i
$551$	0.495015	+	0.495015i	0.0210883	+	0.0210883i
$552$	−6.29722	+	6.29722i	−0.268028	+	0.268028i
$553$	7.65177	−	7.65177i	0.325386	−	0.325386i
$554$	−12.9170	+	12.9170i	−0.548792	+	0.548792i
$555$	−1.48543			−0.0630532
$556$	6.01612			0.255140
$557$	−2.45042	−	2.45042i	−0.103828	−	0.103828i	0.653285	−	0.757112i	$-0.273391\pi$
$557$	−2.45042	−	2.45042i	−0.103828	−	0.103828i	−0.757112	+	0.653285i	$0.773391\pi$
$558$	16.2163			0.686490
$559$	16.3105	+	0.198454i	0.689860	+	0.00839372i
$560$		−	5.47272i		−	0.231264i
$561$	−2.22581	+	24.5459i	−0.0939739	+	1.03633i
$562$	34.2331			1.44404
$563$	17.9163			0.755083			0.377541	−	0.925993i	$-0.376770\pi$
$563$	17.9163			0.755083			0.377541	+	0.925993i	$0.376770\pi$
$564$	1.38801	+	1.38801i	0.0584458	+	0.0584458i
$565$	−15.7255	−	15.7255i	−0.661576	−	0.661576i
$566$	−1.36491	+	1.36491i	−0.0573716	+	0.0573716i
$567$	−0.675060	−	0.675060i	−0.0283499	−	0.0283499i
$568$		−	8.06449i		−	0.338379i
$569$	−35.6567			−1.49481			−0.747403	−	0.664371i	$-0.768699\pi$
$569$	−35.6567			−1.49481			−0.747403	+	0.664371i	$0.768699\pi$
$570$	3.83298	−	3.83298i	0.160546	−	0.160546i
$571$	−33.2072			−1.38968			−0.694838	−	0.719166i	$-0.744524\pi$
$571$	−33.2072			−1.38968			−0.694838	+	0.719166i	$0.744524\pi$
$572$	−6.10913	−	0.628999i	−0.255435	−	0.0262998i
$573$	13.1251			0.548308
$574$	4.21900	−	4.21900i	0.176098	−	0.176098i
$575$	13.4218			0.559727
$576$			5.02615i			0.209423i
$577$	−7.21344	−	7.21344i	−0.300300	−	0.300300i	0.540831	−	0.841131i	$-0.318110\pi$
$577$	−7.21344	−	7.21344i	−0.300300	−	0.300300i	−0.841131	+	0.540831i	$0.818110\pi$
$578$	−42.8508	+	42.8508i	−1.78236	+	1.78236i
$579$	−14.4855	−	14.4855i	−0.601995	−	0.601995i
$580$	0.107689	+	0.107689i	0.00447156	+	0.00447156i
$581$	−3.52834			−0.146380
$582$	−24.0103			−0.995259
$583$	3.72822	−	41.1142i	0.154407	−	1.70278i
$584$		−	19.6297i		−	0.812282i
$585$	−3.03066	−	3.10532i	−0.125302	−	0.128389i
$586$	19.1984			0.793079
$587$	0.242345	+	0.242345i	0.0100026	+	0.0100026i	0.712090	−	0.702088i	$-0.247749\pi$
$587$	0.242345	+	0.242345i	0.0100026	+	0.0100026i	−0.702088	+	0.712090i	$0.747749\pi$
$588$	3.12692			0.128952
$589$	−29.0591			−1.19736
$590$	11.9764	−	11.9764i	0.493059	−	0.493059i
$591$	−1.33757	+	1.33757i	−0.0550203	+	0.0550203i
$592$	4.15743	−	4.15743i	0.170869	−	0.170869i
$593$	13.8714	+	13.8714i	0.569629	+	0.569629i	0.932025	−	0.362395i	$-0.118041\pi$
$593$	13.8714	+	13.8714i	0.569629	+	0.569629i	−0.362395	+	0.932025i	$0.618041\pi$
$594$	3.36717	+	4.03874i	0.138157	+	0.165712i
$595$			8.53784i			0.350017i
$596$	−6.71514	−	6.71514i	−0.275063	−	0.275063i
$597$			5.28728i			0.216394i
$598$	15.0879	+	15.4595i	0.616989	+	0.632188i
$599$	−33.2979			−1.36051			−0.680257	−	0.732973i	$-0.738132\pi$
$599$	−33.2979			−1.36051			−0.680257	+	0.732973i	$0.738132\pi$
$600$	5.91849	−	5.91849i	0.241621	−	0.241621i
$601$			25.1042i			1.02402i	0.858978	+	0.512012i	$0.171100\pi$
$601$			25.1042i			1.02402i	−0.858978	+	0.512012i	$0.828900\pi$
$602$	−6.84747			−0.279082
$603$	6.55818	+	6.55818i	0.267070	+	0.267070i
$604$	4.91646	−	4.91646i	0.200048	−	0.200048i
$605$	−7.52419	−	10.8918i	−0.305902	−	0.442814i
$606$	−2.56751	+	2.56751i	−0.104298	+	0.104298i
$607$		−	2.79022i		−	0.113251i	−0.998395	−	0.0566257i	$-0.981966\pi$
$607$		−	2.79022i		−	0.113251i	0.998395	−	0.0566257i	$-0.0180342\pi$
$608$			8.06498i			0.327078i
$609$	−0.166341	+	0.166341i	−0.00674048	+	0.00674048i
$610$			7.56127i			0.306147i
$611$	−9.86242	+	9.62531i	−0.398991	+	0.389398i
$612$			3.81647i			0.154272i
$613$	−32.3984	+	32.3984i	−1.30856	+	1.30856i	−0.386102	+	0.922456i	$0.626179\pi$
$613$	−32.3984	+	32.3984i	−1.30856	+	1.30856i	−0.922456	+	0.386102i	$0.873821\pi$
$614$	−7.14629			−0.288401
$615$	−4.74407			−0.191299
$616$	−7.43130	−	0.673868i	−0.299416	−	0.0271509i
$617$	10.8226	+	10.8226i	0.435700	+	0.435700i	0.890562	−	0.454862i	$-0.150311\pi$
$617$	10.8226	+	10.8226i	0.435700	+	0.435700i	−0.454862	+	0.890562i	$0.650311\pi$
$618$	12.8146	+	12.8146i	0.515481	+	0.515481i
$619$	9.07149	−	9.07149i	0.364614	−	0.364614i	−0.500895	−	0.865508i	$-0.666996\pi$
$619$	9.07149	−	9.07149i	0.364614	−	0.364614i	0.865508	+	0.500895i	$0.166996\pi$
$620$	−6.32174			−0.253887
$621$		−	3.77898i		−	0.151645i
$622$	−7.39315	−	7.39315i	−0.296438	−	0.296438i
$623$	7.28039			0.291683
$624$	17.1734	+	0.208953i	0.687485	+	0.00836483i
$625$	−5.37304			−0.214921
$626$	27.3960	−	27.3960i	1.09496	−	1.09496i
$627$	−6.03387	−	7.23729i	−0.240970	−	0.289030i
$628$		−	4.18854i		−	0.167141i
$629$	−6.48590	+	6.48590i	−0.258610	+	0.258610i
$630$	1.28801	+	1.28801i	0.0513154	+	0.0513154i
$631$	0.717627	−	0.717627i	0.0285683	−	0.0285683i	−0.692678	−	0.721247i	$-0.743569\pi$
$631$	0.717627	−	0.717627i	0.0285683	−	0.0285683i	0.721247	+	0.692678i	$0.243569\pi$
$632$	18.8884	−	18.8884i	0.751338	−	0.751338i
$633$			1.85803i			0.0738502i
$634$	−48.2742			−1.91722
$635$	−4.16515	−	4.16515i	−0.165289	−	0.165289i
$636$		−	6.39256i		−	0.253482i
$637$	−0.267085	+	21.9511i	−0.0105823	+	0.869734i
$638$	0.995183	−	0.829703i	0.0393997	−	0.0328483i
$639$	2.41976	+	2.41976i	0.0957243	+	0.0957243i
$640$		−	16.4224i		−	0.649154i
$641$		−	3.01763i		−	0.119189i	−0.998223	−	0.0595946i	$-0.981019\pi$
$641$		−	3.01763i		−	0.119189i	0.998223	−	0.0595946i	$-0.0189808\pi$
$642$	21.8647	+	21.8647i	0.862931	+	0.862931i
$643$	−7.27088	−	7.27088i	−0.286736	−	0.286736i	0.549052	−	0.835788i	$-0.314989\pi$
$643$	−7.27088	−	7.27088i	−0.286736	−	0.286736i	−0.835788	+	0.549052i	$0.814989\pi$
$644$	−1.31014	−	1.31014i	−0.0516267	−	0.0516267i
$645$	3.84983	+	3.84983i	0.151587	+	0.151587i
$646$		−	33.4721i		−	1.31694i
$647$			6.96565i			0.273848i	0.990582	+	0.136924i	$0.0437216\pi$
$647$			6.96565i			0.273848i	−0.990582	+	0.136924i	$0.956278\pi$
$648$	−1.66638	−	1.66638i	−0.0654617	−	0.0654617i
$649$	−18.8532	−	22.6133i	−0.740051	−	0.887651i
$650$	−14.1804	−	14.5298i	−0.556202	−	0.569904i
$651$		−	9.76480i		−	0.382713i
$652$	−2.84603	−	2.84603i	−0.111459	−	0.111459i
$653$	−3.51009			−0.137360			−0.0686802	−	0.997639i	$-0.521879\pi$
$653$	−3.51009			−0.137360			−0.0686802	+	0.997639i	$0.521879\pi$
$654$			29.0954i			1.13772i
$655$	1.56719	−	1.56719i	0.0612353	−	0.0612353i
$656$	13.2777	−	13.2777i	0.518407	−	0.518407i
$657$	5.88991	+	5.88991i	0.229787	+	0.229787i
$658$	4.09067	−	4.09067i	0.159471	−	0.159471i
$659$		−	38.2738i		−	1.49094i	−0.666541	−	0.745468i	$-0.732226\pi$
$659$		−	38.2738i		−	1.49094i	0.666541	−	0.745468i	$-0.267774\pi$
$660$	−1.31265	−	1.57446i	−0.0510950	−	0.0612857i
$661$	−5.90612	+	5.90612i	−0.229722	+	0.229722i	−0.812576	−	0.582855i	$-0.801936\pi$
$661$	−5.90612	+	5.90612i	−0.229722	+	0.229722i	0.582855	+	0.812576i	$0.301936\pi$
$662$	−13.1052			−0.509349
$663$	−26.7917	−	0.325983i	−1.04050	−	0.0126601i
$664$	−8.70969			−0.338001
$665$	−2.30806	−	2.30806i	−0.0895029	−	0.0895029i
$666$			1.95690i			0.0758285i
$667$	−0.931175			−0.0360553
$668$	−0.117760	+	0.117760i	−0.00455627	+	0.00455627i
$669$	2.11012	+	2.11012i	0.0815819	+	0.0815819i
$670$	−12.5129	−	12.5129i	−0.483416	−	0.483416i
$671$	13.0899	+	1.18699i	0.505331	+	0.0458232i
$672$	−2.71010			−0.104544
$673$	−25.6800			−0.989890			−0.494945	−	0.868924i	$-0.664812\pi$
$673$	−25.6800			−0.989890			−0.494945	+	0.868924i	$0.664812\pi$
$674$	−5.12739	+	5.12739i	−0.197500	+	0.197500i
$675$			3.55170i			0.136705i
$676$	0.162444	−	6.67445i	0.00624785	−	0.256710i
$677$		−	16.6812i		−	0.641111i	−0.947230	−	0.320555i	$-0.896130\pi$
$677$		−	16.6812i		−	0.641111i	0.947230	−	0.320555i	$-0.103870\pi$
$678$	−20.7167	+	20.7167i	−0.795619	+	0.795619i
$679$			14.4580i			0.554848i
$680$			21.0756i			0.808213i
$681$	−20.5713	+	20.5713i	−0.788295	+	0.788295i
$682$	−4.85713	+	53.5636i	−0.185989	+	2.05106i
$683$	−13.1925	+	13.1925i	−0.504796	+	0.504796i	−0.912925	−	0.408128i	$-0.866182\pi$
$683$	−13.1925	+	13.1925i	−0.504796	+	0.504796i	0.408128	+	0.912925i	$0.366182\pi$
$684$	−1.03172	−	1.03172i	−0.0394488	−	0.0394488i
$685$	21.1368			0.807594
$686$		−	19.8105i		−	0.756369i
$687$	7.75638	−	7.75638i	0.295924	−	0.295924i
$688$	−21.5498			−0.821578
$689$	44.8760	+	0.546019i	1.70964	+	0.0208017i
$690$			7.21024i			0.274489i
$691$	26.0272	+	26.0272i	0.990121	+	0.990121i	0.999952	−	0.00983101i	$-0.00312936\pi$
$691$	26.0272	+	26.0272i	0.990121	+	0.990121i	−0.00983101	+	0.999952i	$0.503129\pi$
$692$			5.60995i			0.213258i
$693$	2.43197	−	2.02758i	0.0923828	−	0.0770213i
$694$	−8.50343	−	8.50343i	−0.322786	−	0.322786i
$695$	−9.96852	+	9.96852i	−0.378127	+	0.378127i
$696$	−0.410612	+	0.410612i	−0.0155642	+	0.0155642i
$697$	−20.7142	+	20.7142i	−0.784605	+	0.784605i
$698$	−13.6615			−0.517096
$699$	20.1032			0.760374
$700$	1.23134	+	1.23134i	0.0465404	+	0.0465404i
$701$	−25.5094			−0.963478			−0.481739	−	0.876315i	$-0.659995\pi$
$701$	−25.5094			−0.963478			−0.481739	+	0.876315i	$0.659995\pi$
$702$	−4.09093	+	3.99258i	−0.154402	+	0.150690i
$703$		−	3.50671i		−	0.132258i
$704$	−16.6017	−	1.50544i	−0.625701	−	0.0567384i
$705$	−4.59977			−0.173238
$706$	22.1743			0.834542
$707$	1.54605	+	1.54605i	0.0581452	+	0.0581452i
$708$	−3.22367	−	3.22367i	−0.121153	−	0.121153i
$709$	−21.5724	+	21.5724i	−0.810169	+	0.810169i	−0.984659	−	0.174490i	$-0.944172\pi$
$709$	−21.5724	+	21.5724i	−0.810169	+	0.810169i	0.174490	+	0.984659i	$0.444172\pi$
$710$	−4.61687	−	4.61687i	−0.173268	−	0.173268i
$711$			11.3349i			0.425094i
$712$	17.9716			0.673515
$713$	27.3316	−	27.3316i	1.02358	−	1.02358i
$714$	11.2477			0.420935
$715$	11.1648	−	9.08039i	0.417542	−	0.339587i
$716$	−5.30345			−0.198199
$717$	10.8128	−	10.8128i	0.403812	−	0.403812i
$718$	−3.92437			−0.146456
$719$		−	17.3939i		−	0.648682i	−0.945940	−	0.324341i	$-0.894857\pi$
$719$		−	17.3939i		−	0.648682i	0.945940	−	0.324341i	$-0.105143\pi$
$720$	4.05350	+	4.05350i	0.151065	+	0.151065i
$721$	7.71646	−	7.71646i	0.287376	−	0.287376i
$722$	−12.2516	−	12.2516i	−0.455958	−	0.455958i
$723$	8.92902	+	8.92902i	0.332074	+	0.332074i
$724$	5.66356			0.210485
$725$	0.875171			0.0325030
$726$	−14.3488	+	9.91233i	−0.532534	+	0.367881i
$727$		−	52.6079i		−	1.95112i	−0.219737	−	0.975559i	$-0.570520\pi$
$727$		−	52.6079i		−	1.95112i	0.219737	−	0.975559i	$-0.429480\pi$
$728$	0.0986917	−	8.11123i	0.00365776	−	0.300622i
$729$	1.00000			0.0370370
$730$	−11.2379	−	11.2379i	−0.415932	−	0.415932i
$731$	33.6193			1.24345
$732$	2.03526			0.0752254
$733$	24.6461	−	24.6461i	0.910323	−	0.910323i	−0.0859740	−	0.996297i	$-0.527400\pi$
$733$	24.6461	−	24.6461i	0.910323	−	0.910323i	0.996297	+	0.0859740i	$0.0274002\pi$
$734$	−4.78722	+	4.78722i	−0.176700	+	0.176700i
$735$	−5.18121	+	5.18121i	−0.191112	+	0.191112i
$736$	−7.58554	−	7.58554i	−0.279607	−	0.279607i
$737$	−23.6264	+	19.6978i	−0.870291	+	0.725579i
$738$			6.24982i			0.230059i
$739$	1.30403	+	1.30403i	0.0479696	+	0.0479696i	0.730685	−	0.682715i	$-0.239201\pi$
$739$	1.30403	+	1.30403i	0.0479696	+	0.0479696i	−0.682715	+	0.730685i	$0.739201\pi$
$740$		−	0.762877i		−	0.0280439i
$741$	7.33082	−	7.15457i	0.269304	−	0.262830i
$742$	−18.8398			−0.691632
$743$	−20.7321	+	20.7321i	−0.760586	+	0.760586i	−0.976428	−	0.215842i	$-0.930750\pi$
$743$	−20.7321	+	20.7321i	−0.760586	+	0.760586i	0.215842	+	0.976428i	$0.430750\pi$
$744$		−	24.1044i		−	0.883709i
$745$	22.2535			0.815306
$746$	29.0935	+	29.0935i	1.06519	+	1.06519i
$747$	2.61335	−	2.61335i	0.0956175	−	0.0956175i
$748$	−12.6061	−	1.14311i	−0.460924	−	0.0417964i
$749$	13.1660	−	13.1660i	0.481077	−	0.481077i
$750$		−	16.3165i		−	0.595795i
$751$			9.40675i			0.343257i	0.985162	+	0.171629i	$0.0549029\pi$
$751$			9.40675i			0.343257i	−0.985162	+	0.171629i	$0.945097\pi$
$752$	12.8738	−	12.8738i	0.469460	−	0.469460i
$753$		−	23.1015i		−	0.841867i
$754$	0.983809	+	1.00804i	0.0358282	+	0.0367108i
$755$			16.2928i			0.592957i
$756$	0.346691	−	0.346691i	0.0126090	−	0.0126090i
$757$	40.3458			1.46639			0.733197	−	0.680017i	$-0.238028\pi$
$757$	40.3458			1.46639			0.733197	+	0.680017i	$0.238028\pi$
$758$	32.3472			1.17490
$759$	12.4822	+	1.13188i	0.453076	+	0.0410848i
$760$	−5.69745	−	5.69745i	−0.206668	−	0.206668i
$761$	21.5979	+	21.5979i	0.782922	+	0.782922i	0.980323	−	0.197401i	$-0.0632501\pi$
$761$	21.5979	+	21.5979i	0.782922	+	0.782922i	−0.197401	+	0.980323i	$0.563250\pi$
$762$	−5.48715	+	5.48715i	−0.198778	+	0.198778i
$763$	17.5201			0.634269
$764$			6.74066i			0.243869i
$765$	−6.32377	−	6.32377i	−0.228636	−	0.228636i
$766$	−7.34184			−0.265271
$767$	22.9056	−	22.3549i	0.827072	−	0.807188i
$768$	−11.5825			−0.417949
$769$	15.9879	−	15.9879i	0.576538	−	0.576538i	−0.357410	−	0.933948i	$-0.616340\pi$
$769$	15.9879	−	15.9879i	0.576538	−	0.576538i	0.933948	+	0.357410i	$0.116340\pi$
$770$	−4.64016	+	3.86859i	−0.167220	+	0.139414i
$771$		−	11.2666i		−	0.405758i
$772$	7.43932	−	7.43932i	0.267747	−	0.267747i
$773$	−8.50452	−	8.50452i	−0.305886	−	0.305886i	0.537425	−	0.843312i	$-0.319397\pi$
$773$	−8.50452	−	8.50452i	−0.305886	−	0.305886i	−0.843312	+	0.537425i	$0.819397\pi$
$774$	5.07175	−	5.07175i	0.182300	−	0.182300i
$775$	−25.6878	+	25.6878i	−0.922733	+	0.922733i
$776$			35.6896i			1.28118i
$777$	1.17837			0.0422737
$778$	38.7991	+	38.7991i	1.39102	+	1.39102i
$779$		−	11.1995i		−	0.401263i
$780$	1.59480	−	1.55646i	0.0571032	−	0.0557303i
$781$	−8.71741	+	7.26787i	−0.311934	+	0.260065i
$782$	31.4823	+	31.4823i	1.12580	+	1.12580i
$783$		−	0.246409i		−	0.00880595i
$784$		−	29.0023i		−	1.03580i
$785$	6.94028	+	6.94028i	0.247709	+	0.247709i
$786$	−2.06461	−	2.06461i	−0.0736423	−	0.0736423i
$787$	−26.7297	−	26.7297i	−0.952810	−	0.952810i	0.0461256	−	0.998936i	$-0.485313\pi$
$787$	−26.7297	−	26.7297i	−0.952810	−	0.952810i	−0.998936	+	0.0461256i	$0.985313\pi$
$788$	−0.686938	−	0.686938i	−0.0244712	−	0.0244712i
$789$		−	6.58637i		−	0.234481i
$790$		−	21.6269i		−	0.769451i
$791$	12.4747	+	12.4747i	0.443551	+	0.443551i
$792$	6.00330	−	5.00506i	0.213318	−	0.177847i
$793$	−0.173841	+	14.2876i	−0.00617328	+	0.507367i
$794$		−	42.1679i		−	1.49648i
$795$	10.5923	+	10.5923i	0.375669	+	0.375669i
$796$	−2.71540			−0.0962447
$797$		−	17.1251i		−	0.606601i	−0.952895	−	0.303301i	$-0.901911\pi$
$797$		−	17.1251i		−	0.606601i	0.952895	−	0.303301i	$-0.0980887\pi$
$798$	−3.04063	+	3.04063i	−0.107637	+	0.107637i
$799$	−20.0841	+	20.0841i	−0.710525	+	0.710525i
$800$	7.12932	+	7.12932i	0.252060	+	0.252060i
$801$	−5.39241	+	5.39241i	−0.190531	+	0.190531i
$802$		−	23.2613i		−	0.821387i
$803$	−21.2189	+	17.6906i	−0.748800	+	0.624289i
$804$	−3.36809	+	3.36809i	−0.118783	+	0.118783i
$805$	4.34172			0.153025
$806$	−58.4643	−	0.711353i	−2.05932	−	0.0250563i
$807$	−8.85053			−0.311554
$808$	3.81642	+	3.81642i	0.134261	+	0.134261i
$809$		−	13.4600i		−	0.473228i	−0.971604	−	0.236614i	$-0.923962\pi$
$809$		−	13.4600i		−	0.473228i	0.971604	−	0.236614i	$-0.0760377\pi$
$810$	−1.90799			−0.0670398
$811$	7.51966	−	7.51966i	0.264051	−	0.264051i	−0.562646	−	0.826698i	$-0.690217\pi$
$811$	7.51966	−	7.51966i	0.264051	−	0.264051i	0.826698	+	0.562646i	$0.190217\pi$
$812$	−0.0854280	−	0.0854280i	−0.00299794	−	0.00299794i
$813$	9.40355	+	9.40355i	0.329797	+	0.329797i
$814$	−6.46380	−	0.586135i	−0.226556	−	0.0205440i
$815$	9.43156			0.330373
$816$	35.3979			1.23917
$817$	−9.08841	+	9.08841i	−0.317963	+	0.317963i
$818$			28.1164i			0.983066i
$819$	2.40417	+	2.46340i	0.0840085	+	0.0860780i
$820$		−	2.43642i		−	0.0850835i
$821$	−27.3995	+	27.3995i	−0.956249	+	0.956249i	−0.999082	−	0.0428337i	$-0.986361\pi$
$821$	−27.3995	+	27.3995i	−0.956249	+	0.956249i	0.0428337	+	0.999082i	$0.486361\pi$
$822$		−	27.8454i		−	0.971221i
$823$		−	36.7296i		−	1.28031i	−0.768244	−	0.640157i	$-0.778869\pi$
$823$		−	36.7296i		−	1.28031i	0.768244	−	0.640157i	$-0.221131\pi$
$824$	19.0481	−	19.0481i	0.663570	−	0.663570i
$825$	−11.7315	−	1.06381i	−0.408439	−	0.0370371i
$826$	−9.50063	+	9.50063i	−0.330569	+	0.330569i
$827$	21.2708	+	21.2708i	0.739658	+	0.739658i	0.972512	−	0.232854i	$-0.0748064\pi$
$827$	21.2708	+	21.2708i	0.739658	+	0.739658i	−0.232854	+	0.972512i	$0.574806\pi$
$828$	1.94077			0.0674466
$829$		−	27.5482i		−	0.956790i	−0.878145	−	0.478395i	$-0.841219\pi$
$829$		−	27.5482i		−	0.956790i	0.878145	−	0.478395i	$-0.158781\pi$
$830$	−4.98624	+	4.98624i	−0.173075	+	0.173075i
$831$	−11.5221			−0.399697
$832$	0.220480	−	18.1207i	0.00764376	−	0.628222i
$833$			45.2457i			1.56767i
$834$	13.1325	+	13.1325i	0.454740	+	0.454740i
$835$		−	0.390248i		−	0.0135051i
$836$	3.71687	−	3.09882i	0.128551	−	0.107175i
$837$	7.23254	+	7.23254i	0.249993	+	0.249993i
$838$	0.0550895	−	0.0550895i	0.00190303	−	0.00190303i
$839$	3.05505	−	3.05505i	0.105472	−	0.105472i	−0.652401	−	0.757874i	$-0.726238\pi$
$839$	3.05505	−	3.05505i	0.105472	−	0.105472i	0.757874	+	0.652401i	$0.226238\pi$
$840$	1.91453	−	1.91453i	0.0660575	−	0.0660575i
$841$	28.9393			0.997906
$842$	17.7875			0.612997
$843$	15.2681	+	15.2681i	0.525862	+	0.525862i
$844$	−0.954233			−0.0328461
$845$	10.7902	+	11.3285i	0.371194	+	0.389713i
$846$			6.05972i			0.208337i
$847$	5.96881	+	8.64026i	0.205091	+	0.296883i
$848$	−59.2912			−2.03607
$849$	−1.21751			−0.0417850
$850$	−29.5888	−	29.5888i	−1.01489	−	1.01489i
$851$	3.29825	+	3.29825i	0.113062	+	0.113062i
$852$	−1.24272	+	1.24272i	−0.0425749	+	0.0425749i
$853$	−3.27233	−	3.27233i	−0.112043	−	0.112043i	0.648863	−	0.760905i	$-0.275245\pi$
$853$	−3.27233	−	3.27233i	−0.112043	−	0.112043i	−0.760905	+	0.648863i	$0.775245\pi$
$854$		−	5.99822i		−	0.205255i
$855$	3.41905			0.116929
$856$	32.5003	−	32.5003i	1.11084	−	1.11084i
$857$	19.4140			0.663170			0.331585	−	0.943425i	$-0.392417\pi$
$857$	19.4140			0.663170			0.331585	+	0.943425i	$0.392417\pi$
$858$	−11.9625	−	14.7085i	−0.408392	−	0.502140i
$859$	−27.1641			−0.926826			−0.463413	−	0.886142i	$-0.653375\pi$
$859$	−27.1641			−0.926826			−0.463413	+	0.886142i	$0.653375\pi$
$860$	−1.97716	+	1.97716i	−0.0674207	+	0.0674207i
$861$	3.76339			0.128256
$862$		−	9.33421i		−	0.317924i
$863$	9.88657	+	9.88657i	0.336543	+	0.336543i	0.855064	−	0.518522i	$-0.173517\pi$
$863$	9.88657	+	9.88657i	0.336543	+	0.336543i	−0.518522	+	0.855064i	$0.673517\pi$
$864$	2.00730	−	2.00730i	0.0682897	−	0.0682897i
$865$	−9.29550	−	9.29550i	−0.316056	−	0.316056i
$866$	−32.9281	−	32.9281i	−1.11894	−	1.11894i
$867$	−38.2233			−1.29813
$868$	5.01492			0.170218
$869$	−37.4401	−	3.39506i	−1.27007	−	0.115169i
$870$			0.470146i			0.0159394i
$871$	−23.3564	−	23.9318i	−0.791402	−	0.810897i
$872$	43.2482			1.46457
$873$	−10.7087	−	10.7087i	−0.362435	−	0.362435i
$874$	−17.0214			−0.575758
$875$	−9.82515			−0.332151
$876$	−3.02489	+	3.02489i	−0.102202	+	0.102202i
$877$	23.9980	−	23.9980i	0.810356	−	0.810356i	−0.174331	−	0.984687i	$-0.555776\pi$
$877$	23.9980	−	23.9980i	0.810356	−	0.810356i	0.984687	+	0.174331i	$0.0557763\pi$
$878$	12.8614	−	12.8614i	0.434050	−	0.434050i
$879$	8.56257	+	8.56257i	0.288808	+	0.288808i
$880$	−14.6031	+	12.1749i	−0.492271	+	0.410416i
$881$		−	32.7833i		−	1.10450i	−0.833679	−	0.552249i	$-0.813770\pi$
$881$		−	32.7833i		−	1.10450i	0.833679	−	0.552249i	$-0.186230\pi$
$882$	6.82570	+	6.82570i	0.229833	+	0.229833i
$883$			0.187257i			0.00630171i	0.999995	+	0.00315085i	$0.00100295\pi$
$883$			0.187257i			0.00630171i	−0.999995	+	0.00315085i	$0.998997\pi$
$884$	0.167415	−	13.7595i	0.00563079	−	0.462781i
$885$	10.6830			0.359106
$886$	−25.4953	+	25.4953i	−0.856531	+	0.856531i
$887$			20.7436i			0.696501i	0.937401	+	0.348251i	$0.113224\pi$
$887$			20.7436i			0.696501i	−0.937401	+	0.348251i	$0.886776\pi$
$888$	2.90880			0.0976129
$889$	3.30414	+	3.30414i	0.110817	+	0.110817i
$890$	10.2886	−	10.2886i	0.344876	−	0.344876i
$891$	−0.299521	+	3.30307i	−0.0100343	+	0.110657i
$892$	−1.08370	+	1.08370i	−0.0362849	+	0.0362849i
$893$		−	10.8588i		−	0.363377i
$894$		−	29.3167i		−	0.980497i
$895$	8.78764	−	8.78764i	0.293738	−	0.293738i
$896$			13.0276i			0.435222i
$897$	−0.165771	+	13.6243i	−0.00553492	+	0.454902i
$898$		−	11.2968i		−	0.376980i
$899$	1.78217	−	1.78217i	0.0594386	−	0.0594386i
$900$	−1.82405			−0.0608017
$901$	92.4986			3.08158
$902$	−20.6436	−	1.87195i	−0.687356	−	0.0623292i
$903$	−3.05400	−	3.05400i	−0.101631	−	0.101631i
$904$	30.7939	+	30.7939i	1.02419	+	1.02419i
$905$	−9.38434	+	9.38434i	−0.311946	+	0.311946i
$906$	21.4641			0.713097
$907$			31.3448i			1.04079i	0.853926	+	0.520394i	$0.174215\pi$
$907$			31.3448i			1.04079i	−0.853926	+	0.520394i	$0.825785\pi$
$908$	−10.5648	−	10.5648i	−0.350607	−	0.350607i
$909$	−2.29024			−0.0759625
$910$	−4.58712	−	4.70013i	−0.152062	−	0.155808i
$911$	−60.2940			−1.99763			−0.998815	−	0.0486660i	$-0.984503\pi$
$911$	−60.2940			−1.99763			−0.998815	+	0.0486660i	$0.984503\pi$
$912$	−9.56922	+	9.56922i	−0.316869	+	0.316869i
$913$	7.84934	+	9.41484i	0.259775	+	0.311586i
$914$			54.1239i			1.79026i
$915$	−3.37236	+	3.37236i	−0.111487	+	0.111487i
$916$	3.98345	+	3.98345i	0.131617	+	0.131617i
$917$	−1.24323	+	1.24323i	−0.0410549	+	0.0410549i
$918$	−8.33090	+	8.33090i	−0.274961	+	0.274961i
$919$			57.7808i			1.90601i	0.302948	+	0.953007i	$0.402029\pi$
$919$			57.7808i			1.90601i	−0.302948	+	0.953007i	$0.597971\pi$
$920$	10.7175			0.353346
$921$	−3.18728	−	3.18728i	−0.105024	−	0.105024i
$922$			43.7587i			1.44112i
$923$	−8.61778	−	8.83007i	−0.283658	−	0.290645i
$924$	1.04131	+	1.24899i	0.0342564	+	0.0410887i
$925$	−3.09988	−	3.09988i	−0.101923	−	0.101923i
$926$			4.32500i			0.142128i
$927$			11.4308i			0.375436i
$928$	−0.494617	−	0.494617i	−0.0162366	−	0.0162366i
$929$	22.2721	+	22.2721i	0.730723	+	0.730723i	0.970763	−	0.240040i	$-0.0771607\pi$
$929$	22.2721	+	22.2721i	0.730723	+	0.730723i	−0.240040	+	0.970763i	$0.577161\pi$
$930$	−13.7996	−	13.7996i	−0.452507	−	0.452507i
$931$	−12.2314	−	12.2314i	−0.400869	−	0.400869i
$932$			10.3244i			0.338188i
$933$		−	6.59476i		−	0.215903i
$934$	34.9106	+	34.9106i	1.14231	+	1.14231i
$935$	22.7820	−	18.9938i	0.745050	−	0.621162i
$936$	5.93468	+	6.08088i	0.193981	+	0.198760i
$937$		−	29.1339i		−	0.951763i	−0.879510	−	0.475881i	$-0.842129\pi$
$937$		−	29.1339i		−	0.951763i	0.879510	−	0.475881i	$-0.157871\pi$
$938$	9.92627	+	9.92627i	0.324104	+	0.324104i
$939$	24.4375			0.797487
$940$		−	2.36231i		−	0.0770501i
$941$	0.967107	−	0.967107i	0.0315268	−	0.0315268i	−0.691168	−	0.722694i	$-0.742903\pi$
$941$	0.967107	−	0.967107i	0.0315268	−	0.0315268i	0.722694	+	0.691168i	$0.242903\pi$
$942$	9.14309	−	9.14309i	0.297898	−	0.297898i
$943$	10.5337	+	10.5337i	0.343024	+	0.343024i
$944$	−29.8996	+	29.8996i	−0.973149	+	0.973149i
$945$			1.14891i			0.0373741i
$946$	15.2333	+	18.2714i	0.495276	+	0.594056i
$947$	1.96456	−	1.96456i	0.0638395	−	0.0638395i	−0.674466	−	0.738306i	$-0.735626\pi$
$947$	1.96456	−	1.96456i	0.0638395	−	0.0638395i	0.738306	+	0.674466i	$0.235626\pi$
$948$	−5.82130			−0.189067
$949$	−20.9764	−	21.4932i	−0.680924	−	0.697698i
$950$	15.9977			0.519034
$951$	−21.5305	−	21.5305i	−0.698175	−	0.698175i
$952$		−	16.7189i		−	0.541863i
$953$	−37.6571			−1.21983			−0.609917	−	0.792465i	$-0.708797\pi$
$953$	−37.6571			−1.21983			−0.609917	+	0.792465i	$0.708797\pi$
$954$	13.9542	−	13.9542i	0.451784	−	0.451784i
$955$	−11.1691	−	11.1691i	−0.361422	−	0.361422i
$956$	5.55315	+	5.55315i	0.179602	+	0.179602i
$957$	0.813908	+	0.0738049i	0.0263099	+	0.00238577i
$958$	28.0568			0.906476
$959$	−16.7674			−0.541448
$960$	4.27711	−	4.27711i	0.138043	−	0.138043i
$961$			73.6193i			2.37482i
$962$	0.0858426	−	7.05520i	0.00276768	−	0.227469i
$963$			19.5035i			0.628492i
$964$	−4.58569	+	4.58569i	−0.147695	+	0.147695i
$965$			24.6534i			0.793622i
$966$		−	5.71975i		−	0.184030i
$967$	−27.9252	+	27.9252i	−0.898014	+	0.898014i	−0.995260	−	0.0972465i	$-0.968996\pi$
$967$	−27.9252	+	27.9252i	−0.898014	+	0.898014i	0.0972465	+	0.995260i	$0.468996\pi$
$968$	14.7340	+	21.3285i	0.473568	+	0.685522i
$969$	14.9287	−	14.9287i	0.479579	−	0.479579i
$970$	20.4321	+	20.4321i	0.656034	+	0.656034i
$971$	19.4007			0.622597			0.311299	−	0.950312i	$-0.399236\pi$
$971$	19.4007			0.622597			0.311299	+	0.950312i	$0.399236\pi$
$972$			0.513571i			0.0164728i
$973$	7.90785	−	7.90785i	0.253514	−	0.253514i
$974$	25.2237			0.808220
$975$	0.155801	−	12.8049i	0.00498962	−	0.410084i
$976$		−	18.8771i		−	0.604241i
$977$	−24.7208	−	24.7208i	−0.790887	−	0.790887i	0.190751	−	0.981638i	$-0.438908\pi$
$977$	−24.7208	−	24.7208i	−0.790887	−	0.790887i	−0.981638	+	0.190751i	$0.938908\pi$
$978$		−	12.4251i		−	0.397310i
$979$	−16.1964	−	19.4266i	−0.517638	−	0.620878i
$980$	−2.66092	−	2.66092i	−0.0850000	−	0.0850000i
$981$	−12.9767	+	12.9767i	−0.414313	+	0.414313i
$982$	−2.68277	+	2.68277i	−0.0856105	+	0.0856105i
$983$	−14.5113	+	14.5113i	−0.462838	+	0.462838i	−0.899585	−	0.436746i	$-0.856131\pi$
$983$	−14.5113	+	14.5113i	−0.462838	+	0.462838i	0.436746	+	0.899585i	$0.356131\pi$
$984$	9.28990			0.296151
$985$	2.27647			0.0725343
$986$	2.05281	+	2.05281i	0.0653748	+	0.0653748i
$987$	3.64892			0.116146
$988$	3.67438	+	3.76490i	0.116898	+	0.119777i
$989$		−	17.0963i		−	0.543630i
$990$	0.571483	−	6.30222i	0.0181629	−	0.200298i
$991$	30.6304			0.973007			0.486504	−	0.873679i	$-0.338272\pi$
$991$	30.6304			0.973007			0.486504	+	0.873679i	$0.338272\pi$
$992$	29.0358			0.921886
$993$	−5.84499	−	5.84499i	−0.185485	−	0.185485i
$994$	3.66248	+	3.66248i	0.116167	+	0.116167i
$995$	4.49933	−	4.49933i	0.142638	−	0.142638i
$996$	1.34214	+	1.34214i	0.0425274	+	0.0425274i
$997$			62.8288i			1.98981i	0.100834	+	0.994903i	$0.467849\pi$
$997$			62.8288i			1.98981i	−0.100834	+	0.994903i	$0.532151\pi$
$998$	−26.9829			−0.854130
$999$	−0.872788	+	0.872788i	−0.0276138	+	0.0276138i

Twists

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

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

\(f(q)\)	\(=\)	\(q+(-1.12106 + 1.12106i) q^{2} -1.00000 q^{3} -0.513571i q^{4} +(0.850971 + 0.850971i) q^{5} +(1.12106 - 1.12106i) q^{6} +(-0.675060 - 0.675060i) q^{7} +(-1.66638 - 1.66638i) q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+(-1.12106 + 1.12106i) q^{2} -1.00000 q^{3} -0.513571i q^{4} +(0.850971 + 0.850971i) q^{5} +(1.12106 - 1.12106i) q^{6} +(-0.675060 - 0.675060i) q^{7} +(-1.66638 - 1.66638i) q^{8} +1.00000 q^{9} -1.90799 q^{10} +(-0.299521 + 3.30307i) q^{11} +0.513571i q^{12} +(-3.60528 - 0.0438666i) q^{13} +1.51357 q^{14} +(-0.850971 - 0.850971i) q^{15} +4.76339 q^{16} -7.43124 q^{17} +(-1.12106 + 1.12106i) q^{18} +(2.00891 - 2.00891i) q^{19} +(0.437034 - 0.437034i) q^{20} +(0.675060 + 0.675060i) q^{21} +(-3.36717 - 4.03874i) q^{22} +3.77898i q^{23} +(1.66638 + 1.66638i) q^{24} -3.55170i q^{25} +(4.09093 - 3.99258i) q^{26} -1.00000 q^{27} +(-0.346691 + 0.346691i) q^{28} +0.246409i q^{29} +1.90799 q^{30} +(-7.23254 - 7.23254i) q^{31} +(-2.00730 + 2.00730i) q^{32} +(0.299521 - 3.30307i) q^{33} +(8.33090 - 8.33090i) q^{34} -1.14891i q^{35} -0.513571i q^{36} +(0.872788 - 0.872788i) q^{37} +4.50424i q^{38} +(3.60528 + 0.0438666i) q^{39} -2.83609i q^{40} +(2.78745 - 2.78745i) q^{41} -1.51357 q^{42} -4.52405 q^{43} +(1.69636 + 0.153826i) q^{44} +(0.850971 + 0.850971i) q^{45} +(-4.23648 - 4.23648i) q^{46} +(2.70266 - 2.70266i) q^{47} -4.76339 q^{48} -6.08859i q^{49} +(3.98168 + 3.98168i) q^{50} +7.43124 q^{51} +(-0.0225286 + 1.85157i) q^{52} -12.4473 q^{53} +(1.12106 - 1.12106i) q^{54} +(-3.06570 + 2.55593i) q^{55} +2.24982i q^{56} +(-2.00891 + 2.00891i) q^{57} +(-0.276241 - 0.276241i) q^{58} +(-6.27696 + 6.27696i) q^{59} +(-0.437034 + 0.437034i) q^{60} -3.96296i q^{61} +16.2163 q^{62} +(-0.675060 - 0.675060i) q^{63} +5.02615i q^{64} +(-3.03066 - 3.10532i) q^{65} +(3.36717 + 4.03874i) q^{66} +(6.55818 + 6.55818i) q^{67} +3.81647i q^{68} -3.77898i q^{69} +(1.28801 + 1.28801i) q^{70} +(2.41976 + 2.41976i) q^{71} +(-1.66638 - 1.66638i) q^{72} +(5.88991 + 5.88991i) q^{73} +1.95690i q^{74} +3.55170i q^{75} +(-1.03172 - 1.03172i) q^{76} +(2.43197 - 2.02758i) q^{77} +(-4.09093 + 3.99258i) q^{78} +11.3349i q^{79} +(4.05350 + 4.05350i) q^{80} +1.00000 q^{81} +6.24982i q^{82} +(2.61335 - 2.61335i) q^{83} +(0.346691 - 0.346691i) q^{84} +(-6.32377 - 6.32377i) q^{85} +(5.07175 - 5.07175i) q^{86} -0.246409i q^{87} +(6.00330 - 5.00506i) q^{88} +(-5.39241 + 5.39241i) q^{89} -1.90799 q^{90} +(2.40417 + 2.46340i) q^{91} +1.94077 q^{92} +(7.23254 + 7.23254i) q^{93} +6.05972i q^{94} +3.41905 q^{95} +(2.00730 - 2.00730i) q^{96} +(-10.7087 - 10.7087i) q^{97} +(6.82570 + 6.82570i) q^{98} +(-0.299521 + 3.30307i) 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	\( 28 q - 28 q^{3} + 4 q^{5} + 28 q^{9} + 4 q^{11} + 48 q^{14} - 4 q^{15} - 52 q^{16} - 8 q^{20} - 32 q^{22} - 4 q^{26} - 28 q^{27} + 24 q^{31} - 4 q^{33} + 16 q^{34} - 12 q^{37} - 48 q^{42} - 24 q^{44} + 4 q^{45} - 8 q^{47} + 52 q^{48} - 8 q^{53} + 48 q^{55} - 64 q^{58} + 4 q^{59} + 8 q^{60} + 32 q^{66} + 28 q^{67} - 4 q^{70} + 12 q^{71} + 4 q^{78} + 56 q^{80} + 28 q^{81} - 8 q^{86} - 104 q^{89} - 76 q^{91} - 24 q^{93} - 8 q^{97} + 4 q^{99}+O(q^{100}) \) 28 * q - 28 * q^3 + 4 * q^5 + 28 * q^9 + 4 * q^11 + 48 * q^14 - 4 * q^15 - 52 * q^16 - 8 * q^20 - 32 * q^22 - 4 * q^26 - 28 * q^27 + 24 * q^31 - 4 * q^33 + 16 * q^34 - 12 * q^37 - 48 * q^42 - 24 * q^44 + 4 * q^45 - 8 * q^47 + 52 * q^48 - 8 * q^53 + 48 * q^55 - 64 * q^58 + 4 * q^59 + 8 * q^60 + 32 * q^66 + 28 * q^67 - 4 * q^70 + 12 * q^71 + 4 * q^78 + 56 * q^80 + 28 * q^81 - 8 * q^86 - 104 * q^89 - 76 * q^91 - 24 * q^93 - 8 * q^97 + 4 * q^99

Introduction

L-functions

Modular forms

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Database

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