LMFDB - Embedded newform 252.2.ba.a.155.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,2,Mod(155,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1, 0]))

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

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

chi := DirichletCharacter("252.155");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	252.ba (of order $6$, 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:	$2.01223013094$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$36$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			155.14
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.553365 - 1.30146i) q^{2} +(1.10270 + 1.33569i) q^{3} +(-1.38757 + 1.44036i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.12814 - 2.17423i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +O(q^{10})$	\(q+(-0.553365 - 1.30146i) q^{2} +(1.10270 + 1.33569i) q^{3} +(-1.38757 + 1.44036i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.12814 - 2.17423i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +(-4.75149 - 3.57600i) q^{10} +(-1.11389 + 1.92931i) q^{11} +(-3.45394 - 0.265082i) q^{12} +(1.14629 + 1.98544i) q^{13} +(-0.171499 + 1.40378i) q^{14} +(6.82394 + 2.54568i) q^{15} +(-0.149279 - 3.99721i) q^{16} -3.74182i q^{17} +(4.14810 - 0.890676i) q^{18} -4.90288i q^{19} +(-2.02469 + 8.16269i) q^{20} +(-0.287120 - 1.70809i) q^{21} +(3.12730 + 0.382063i) q^{22} +(2.71771 + 4.70721i) q^{23} +(1.56630 + 4.64184i) q^{24} +(6.34110 - 10.9831i) q^{25} +(1.94964 - 2.59053i) q^{26} +(-4.56102 + 2.48940i) q^{27} +(1.92185 - 0.553602i) q^{28} +(0.985523 + 0.568992i) q^{29} +(-0.463043 - 10.2897i) q^{30} +(-1.45004 + 0.837182i) q^{31} +(-5.11959 + 2.40620i) q^{32} +(-3.80524 + 0.639641i) q^{33} +(-4.86981 + 2.07059i) q^{34} -4.20502 q^{35} +(-3.45459 - 4.90569i) q^{36} -11.8022 q^{37} +(-6.38088 + 2.71308i) q^{38} +(-1.38791 + 3.72043i) q^{39} +(11.7438 - 1.88190i) q^{40} +(-2.39482 + 1.38265i) q^{41} +(-2.06412 + 1.31887i) q^{42} +(-0.416255 - 0.240325i) q^{43} +(-1.23330 - 4.28147i) q^{44} +(4.12451 + 11.9218i) q^{45} +(4.62234 - 6.14179i) q^{46} +(1.47406 - 2.55314i) q^{47} +(5.17442 - 4.60711i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-17.8030 - 2.17499i) q^{50} +(4.99790 - 4.12609i) q^{51} +(-4.45032 - 1.10387i) q^{52} +4.61318i q^{53} +(5.76376 + 4.55841i) q^{54} +9.36786i q^{55} +(-1.78398 - 2.19486i) q^{56} +(6.54871 - 5.40639i) q^{57} +(0.195164 - 1.59747i) q^{58} +(-1.12516 - 1.94884i) q^{59} +(-13.1354 + 6.29662i) q^{60} +(-2.35467 + 4.07841i) q^{61} +(1.89196 + 1.42390i) q^{62} +(1.96486 - 2.26701i) q^{63} +(5.96457 + 5.33141i) q^{64} +(8.34882 + 4.82020i) q^{65} +(2.93815 + 4.59840i) q^{66} +(-11.4941 + 6.63610i) q^{67} +(5.38957 + 5.19205i) q^{68} +(-3.29055 + 8.82064i) q^{69} +(2.32691 + 5.47265i) q^{70} -1.00681 q^{71} +(-4.47289 + 7.21063i) q^{72} -5.14489 q^{73} +(6.53091 + 15.3600i) q^{74} +(21.6623 - 3.64132i) q^{75} +(7.06192 + 6.80311i) q^{76} +(1.92931 - 1.11389i) q^{77} +(5.61000 - 0.252452i) q^{78} +(-11.6396 - 6.72012i) q^{79} +(-8.94781 - 14.2426i) q^{80} +(-8.35448 - 3.34703i) q^{81} +(3.12467 + 2.35164i) q^{82} +(6.65730 - 11.5308i) q^{83} +(2.85866 + 1.95654i) q^{84} +(-7.86721 - 13.6264i) q^{85} +(-0.0824311 + 0.674725i) q^{86} +(0.326738 + 1.94378i) q^{87} +(-4.88967 + 3.97431i) q^{88} +12.3797i q^{89} +(13.2333 - 11.9649i) q^{90} -2.29259i q^{91} +(-10.5511 - 2.61712i) q^{92} +(-2.71717 - 1.01364i) q^{93} +(-4.13850 - 0.505600i) q^{94} +(-10.3084 - 17.8546i) q^{95} +(-8.85929 - 4.18486i) q^{96} +(2.52467 - 4.37286i) q^{97} +(0.850411 - 1.12996i) q^{98} +(-5.05039 - 4.37728i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) $ 72 * q + 6 * q^6 + 4 * q^9	$ 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) $ 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$	$-1$

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 $

$2$	−0.553365	−	1.30146i	−0.391288	−	0.920268i
$2$	−0.553365	−	1.30146i	−0.391288	−	0.920268i
$3$	1.10270	+	1.33569i	0.636642	+	0.771159i
$3$	1.10270	+	1.33569i	0.636642	+	0.771159i
$4$	−1.38757	+	1.44036i	−0.693787	+	0.720180i
$5$	3.64166	−	2.10251i	1.62860	−	0.940271i	0.644086	−	0.764953i	$-0.277238\pi$
$5$	3.64166	−	2.10251i	1.62860	−	0.940271i	0.984512	−	0.175318i	$-0.0560955\pi$
$6$	1.12814	−	2.17423i	0.460562	−	0.887627i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$7$	−0.866025	−	0.500000i	−0.327327	−	0.188982i
$8$	2.64240	+	1.00882i	0.934230	+	0.356672i
$9$	−0.568119	+	2.94572i	−0.189373	+	0.981905i
$10$	−4.75149	−	3.57600i	−1.50255	−	1.13083i
$11$	−1.11389	+	1.92931i	−0.335850	+	0.581710i	−0.983648	−	0.180103i	$-0.942357\pi$
$11$	−1.11389	+	1.92931i	−0.335850	+	0.581710i	0.647797	+	0.761813i	$0.275690\pi$
$12$	−3.45394	−	0.265082i	−0.997068	−	0.0765226i
$13$	1.14629	+	1.98544i	0.317925	+	0.550662i	0.980055	−	0.198727i	$-0.0636806\pi$
$13$	1.14629	+	1.98544i	0.317925	+	0.550662i	−0.662130	+	0.749389i	$0.730347\pi$
$14$	−0.171499	+	1.40378i	−0.0458351	+	0.375175i
$15$	6.82394	+	2.54568i	1.76193	+	0.657292i
$16$	−0.149279	−	3.99721i	−0.0373198	−	0.999303i
$17$		−	3.74182i		−	0.907524i	−0.891123	−	0.453762i	$-0.850082\pi$
$17$		−	3.74182i		−	0.907524i	0.891123	−	0.453762i	$-0.149918\pi$
$18$	4.14810	−	0.890676i	0.977716	−	0.209934i
$19$		−	4.90288i		−	1.12480i	−0.826866	−	0.562399i	$-0.809879\pi$
$19$		−	4.90288i		−	1.12480i	0.826866	−	0.562399i	$-0.190121\pi$
$20$	−2.02469	+	8.16269i	−0.452735	+	1.82523i
$21$	−0.287120	−	1.70809i	−0.0626548	−	0.372735i
$22$	3.12730	+	0.382063i	0.666744	+	0.0814561i
$23$	2.71771	+	4.70721i	0.566682	+	0.981522i	0.996891	+	0.0787925i	$0.0251065\pi$
$23$	2.71771	+	4.70721i	0.566682	+	0.981522i	−0.430209	+	0.902729i	$0.641560\pi$
$24$	1.56630	+	4.64184i	0.319720	+	0.947512i
$25$	6.34110	−	10.9831i	1.26822	−	2.19662i
$26$	1.94964	−	2.59053i	0.382357	−	0.508044i
$27$	−4.56102	+	2.48940i	−0.877768	+	0.479086i
$28$	1.92185	−	0.553602i	0.363196	−	0.104621i
$29$	0.985523	+	0.568992i	0.183007	+	0.105659i	0.588705	−	0.808348i	$-0.299638\pi$
$29$	0.985523	+	0.568992i	0.183007	+	0.105659i	−0.405698	+	0.914007i	$0.632971\pi$
$30$	−0.463043	−	10.2897i	−0.0845396	−	1.87864i
$31$	−1.45004	+	0.837182i	−0.260435	+	0.150362i	−0.624533	−	0.780998i	$-0.714711\pi$
$31$	−1.45004	+	0.837182i	−0.260435	+	0.150362i	0.364098	+	0.931361i	$0.381377\pi$
$32$	−5.11959	+	2.40620i	−0.905024	+	0.425360i
$33$	−3.80524	+	0.639641i	−0.662408	+	0.111347i
$34$	−4.86981	+	2.07059i	−0.835165	+	0.355104i
$35$	−4.20502			−0.710778
$36$	−3.45459	−	4.90569i	−0.575765	−	0.817616i
$37$	−11.8022			−1.94026			−0.970132	−	0.242576i	$-0.922008\pi$
$37$	−11.8022			−1.94026			−0.970132	+	0.242576i	$0.922008\pi$
$38$	−6.38088	+	2.71308i	−1.03512	+	0.440120i
$39$	−1.38791	+	3.72043i	−0.222244	+	0.595746i
$40$	11.7438	−	1.88190i	1.85685	−	0.297555i
$41$	−2.39482	+	1.38265i	−0.374008	+	0.215934i	−0.675208	−	0.737627i	$-0.735946\pi$
$41$	−2.39482	+	1.38265i	−0.374008	+	0.215934i	0.301200	+	0.953561i	$0.402613\pi$
$42$	−2.06412	+	1.31887i	−0.318500	+	0.203506i
$43$	−0.416255	−	0.240325i	−0.0634783	−	0.0366492i	0.467925	−	0.883768i	$-0.345002\pi$
$43$	−0.416255	−	0.240325i	−0.0634783	−	0.0366492i	−0.531403	+	0.847119i	$0.678335\pi$
$44$	−1.23330	−	4.28147i	−0.185928	−	0.645456i
$45$	4.12451	+	11.9218i	0.614845	+	1.77719i
$46$	4.62234	−	6.14179i	0.681527	−	0.905557i
$47$	1.47406	−	2.55314i	0.215014	−	0.372414i	−0.738263	−	0.674513i	$-0.764354\pi$
$47$	1.47406	−	2.55314i	0.215014	−	0.372414i	0.953277	+	0.302098i	$0.0976871\pi$
$48$	5.17442	−	4.60711i	0.746863	−	0.664978i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−17.8030	−	2.17499i	−2.51772	−	0.307590i
$51$	4.99790	−	4.12609i	0.699845	−	0.577768i
$52$	−4.45032	−	1.10387i	−0.617148	−	0.153079i
$53$			4.61318i			0.633670i	0.948481	+	0.316835i	$0.102620\pi$
$53$			4.61318i			0.633670i	−0.948481	+	0.316835i	$0.897380\pi$
$54$	5.76376	+	4.55841i	0.784348	+	0.620321i
$55$			9.36786i			1.26316i
$56$	−1.78398	−	2.19486i	−0.238394	−	0.293301i
$57$	6.54871	−	5.40639i	0.867398	−	0.716094i
$58$	0.195164	−	1.59747i	0.0256262	−	0.209759i
$59$	−1.12516	−	1.94884i	−0.146484	−	0.253718i	0.783442	−	0.621465i	$-0.213462\pi$
$59$	−1.12516	−	1.94884i	−0.146484	−	0.253718i	−0.929926	+	0.367748i	$0.880129\pi$
$60$	−13.1354	+	6.29662i	−1.69577	+	0.812890i
$61$	−2.35467	+	4.07841i	−0.301485	+	0.522187i	−0.976472	−	0.215642i	$-0.930815\pi$
$61$	−2.35467	+	4.07841i	−0.301485	+	0.522187i	0.674988	+	0.737829i	$0.264149\pi$
$62$	1.89196	+	1.42390i	0.240279	+	0.180835i
$63$	1.96486	−	2.26701i	0.247549	−	0.285616i
$64$	5.96457	+	5.33141i	0.745571	+	0.666427i
$65$	8.34882	+	4.82020i	1.03554	+	0.597872i
$66$	2.93815	+	4.59840i	0.361662	+	0.566024i
$67$	−11.4941	+	6.63610i	−1.40422	+	0.810729i	−0.994823	−	0.101626i	$-0.967596\pi$
$67$	−11.4941	+	6.63610i	−1.40422	+	0.810729i	−0.409401	+	0.912355i	$0.634262\pi$
$68$	5.38957	+	5.19205i	0.653581	+	0.629628i
$69$	−3.29055	+	8.82064i	−0.396136	+	1.06188i
$70$	2.32691	+	5.47265i	0.278119	+	0.654107i
$71$	−1.00681			−0.119486			−0.0597431	−	0.998214i	$-0.519028\pi$
$71$	−1.00681			−0.119486			−0.0597431	+	0.998214i	$0.519028\pi$
$72$	−4.47289	+	7.21063i	−0.527136	+	0.849781i
$73$	−5.14489			−0.602163			−0.301082	−	0.953598i	$-0.597348\pi$
$73$	−5.14489			−0.602163			−0.301082	+	0.953598i	$0.597348\pi$
$74$	6.53091	+	15.3600i	0.759203	+	1.78556i
$75$	21.6623	−	3.64132i	2.50135	−	0.420463i
$76$	7.06192	+	6.80311i	0.810057	+	0.780370i
$77$	1.92931	−	1.11389i	0.219866	−	0.126940i
$78$	5.61000	−	0.252452i	0.635207	−	0.0285846i
$79$	−11.6396	−	6.72012i	−1.30956	−	0.756073i	−0.327535	−	0.944839i	$-0.606218\pi$
$79$	−11.6396	−	6.72012i	−1.30956	−	0.756073i	−0.982022	+	0.188766i	$0.939551\pi$
$80$	−8.94781	−	14.2426i	−1.00040	−	1.59237i
$81$	−8.35448	−	3.34703i	−0.928276	−	0.371893i
$82$	3.12467	+	2.35164i	0.345062	+	0.259695i
$83$	6.65730	−	11.5308i	0.730734	−	1.26567i	−0.225836	−	0.974165i	$-0.572511\pi$
$83$	6.65730	−	11.5308i	0.730734	−	1.26567i	0.956570	−	0.291503i	$-0.0941553\pi$
$84$	2.85866	+	1.95654i	0.311906	+	0.213476i
$85$	−7.86721	−	13.6264i	−0.853319	−	1.47799i
$86$	−0.0824311	+	0.674725i	−0.00888878	+	0.0727574i
$87$	0.326738	+	1.94378i	0.0350300	+	0.208395i
$88$	−4.88967	+	3.97431i	−0.521241	+	0.423663i
$89$			12.3797i			1.31225i	0.754652	+	0.656125i	$0.227806\pi$
$89$			12.3797i			1.31225i	−0.754652	+	0.656125i	$0.772194\pi$
$90$	13.2333	−	11.9649i	1.39491	−	1.26122i
$91$		−	2.29259i		−	0.240329i
$92$	−10.5511	−	2.61712i	−1.10003	−	0.272854i
$93$	−2.71717	−	1.01364i	−0.281757	−	0.105110i
$94$	−4.13850	−	0.505600i	−0.426853	−	0.0521487i
$95$	−10.3084	−	17.8546i	−1.05762	−	1.83184i
$96$	−8.85929	−	4.18486i	−0.904197	−	0.427116i
$97$	2.52467	−	4.37286i	0.256342	−	0.443997i	−0.708917	−	0.705291i	$-0.750816\pi$
$97$	2.52467	−	4.37286i	0.256342	−	0.443997i	0.965259	+	0.261295i	$0.0841495\pi$
$98$	0.850411	−	1.12996i	0.0859045	−	0.114143i
$99$	−5.05039	−	4.37728i	−0.507583	−	0.439933i
$100$	7.02090	+	24.3734i	0.702090	+	2.43734i
$101$	5.74352	+	3.31603i	0.571502	+	0.329957i	0.757749	−	0.652546i	$-0.226299\pi$
$101$	5.74352	+	3.31603i	0.571502	+	0.329957i	−0.186247	+	0.982503i	$0.559632\pi$
$102$	−8.13559	−	4.22130i	−0.805543	−	0.417971i
$103$	−3.08323	+	1.78010i	−0.303799	+	0.175399i	−0.644148	−	0.764901i	$-0.722788\pi$
$103$	−3.08323	+	1.78010i	−0.303799	+	0.175399i	0.340349	+	0.940299i	$0.389455\pi$
$104$	1.02602	+	6.40274i	0.100609	+	0.627840i
$105$	−4.63686	−	5.61659i	−0.452512	−	0.548123i
$106$	6.00385	−	2.55278i	0.583146	−	0.247948i
$107$	5.03423			0.486678			0.243339	−	0.969941i	$-0.421757\pi$
$107$	5.03423			0.486678			0.243339	+	0.969941i	$0.421757\pi$
$108$	2.74311	−	10.0237i	0.263956	−	0.964535i
$109$	4.77634			0.457491			0.228745	−	0.973486i	$-0.426538\pi$
$109$	4.77634			0.457491			0.228745	+	0.973486i	$0.426538\pi$
$110$	12.1919	−	5.18385i	1.16245	−	0.494261i
$111$	−13.0142	−	15.7640i	−1.23525	−	1.49625i
$112$	−1.86933	+	3.53633i	−0.176635	+	0.334152i
$113$	−4.55672	+	2.63082i	−0.428660	+	0.247487i	−0.698776	−	0.715341i	$-0.746271\pi$
$113$	−4.55672	+	2.63082i	−0.428660	+	0.247487i	0.270116	+	0.962828i	$0.412938\pi$
$114$	−10.6600	−	5.53115i	−0.998401	−	0.518040i
$115$	19.7939	+	11.4280i	1.84579	+	1.06567i
$116$	−2.18704	+	0.629991i	−0.203062	+	0.0584932i
$117$	−6.49978	+	2.24869i	−0.600905	+	0.207892i
$118$	−1.91370	+	2.54277i	−0.176171	+	0.234081i
$119$	−1.87091	+	3.24051i	−0.171506	+	0.297057i
$120$	15.4635	+	13.6108i	1.41161	+	1.24249i
$121$	3.01850	+	5.22819i	0.274409	+	0.475290i
$122$	6.61086	+	0.807649i	0.598519	+	0.0731211i
$123$	−4.48755	−	1.67409i	−0.404629	−	0.150947i
$124$	0.806196	−	3.25024i	0.0723985	−	0.291880i
$125$		−	32.3038i		−	2.88934i
$126$	−4.03769	−	1.30270i	−0.359706	−	0.116054i
$127$		−	8.20958i		−	0.728482i	−0.931305	−	0.364241i	$-0.881328\pi$
$127$		−	8.20958i		−	0.728482i	0.931305	−	0.364241i	$-0.118672\pi$
$128$	3.63801	−	10.7128i	0.321558	−	0.946890i
$129$	−0.138004	−	0.820992i	−0.0121506	−	0.0722843i
$130$	1.65332	−	13.5330i	0.145006	−	1.18692i
$131$	0.563287	+	0.975641i	0.0492146	+	0.0852422i	0.889583	−	0.456773i	$-0.150995\pi$
$131$	0.563287	+	0.975641i	0.0492146	+	0.0852422i	−0.840369	+	0.542015i	$0.817662\pi$
$132$	4.35874	−	6.36847i	0.379380	−	0.554304i
$133$	−2.45144	+	4.24602i	−0.212567	+	0.368176i
$134$	14.9970	+	11.2868i	1.29554	+	0.975033i
$135$	−11.3757	+	18.6551i	−0.979060	+	1.60558i
$136$	3.77482	−	9.88738i	0.323688	−	0.847836i
$137$	−3.55214	−	2.05083i	−0.303480	−	0.175214i	0.340525	−	0.940235i	$-0.389395\pi$
$137$	−3.55214	−	2.05083i	−0.303480	−	0.175214i	−0.644005	+	0.765021i	$0.722729\pi$
$138$	13.3005	−	0.598530i	1.13222	−	0.0509503i
$139$	4.91308	−	2.83657i	0.416722	−	0.240595i	−0.276952	−	0.960884i	$-0.589324\pi$
$139$	4.91308	−	2.83657i	0.416722	−	0.240595i	0.693674	+	0.720289i	$0.255991\pi$
$140$	5.83478	−	6.05675i	0.493129	−	0.511889i
$141$	5.03564	−	0.846464i	0.424078	−	0.0712851i
$142$	0.557133	+	1.31032i	0.0467536	+	0.109959i
$143$	−5.10739			−0.427101
$144$	11.8595	+	1.83116i	0.988289	+	0.152597i
$145$	4.78525			0.397393
$146$	2.84700	+	6.69584i	0.235620	+	0.554152i
$147$	−0.605390	+	1.62281i	−0.0499317	+	0.133847i
$148$	16.3764	−	16.9994i	1.34613	−	1.39734i
$149$	13.9530	−	8.05575i	1.14307	−	0.659953i	0.195882	−	0.980627i	$-0.437243\pi$
$149$	13.9530	−	8.05575i	1.14307	−	0.659953i	0.947189	+	0.320675i	$0.103910\pi$
$150$	−16.7262	−	26.1776i	−1.36569	−	2.13739i
$151$	11.1164	+	6.41803i	0.904637	+	0.522292i	0.878702	−	0.477371i	$-0.158410\pi$
$151$	11.1164	+	6.41803i	0.904637	+	0.522292i	0.0259350	+	0.999664i	$0.491744\pi$
$152$	4.94612	−	12.9554i	0.401183	−	1.05082i
$153$	11.0223	+	2.12580i	0.891103	+	0.171860i
$154$	−2.51729	−	1.89453i	−0.202849	−	0.152665i
$155$	−3.52037	+	6.09746i	−0.282763	+	0.489760i
$156$	−3.43293	−	7.16147i	−0.274855	−	0.573376i
$157$	7.29242	+	12.6308i	0.581999	+	1.00805i	0.995242	+	0.0974306i	$0.0310624\pi$
$157$	7.29242	+	12.6308i	0.581999	+	1.00805i	−0.413244	+	0.910620i	$0.635604\pi$
$158$	−2.30499	+	18.8671i	−0.183375	+	1.50099i
$159$	−6.16177	+	5.08694i	−0.488660	+	0.403421i
$160$	−13.5847	+	19.5265i	−1.07397	+	1.54371i
$161$		−	5.43542i		−	0.428371i
$162$	0.267066	+	12.7251i	0.0209827	+	0.999780i
$163$		−	14.4179i		−	1.12930i	−0.825330	−	0.564650i	$-0.809011\pi$
$163$		−	14.4179i		−	1.12930i	0.825330	−	0.564650i	$-0.190989\pi$
$164$	1.33147	−	5.36793i	0.103971	−	0.419165i
$165$	−12.5125	+	10.3299i	−0.974099	+	0.804183i
$166$	−18.6907	−	2.28345i	−1.45068	−	0.177230i
$167$	−0.239831	−	0.415400i	−0.0185587	−	0.0321446i	0.856597	−	0.515986i	$-0.172574\pi$
$167$	−0.239831	−	0.415400i	−0.0185587	−	0.0321446i	−0.875156	+	0.483842i	$0.839241\pi$
$168$	0.964465	−	4.80310i	0.0744101	−	0.370568i
$169$	3.87202	−	6.70653i	0.297847	−	0.515887i
$170$	−13.3807	+	17.7792i	−1.02625	+	1.36360i
$171$	14.4425	+	2.78542i	1.10444	+	0.213006i
$172$	0.923739	−	0.266089i	0.0704344	−	0.0202891i
$173$	9.61948	+	5.55381i	0.731356	+	0.422248i	0.818918	−	0.573911i	$-0.194574\pi$
$173$	9.61948	+	5.55381i	0.731356	+	0.422248i	−0.0875622	+	0.996159i	$0.527908\pi$
$174$	2.34893	−	1.50085i	0.178072	−	0.113779i
$175$	−10.9831	+	6.34110i	−0.830245	+	0.479342i
$176$	7.87816	+	4.16445i	0.593839	+	0.313907i
$177$	1.36233	−	3.65185i	0.102399	−	0.274490i
$178$	16.1117	−	6.85052i	1.20762	−	0.513468i
$179$	18.9784			1.41851			0.709257	−	0.704950i	$-0.249031\pi$
$179$	18.9784			1.41851			0.709257	+	0.704950i	$0.249031\pi$
$180$	−22.8947	−	10.6015i	−1.70647	−	0.790192i
$181$	−12.0972			−0.899177			−0.449588	−	0.893236i	$-0.648429\pi$
$181$	−12.0972			−0.899177			−0.449588	+	0.893236i	$0.648429\pi$
$182$	−2.98370	+	1.26864i	−0.221167	+	0.0940378i
$183$	−8.04396	+	1.35215i	−0.594627	+	0.0999535i
$184$	2.43255	+	15.1800i	0.179330	+	1.11909i
$185$	−42.9794	+	24.8142i	−3.15991	+	1.82438i
$186$	0.184375	+	4.09719i	0.0135191	+	0.300421i
$187$	7.21914	+	4.16797i	0.527916	+	0.304792i
$188$	1.63208	+	5.66585i	0.119032	+	0.413225i
$189$	5.19466	+	0.124622i	0.377856	+	0.00906492i
$190$	−17.5327	+	23.2960i	−1.27195	+	1.69007i
$191$	−2.09590	+	3.63021i	−0.151654	+	0.262672i	−0.931836	−	0.362881i	$-0.881793\pi$
$191$	−2.09590	+	3.63021i	−0.151654	+	0.262672i	0.780182	+	0.625553i	$0.215127\pi$
$192$	−0.543989	+	13.8457i	−0.0392590	+	0.999229i
$193$	−6.58318	−	11.4024i	−0.473867	−	0.820762i	0.525685	−	0.850679i	$-0.323809\pi$
$193$	−6.58318	−	11.4024i	−0.473867	−	0.820762i	−0.999552	+	0.0299170i	$0.990476\pi$
$194$	−7.08815	−	0.865959i	−0.508899	−	0.0621723i
$195$	2.76795	+	16.4666i	0.198217	+	1.17920i
$196$	−1.94118	−	0.481494i	−0.138655	−	0.0343924i
$197$		−	7.04171i		−	0.501701i	−0.968026	−	0.250851i	$-0.919290\pi$
$197$		−	7.04171i		−	0.501701i	0.968026	−	0.250851i	$-0.0807103\pi$
$198$	−2.90213	+	8.99509i	−0.206245	+	0.639254i
$199$			2.66860i			0.189172i	0.995517	+	0.0945859i	$0.0301527\pi$
$199$			2.66860i			0.189172i	−0.995517	+	0.0945859i	$0.969847\pi$
$200$	27.8357	−	22.6248i	1.96828	−	1.59981i
$201$	−21.5382	−	8.03486i	−1.51919	−	0.566735i
$202$	1.13739	−	9.30992i	0.0800267	−	0.655043i
$203$	−0.568992	−	0.985523i	−0.0399354	−	0.0691702i
$204$	−0.991889	+	12.9240i	−0.0694461	+	0.904863i
$205$	−5.81407	+	10.0703i	−0.406072	+	0.703338i
$206$	4.02287	+	3.02764i	0.280287	+	0.210945i
$207$	−15.4101	+	5.33135i	−1.07108	+	0.370554i
$208$	7.76511	−	4.87837i	0.538414	−	0.338254i
$209$	9.45919	+	5.46127i	0.654306	+	0.377764i
$210$	−4.74387	+	9.14270i	−0.327358	+	0.630906i
$211$	2.44886	−	1.41385i	0.168587	−	0.0973335i	−0.413333	−	0.910580i	$-0.635635\pi$
$211$	2.44886	−	1.41385i	0.168587	−	0.0973335i	0.581919	+	0.813247i	$0.302302\pi$
$212$	−6.64465	−	6.40113i	−0.456356	−	0.439632i
$213$	−1.11021	−	1.34478i	−0.0760700	−	0.0921429i
$214$	−2.78577	−	6.55183i	−0.190431	−	0.447874i
$215$	−2.02114			−0.137841
$216$	−14.5634	+	1.97676i	−0.990913	+	0.134501i
$217$	1.67436			0.113663
$218$	−2.64306	−	6.21620i	−0.179011	−	0.421014i
$219$	−5.67325	−	6.87196i	−0.383363	−	0.464364i
$220$	−13.4931	−	12.9986i	−0.909705	−	0.876365i
$221$	7.42916	−	4.28923i	0.499739	−	0.288525i
$222$	−13.3145	+	25.6607i	−0.893613	+	1.72223i
$223$	−5.39092	−	3.11245i	−0.361003	−	0.208425i	0.308518	−	0.951219i	$-0.400167\pi$
$223$	−5.39092	−	3.11245i	−0.361003	−	0.208425i	−0.669521	+	0.742794i	$0.733500\pi$
$224$	5.63679	+	0.475965i	0.376624	+	0.0318018i
$225$	28.7506	+	24.9188i	1.91671	+	1.66125i
$226$	5.94543	+	4.47456i	0.395484	+	0.297643i
$227$	11.2546	−	19.4936i	0.746995	−	1.29383i	−0.202262	−	0.979331i	$-0.564829\pi$
$227$	11.2546	−	19.4936i	0.746995	−	1.29383i	0.949257	−	0.314501i	$-0.101837\pi$
$228$	−1.29967	+	16.9343i	−0.0860725	+	1.12150i
$229$	10.3710	+	17.9631i	0.685334	+	1.18703i	0.973332	+	0.229403i	$0.0736773\pi$
$229$	10.3710	+	17.9631i	0.685334	+	1.18703i	−0.287997	+	0.957631i	$0.592989\pi$
$230$	3.91980	−	32.0848i	0.258464	−	2.11561i
$231$	3.61526	+	1.34868i	0.237866	+	0.0887364i
$232$	2.03014	+	2.49772i	0.133285	+	0.163983i
$233$		−	4.33562i		−	0.284036i	−0.989864	−	0.142018i	$-0.954641\pi$
$233$		−	4.33562i		−	0.284036i	0.989864	−	0.142018i	$-0.0453591\pi$
$234$	6.52333	+	7.21482i	0.426443	+	0.471648i
$235$		−	12.3969i		−	0.808685i
$236$	4.36829	+	1.08352i	0.284351	+	0.0705311i
$237$	−3.85897	−	22.9571i	−0.250667	−	1.49122i
$238$	5.25267	+	0.641719i	0.340480	+	0.0415965i
$239$	−3.20026	−	5.54301i	−0.207008	−	0.358548i	0.743763	−	0.668444i	$-0.233039\pi$
$239$	−3.20026	−	5.54301i	−0.207008	−	0.358548i	−0.950771	+	0.309896i	$0.899706\pi$
$240$	9.15695	−	27.6568i	0.591079	−	1.78524i
$241$	3.59496	−	6.22666i	0.231572	−	0.401094i	−0.726699	−	0.686956i	$-0.758946\pi$
$241$	3.59496	−	6.22666i	0.231572	−	0.401094i	0.958271	+	0.285862i	$0.0922798\pi$
$242$	5.13393	−	6.82154i	0.330021	−	0.438505i
$243$	−4.74187	−	14.8497i	−0.304191	−	0.952611i
$244$	−2.60710	−	9.05066i	−0.166903	−	0.579409i
$245$	3.64166	+	2.10251i	0.232657	+	0.134324i
$246$	0.304505	+	6.76673i	0.0194146	+	0.431431i
$247$	9.73438	−	5.62015i	0.619384	−	0.357601i
$248$	−4.67616	+	0.749340i	−0.296936	+	0.0475831i
$249$	22.7425	−	3.82289i	1.44125	−	0.242266i
$250$	−42.0420	+	17.8758i	−2.65897	+	1.13057i
$251$	19.1515			1.20883			0.604416	−	0.796669i	$-0.293406\pi$
$251$	19.1515			1.20883			0.604416	+	0.796669i	$0.293406\pi$
$252$	0.538914	+	5.97575i	0.0339484	+	0.376437i
$253$	−12.1089			−0.761282
$254$	−10.6844	+	4.54290i	−0.670399	+	0.285047i
$255$	9.52547	−	25.5339i	0.596508	−	1.59900i
$256$	−15.9554	+	1.19340i	−0.997214	+	0.0745875i
$257$	9.23895	−	5.33411i	0.576310	−	0.332733i	−0.183356	−	0.983047i	$-0.558696\pi$
$257$	9.23895	−	5.33411i	0.576310	−	0.332733i	0.759666	+	0.650314i	$0.225363\pi$
$258$	−0.992118	+	0.633915i	−0.0617665	+	0.0394658i
$259$	10.2210	+	5.90109i	0.635101	+	0.366676i
$260$	−18.5274	+	5.33694i	−1.14902	+	0.330983i
$261$	−2.23598	+	2.57982i	−0.138404	+	0.159687i
$262$	0.958051	−	1.27298i	0.0591886	−	0.0786449i
$263$	−11.3306	+	19.6253i	−0.698678	+	1.21015i	0.270247	+	0.962791i	$0.412895\pi$
$263$	−11.3306	+	19.6253i	−0.698678	+	1.21015i	−0.968925	+	0.247354i	$0.920439\pi$
$264$	−10.7003	−	2.14862i	−0.658555	−	0.132238i
$265$	9.69927	+	16.7996i	0.595821	+	1.03199i
$266$	6.88255	+	0.840841i	0.421996	+	0.0515553i
$267$	−16.5355	+	13.6511i	−1.01195	+	0.835434i
$268$	6.39048	−	25.7637i	0.390361	−	1.57377i
$269$			25.6002i			1.56087i	0.625235	+	0.780436i	$0.285003\pi$
$269$			25.6002i			1.56087i	−0.625235	+	0.780436i	$0.714997\pi$
$270$	30.5737	+	4.48180i	1.86066	+	0.272754i
$271$			30.6496i			1.86183i	0.365237	+	0.930914i	$0.380988\pi$
$271$			30.6496i			1.86183i	−0.365237	+	0.930914i	$0.619012\pi$
$272$	−14.9568	+	0.558575i	−0.906892	+	0.0338686i
$273$	3.06218	−	2.52803i	0.185332	−	0.153003i
$274$	−0.703432	+	5.75782i	−0.0424959	+	0.347842i
$275$	14.1266	+	24.4680i	0.851865	+	1.47547i
$276$	−8.13902	−	16.9789i	−0.489912	−	1.02201i
$277$	3.60137	−	6.23775i	0.216385	−	0.374790i	−0.737315	−	0.675549i	$-0.763907\pi$
$277$	3.60137	−	6.23775i	0.216385	−	0.374790i	0.953700	+	0.300759i	$0.0972400\pi$
$278$	−6.41040	−	4.82450i	−0.384470	−	0.289354i
$279$	−1.64230	−	4.74703i	−0.0983222	−	0.284197i
$280$	−11.1114	−	4.24211i	−0.664030	−	0.253514i
$281$	−19.5163	−	11.2677i	−1.16424	−	0.672176i	−0.211926	−	0.977286i	$-0.567973\pi$
$281$	−19.5163	−	11.2677i	−1.16424	−	0.672176i	−0.952317	+	0.305110i	$0.901307\pi$
$282$	−3.88819	−	6.08526i	−0.231538	−	0.362372i
$283$	−16.5283	+	9.54263i	−0.982507	+	0.567251i	−0.903026	−	0.429586i	$-0.858660\pi$
$283$	−16.5283	+	9.54263i	−0.982507	+	0.567251i	−0.0794809	+	0.996836i	$0.525326\pi$
$284$	1.39702	−	1.45017i	0.0828980	−	0.0860517i
$285$	12.4812	−	33.4569i	0.739320	−	1.98182i
$286$	2.82625	+	6.64704i	0.167120	+	0.393048i
$287$	2.76530			0.163230
$288$	−4.17944	−	16.4479i	−0.246276	−	0.969200i
$289$	2.99880			0.176400
$290$	−2.64799	−	6.22779i	−0.155495	−	0.365708i
$291$	8.62472	−	1.44977i	0.505590	−	0.0849869i
$292$	7.13891	−	7.41049i	0.417773	−	0.433666i
$293$	5.97263	−	3.44830i	0.348925	−	0.201452i	−0.315287	−	0.948996i	$-0.602101\pi$
$293$	5.97263	−	3.44830i	0.348925	−	0.201452i	0.664212	+	0.747545i	$0.268767\pi$
$294$	2.44701	−	0.110117i	0.142713	−	0.00642213i
$295$	−8.19493	−	4.73134i	−0.477127	−	0.275469i
$296$	−31.1861	−	11.9063i	−1.81265	−	0.692037i
$297$	0.277630	−	11.5726i	0.0161098	−	0.671508i
$298$	−18.2053	−	13.7014i	−1.05460	−	0.793700i
$299$	−6.23060	+	10.7917i	−0.360325	+	0.624101i
$300$	−24.8132	+	36.2541i	−1.43259	+	2.09313i
$301$	0.240325	+	0.416255i	0.0138521	+	0.0239925i
$302$	2.20138	−	18.0190i	0.126675	−	1.03688i
$303$	1.90420	+	11.3281i	0.109393	+	0.650784i
$304$	−19.5979	+	0.731897i	−1.12401	+	0.0419772i
$305$			19.8029i			1.13391i
$306$	−3.33275	−	15.5214i	−0.190520	−	0.887300i
$307$		−	23.7896i		−	1.35775i	−0.734255	−	0.678873i	$-0.762468\pi$
$307$		−	23.7896i		−	1.35775i	0.734255	−	0.678873i	$-0.237532\pi$
$308$	−1.07266	+	4.32451i	−0.0611206	+	0.246412i
$309$	−5.77752	−	2.15531i	−0.328672	−	0.122611i
$310$	9.88362	+	1.20748i	0.561352	+	0.0685804i
$311$	10.2030	+	17.6722i	0.578562	+	1.00210i	0.995645	+	0.0932300i	$0.0297192\pi$
$311$	10.2030	+	17.6722i	0.578562	+	1.00210i	−0.417083	+	0.908868i	$0.636947\pi$
$312$	−7.42066	+	8.43072i	−0.420112	+	0.477295i
$313$	−0.690627	+	1.19620i	−0.0390365	+	0.0676133i	−0.884884	−	0.465812i	$-0.845762\pi$
$313$	−0.690627	+	1.19620i	−0.0390365	+	0.0676133i	0.845847	+	0.533426i	$0.179096\pi$
$314$	12.4031	−	16.4802i	0.699948	−	0.930033i
$315$	2.38895	−	12.3868i	0.134602	−	0.697917i
$316$	25.8302	−	7.44055i	1.45306	−	0.418564i
$317$	−19.0330	−	10.9887i	−1.06900	−	0.617188i	−0.141093	−	0.989996i	$-0.545062\pi$
$317$	−19.0330	−	10.9887i	−1.06900	−	0.617188i	−0.927908	+	0.372808i	$0.878395\pi$
$318$	10.0301	+	5.20433i	0.562462	+	0.291844i
$319$	−2.19553	+	1.26759i	−0.122926	+	0.0709714i
$320$	32.9302	+	6.87460i	1.84086	+	0.384302i
$321$	5.55123	+	6.72416i	0.309840	+	0.375306i
$322$	−7.07396	+	3.00777i	−0.394216	+	0.167617i
$323$	−18.3457			−1.02078
$324$	16.4134	−	7.38922i	0.911855	−	0.410512i
$325$	29.0751			1.61280
$326$	−18.7643	+	7.97839i	−1.03926	+	0.441882i
$327$	5.26686	+	6.37970i	0.291258	+	0.352798i
$328$	−7.72292	+	1.23757i	−0.426427	+	0.0683336i
$329$	−2.55314	+	1.47406i	−0.140759	+	0.0812675i
$330$	20.3679	+	10.5683i	1.12122	+	0.581765i
$331$	29.4795	+	17.0200i	1.62034	+	0.935504i	0.986828	+	0.161770i	$0.0517204\pi$
$331$	29.4795	+	17.0200i	1.62034	+	0.935504i	0.633511	+	0.773733i	$0.281613\pi$
$332$	7.37100	+	25.5887i	0.404536	+	1.40436i
$333$	6.70503	−	34.7658i	0.367434	−	1.90516i
$334$	−0.407910	+	0.541997i	−0.0223198	+	0.0296568i
$335$	−27.9049	+	48.3328i	−1.52461	+	2.64070i
$336$	−6.78473	+	1.40266i	−0.370137	+	0.0765215i
$337$	−4.98567	−	8.63543i	−0.271587	−	0.470402i	0.697682	−	0.716408i	$-0.254215\pi$
$337$	−4.98567	−	8.63543i	−0.271587	−	0.470402i	−0.969268	+	0.246006i	$0.920882\pi$
$338$	−10.8709	−	1.32810i	−0.591298	−	0.0722389i
$339$	−8.53864	−	3.18535i	−0.463755	−	0.173004i
$340$	30.5433	+	7.57602i	1.65644	+	0.410868i
$341$		−	3.73012i		−	0.201997i
$342$	−4.36688	−	20.3376i	−0.236134	−	1.09973i
$343$		−	1.00000i		−	0.0539949i
$344$	−0.857468	−	1.05496i	−0.0462316	−	0.0568797i
$345$	6.56244	+	39.0402i	0.353310	+	2.10185i
$346$	1.90495	−	15.5926i	0.102411	−	0.838264i
$347$	−9.75697	−	16.8996i	−0.523782	−	0.907217i	−0.999617	−	0.0276820i	$-0.991187\pi$
$347$	−9.75697	−	16.8996i	−0.523782	−	0.907217i	0.475835	−	0.879535i	$-0.342146\pi$
$348$	−3.25311	−	2.22651i	−0.174385	−	0.119354i
$349$	−7.72518	+	13.3804i	−0.413520	+	0.716237i	−0.995272	−	0.0971292i	$-0.969034\pi$
$349$	−7.72518	+	13.3804i	−0.413520	+	0.716237i	0.581752	+	0.813366i	$0.302367\pi$
$350$	14.3303	+	10.7851i	0.765989	+	0.576487i
$351$	−10.1708	−	6.20204i	−0.542879	−	0.331040i
$352$	1.06035	−	12.5575i	0.0565166	−	0.669319i
$353$	1.20451	+	0.695424i	0.0641096	+	0.0370137i	0.531712	−	0.846925i	$-0.321549\pi$
$353$	1.20451	+	0.695424i	0.0641096	+	0.0370137i	−0.467603	+	0.883939i	$0.654882\pi$
$354$	−5.50659	+	0.247799i	−0.292672	+	0.0131703i
$355$	−3.66645	+	2.11683i	−0.194595	+	0.112350i
$356$	−17.8313	−	17.1778i	−0.945056	−	0.910421i
$357$	−6.39135	+	1.07435i	−0.338266	+	0.0568607i
$358$	−10.5020	−	24.6996i	−0.555048	−	1.30541i
$359$	29.0848			1.53504			0.767519	−	0.641026i	$-0.221491\pi$
$359$	29.0848			1.53504			0.767519	+	0.641026i	$0.221491\pi$
$360$	−1.12830	+	35.6629i	−0.0594669	+	1.87960i
$361$	−5.03823			−0.265170
$362$	6.69416	+	15.7440i	0.351837	+	0.827484i
$363$	−3.65474	+	9.79688i	−0.191824	+	0.514203i
$364$	3.30216	+	3.18114i	0.173080	+	0.166737i
$365$	−18.7359	+	10.8172i	−0.980682	+	0.566197i
$366$	6.21101	+	9.72063i	0.324655	+	0.508105i
$367$	9.75962	+	5.63472i	0.509448	+	0.294130i	0.732607	−	0.680652i	$-0.238303\pi$
$367$	9.75962	+	5.63472i	0.509448	+	0.294130i	−0.223159	+	0.974782i	$0.571637\pi$
$368$	18.4100	−	11.5660i	0.959690	−	0.602917i
$369$	−2.71235	−	7.83997i	−0.141199	−	0.408132i
$370$	56.0779	+	42.2045i	2.91535	+	2.19411i
$371$	2.30659	−	3.99513i	0.119752	−	0.207417i
$372$	5.23029	−	2.50720i	0.271178	−	0.129992i
$373$	2.00707	+	3.47635i	0.103922	+	0.179998i	0.913297	−	0.407294i	$-0.133527\pi$
$373$	2.00707	+	3.47635i	0.103922	+	0.179998i	−0.809375	+	0.587292i	$0.800194\pi$
$374$	1.42961	−	11.7018i	0.0739234	−	0.605086i
$375$	43.1478	−	35.6214i	2.22814	−	1.83948i
$376$	6.47072	−	5.25937i	0.333702	−	0.271231i
$377$			2.60893i			0.134367i
$378$	−2.71235	−	6.82958i	−0.139508	−	0.351276i
$379$			0.667011i			0.0342620i	0.999853	+	0.0171310i	$0.00545324\pi$
$379$			0.667011i			0.0342620i	−0.999853	+	0.0171310i	$0.994547\pi$
$380$	40.0207	+	9.92681i	2.05302	+	0.509235i
$381$	10.9654	−	9.05268i	0.561776	−	0.463783i
$382$	5.88435	+	0.718891i	0.301070	+	0.0367817i
$383$	−4.84288	−	8.38811i	−0.247460	−	0.428613i	0.715361	−	0.698755i	$-0.246262\pi$
$383$	−4.84288	−	8.38811i	−0.247460	−	0.428613i	−0.962820	+	0.270143i	$0.912929\pi$
$384$	18.3206	−	6.95377i	0.934920	−	0.354858i
$385$	4.68393	−	8.11281i	0.238715	−	0.413467i
$386$	−11.1968	+	14.8774i	−0.569903	+	0.757240i
$387$	0.944411	−	1.08964i	0.0480071	−	0.0553893i
$388$	2.79533	+	9.70410i	0.141911	+	0.492651i
$389$	−28.0925	−	16.2192i	−1.42435	−	0.822348i	−0.427682	−	0.903929i	$-0.640670\pi$
$389$	−28.0925	−	16.2192i	−1.42435	−	0.822348i	−0.996667	+	0.0815814i	$0.974003\pi$
$390$	19.8989	−	12.7144i	1.00762	−	0.643820i
$391$	17.6135	−	10.1692i	0.890755	−	0.514277i
$392$	0.447537	+	2.79280i	0.0226040	+	0.141058i
$393$	−0.682017	+	1.82821i	−0.0344032	+	0.0922211i
$394$	−9.16448	+	3.89664i	−0.461700	+	0.196310i
$395$	−56.5165			−2.84365
$396$	13.3127	−	1.20058i	0.668986	−	0.0603315i
$397$	25.7154			1.29062			0.645310	−	0.763921i	$-0.276728\pi$
$397$	25.7154			1.29062			0.645310	+	0.763921i	$0.276728\pi$
$398$	3.47306	−	1.47671i	0.174089	−	0.0740207i
$399$	−8.37455	+	1.40772i	−0.419252	+	0.0704739i
$400$	−44.8484	−	23.7072i	−2.24242	−	1.18536i
$401$	10.6993	−	6.17724i	0.534298	−	0.308477i	−0.208467	−	0.978029i	$-0.566847\pi$
$401$	10.6993	−	6.17724i	0.534298	−	0.308477i	0.742765	+	0.669553i	$0.233514\pi$
$402$	1.46149	+	32.4773i	0.0728925	+	1.61982i
$403$	−3.32435	−	1.91932i	−0.165598	−	0.0956079i
$404$	−12.7458	+	3.67152i	−0.634129	+	0.182665i
$405$	−37.4613	+	5.37665i	−1.86147	+	0.267168i
$406$	−0.967754	+	1.28587i	−0.0480288	+	0.0638168i
$407$	13.1463	−	22.7701i	0.651639	−	1.12867i
$408$	17.3689	−	5.86081i	0.859890	−	0.290153i
$409$	−5.59145	−	9.68467i	−0.276479	−	0.478876i	0.694028	−	0.719948i	$-0.255834\pi$
$409$	−5.59145	−	9.68467i	−0.276479	−	0.478876i	−0.970507	+	0.241072i	$0.922501\pi$
$410$	16.3233	+	1.99422i	0.806151	+	0.0984875i
$411$	−1.17767	−	7.00600i	−0.0580902	−	0.345580i
$412$	1.71421	−	6.91098i	0.0844533	−	0.340480i
$413$			2.25033i			0.110731i
$414$	15.4659	+	17.1054i	0.760109	+	0.840683i
$415$		−	55.9882i		−	2.74835i
$416$	−10.6459	−	7.40643i	−0.521960	−	0.363130i
$417$	9.20641	+	3.43446i	0.450840	+	0.168186i
$418$	1.87321	−	15.3328i	0.0916216	−	0.749952i
$419$	16.0870	+	27.8635i	0.785901	+	1.36122i	0.928459	+	0.371434i	$0.121134\pi$
$419$	16.0870	+	27.8635i	0.785901	+	1.36122i	−0.142559	+	0.989786i	$0.545533\pi$
$420$	14.5239	+	1.11468i	0.708694	+	0.0543906i
$421$	8.29402	−	14.3657i	0.404226	−	0.700140i	−0.590005	−	0.807399i	$-0.700874\pi$
$421$	8.29402	−	14.3657i	0.404226	−	0.700140i	0.994231	+	0.107260i	$0.0342077\pi$
$422$	−3.19518	−	2.40471i	−0.155539	−	0.117059i
$423$	6.68340	+	5.79265i	0.324958	+	0.281648i
$424$	−4.65387	+	12.1899i	−0.226012	+	0.591993i
$425$	−41.0968	−	23.7273i	−1.99349	−	1.15094i
$426$	−1.13582	+	2.18904i	−0.0550309	+	0.106059i
$427$	4.07841	−	2.35467i	0.197368	−	0.113950i
$428$	−6.98537	+	7.25111i	−0.337651	+	0.350496i
$429$	−5.63190	−	6.82187i	−0.271911	−	0.329363i
$430$	1.11843	+	2.63043i	0.0539355	+	0.126850i
$431$	−14.0003			−0.674370			−0.337185	−	0.941438i	$-0.609475\pi$
$431$	−14.0003			−0.674370			−0.337185	+	0.941438i	$0.609475\pi$
$432$	10.6315	+	17.8597i	0.511510	+	0.859277i
$433$	−28.9725			−1.39233			−0.696164	−	0.717883i	$-0.745111\pi$
$433$	−28.9725			−1.39233			−0.696164	+	0.717883i	$0.745111\pi$
$434$	−0.926535	−	2.17911i	−0.0444751	−	0.104601i
$435$	5.27668	+	6.39159i	0.252997	+	0.306453i
$436$	−6.62753	+	6.87966i	−0.317401	+	0.329476i
$437$	23.0789	−	13.3246i	1.10401	−	0.637402i
$438$	−5.80417	+	11.1862i	−0.277334	+	0.534497i
$439$	−26.3297	−	15.2014i	−1.25665	−	0.725525i	−0.284225	−	0.958758i	$-0.591736\pi$
$439$	−26.3297	−	15.2014i	−1.25665	−	0.725525i	−0.972421	+	0.233232i	$0.925070\pi$
$440$	−9.45048	+	24.7537i	−0.450534	+	1.18008i
$441$	−2.83512	+	0.980853i	−0.135006	+	0.0467073i
$442$	−9.69328	−	7.29521i	−0.461062	−	0.346998i
$443$	10.9707	−	19.0019i	0.521235	−	0.902805i	−0.478460	−	0.878109i	$-0.658805\pi$
$443$	10.9707	−	19.0019i	0.521235	−	0.902805i	0.999695	−	0.0246960i	$-0.00786178\pi$
$444$	40.7640	+	3.12855i	1.93458	+	0.148474i
$445$	26.0285	+	45.0827i	1.23387	+	2.13713i
$446$	−1.06757	+	8.73837i	−0.0505507	+	0.413774i
$447$	26.1458	+	9.75374i	1.23666	+	0.461336i
$448$	−2.49976	−	7.59942i	−0.118103	−	0.359039i
$449$			21.1481i			0.998043i	0.866590	+	0.499021i	$0.166307\pi$
$449$			21.1481i			0.998043i	−0.866590	+	0.499021i	$0.833693\pi$
$450$	16.5211	−	51.2069i	0.778813	−	2.41391i
$451$		−	6.16048i		−	0.290086i
$452$	2.53345	−	10.2138i	0.119163	−	0.480416i
$453$	3.68549	+	21.9251i	0.173160	+	1.03013i
$454$	−31.5979	−	3.86032i	−1.48296	−	0.181174i
$455$	−4.82020	−	8.34882i	−0.225974	−	0.391399i
$456$	22.7584	−	7.67938i	1.06576	−	0.359620i
$457$	−13.6365	+	23.6191i	−0.637887	+	1.10485i	0.348009	+	0.937491i	$0.386858\pi$
$457$	−13.6365	+	23.6191i	−0.637887	+	1.10485i	−0.985896	+	0.167361i	$0.946475\pi$
$458$	17.6392	−	23.4375i	0.824226	−	1.09516i
$459$	9.31489	+	17.0665i	0.434782	+	0.796596i
$460$	−43.9260	+	12.6532i	−2.04806	+	0.589957i
$461$	21.9447	+	12.6698i	1.02206	+	0.590089i	0.914701	−	0.404130i	$-0.132426\pi$
$461$	21.9447	+	12.6698i	1.02206	+	0.590089i	0.107363	+	0.994220i	$0.465759\pi$
$462$	−0.245316	−	5.45141i	−0.0114131	−	0.253622i
$463$	7.18441	−	4.14792i	0.333888	−	0.192770i	−0.323678	−	0.946167i	$-0.604919\pi$
$463$	7.18441	−	4.14792i	0.333888	−	0.192770i	0.657566	+	0.753397i	$0.271586\pi$
$464$	2.12726	−	4.02428i	0.0987558	−	0.186823i
$465$	−12.0262	+	2.02154i	−0.557701	+	0.0937466i
$466$	−5.64262	+	2.39918i	−0.261389	+	0.111140i
$467$	−23.3145			−1.07887			−0.539434	−	0.842028i	$-0.681362\pi$
$467$	−23.3145			−1.07887			−0.539434	+	0.842028i	$0.681362\pi$
$468$	5.77999	−	12.4823i	0.267180	−	0.576992i
$469$	13.2722			0.612853
$470$	−16.1340	+	6.86001i	−0.744207	+	0.316429i
$471$	−8.82952	+	23.6684i	−0.406843	+	1.09058i
$472$	−1.00711	−	6.28471i	−0.0463558	−	0.289277i
$473$	0.927324	−	0.535391i	0.0426384	−	0.0246173i
$474$	−27.7422	+	17.7259i	−1.27424	+	0.814179i
$475$	−53.8489	−	31.0897i	−2.47076	−	1.42649i
$476$	−2.07148	−	7.19123i	−0.0949461	−	0.329609i
$477$	−13.5891	−	2.62084i	−0.622203	−	0.120000i
$478$	−5.44307	+	7.23231i	−0.248960	+	0.330798i
$479$	12.1862	−	21.1071i	0.556802	−	0.964410i	−0.440958	−	0.897528i	$-0.645361\pi$
$479$	12.1862	−	21.1071i	0.556802	−	0.964410i	0.997761	−	0.0668826i	$-0.0213053\pi$
$480$	−41.0612	+	3.38692i	−1.87418	+	0.154591i
$481$	−13.5288	−	23.4325i	−0.616859	−	1.06843i
$482$	−10.0930	−	1.23307i	−0.459726	−	0.0561647i
$483$	7.26002	−	5.99362i	0.330342	−	0.272719i
$484$	−11.7189	−	2.90677i	−0.532676	−	0.132126i
$485$		−	21.2326i		−	0.964123i
$486$	−16.7023	+	14.3887i	−0.757631	+	0.652683i
$487$			19.2798i			0.873652i	0.899546	+	0.436826i	$0.143897\pi$
$487$			19.2798i			0.873652i	−0.899546	+	0.436826i	$0.856103\pi$
$488$	−10.3364	+	8.40135i	−0.467905	+	0.380311i
$489$	19.2578	−	15.8986i	0.870870	−	0.718960i
$490$	0.721159	−	5.90291i	0.0325786	−	0.266666i
$491$	5.83130	+	10.1001i	0.263163	+	0.455812i	0.967081	−	0.254470i	$-0.0819010\pi$
$491$	5.83130	+	10.1001i	0.263163	+	0.455812i	−0.703918	+	0.710282i	$0.748568\pi$
$492$	8.63809	−	4.14077i	0.389435	−	0.186680i
$493$	2.12906	−	3.68765i	0.0958882	−	0.166083i
$494$	−12.7010	−	9.55887i	−0.571447	−	0.430074i
$495$	−27.5951	−	5.32206i	−1.24031	−	0.239209i
$496$	3.56286	+	5.67115i	0.159977	+	0.254642i
$497$	0.871922	+	0.503405i	0.0391111	+	0.0225808i
$498$	−17.5602	−	27.4829i	−0.786893	−	1.23154i
$499$	−7.81906	+	4.51434i	−0.350029	+	0.202089i	−0.664698	−	0.747112i	$-0.731440\pi$
$499$	−7.81906	+	4.51434i	−0.350029	+	0.202089i	0.314669	+	0.949201i	$0.398107\pi$
$500$	46.5292	+	44.8240i	2.08085	+	2.00459i
$501$	0.290383	−	0.778399i	0.0129733	−	0.0347763i
$502$	−10.5978	−	24.9248i	−0.473002	−	1.11245i
$503$	−31.2652			−1.39405			−0.697023	−	0.717049i	$-0.745492\pi$
$503$	−31.2652			−1.39405			−0.697023	+	0.717049i	$0.745492\pi$
$504$	7.47896	−	4.00814i	0.333139	−	0.178537i
$505$	27.8879			1.24100
$506$	6.70066	+	15.7592i	0.297881	+	0.700583i
$507$	13.2275	−	2.22347i	0.587453	−	0.0987477i
$508$	11.8248	+	11.3914i	0.524639	+	0.505412i
$509$	−14.7396	+	8.50991i	−0.653321	+	0.377195i	−0.789728	−	0.613458i	$-0.789778\pi$
$509$	−14.7396	+	8.50991i	−0.653321	+	0.377195i	0.136406	+	0.990653i	$0.456445\pi$
$510$	−38.5023	+	1.73262i	−1.70491	+	0.0767217i
$511$	4.45560	+	2.57244i	0.197104	+	0.113798i
$512$	10.3823	+	20.1049i	0.458839	+	0.888519i
$513$	12.2052	+	22.3621i	0.538875	+	0.987311i
$514$	−12.0546	−	9.07237i	−0.531707	−	0.400165i
$515$	−7.48536	+	12.9650i	−0.329845	+	0.571308i
$516$	1.37402	+	0.940411i	0.0604877	+	0.0413993i
$517$	3.28388	+	5.68785i	0.144425	+	0.250151i
$518$	2.02407	−	16.5676i	0.0889323	−	0.727939i
$519$	3.18922	+	18.9728i	0.139991	+	0.832813i
$520$	17.1982	+	21.1593i	0.754192	+	0.927899i
$521$		−	26.5870i		−	1.16480i	−0.812904	−	0.582398i	$-0.802115\pi$
$521$		−	26.5870i		−	1.16480i	0.812904	−	0.582398i	$-0.197885\pi$
$522$	4.59483	+	1.48245i	0.201110	+	0.0648851i
$523$			10.3523i			0.452675i	0.974049	+	0.226338i	$0.0726753\pi$
$523$			10.3523i			0.452675i	−0.974049	+	0.226338i	$0.927325\pi$
$524$	−2.18688	−	0.542438i	−0.0955342	−	0.0236965i
$525$	−20.5808	−	7.67768i	−0.898219	−	0.335082i
$526$	31.8114	+	3.88640i	1.38704	+	0.169455i
$527$	3.13258	+	5.42579i	0.136457	+	0.236351i
$528$	3.12482	+	15.1149i	0.135990	+	0.657791i
$529$	−3.27190	+	5.66710i	−0.142257	+	0.246396i
$530$	16.4967	−	21.9195i	0.716572	−	0.952122i
$531$	6.37996	−	2.20724i	0.276867	−	0.0957861i
$532$	−2.71425	−	9.42262i	−0.117677	−	0.408522i
$533$	−5.49034	−	3.16985i	−0.237813	−	0.137301i
$534$	26.9164	+	13.9661i	1.16479	+	0.604373i
$535$	18.3329	−	10.5845i	0.792602	−	0.457609i
$536$	−37.0666	+	5.93980i	−1.60103	+	0.256560i
$537$	20.9274	+	25.3492i	0.903086	+	1.09390i
$538$	33.3175	−	14.1663i	1.43642	−	0.610751i
$539$	−2.22778			−0.0959573
$540$	−11.0856	−	42.2704i	−0.477047	−	1.81903i
$541$	−10.3163			−0.443534			−0.221767	−	0.975100i	$-0.571182\pi$
$541$	−10.3163			−0.443534			−0.221767	+	0.975100i	$0.571182\pi$
$542$	39.8891	−	16.9604i	1.71338	−	0.728512i
$543$	−13.3395	−	16.1581i	−0.572454	−	0.693408i
$544$	9.00356	+	19.1566i	0.386024	+	0.821331i
$545$	17.3938	−	10.0423i	0.745068	−	0.430165i
$546$	−4.98463	−	2.58637i	−0.213322	−	0.110686i
$547$	33.4294	+	19.3005i	1.42934	+	0.825229i	0.997068	−	0.0765150i	$-0.0243793\pi$
$547$	33.4294	+	19.3005i	1.42934	+	0.825229i	0.432270	+	0.901744i	$0.357713\pi$
$548$	7.88280	−	2.27069i	0.336736	−	0.0969991i
$549$	−10.6761	−	9.25321i	−0.455645	−	0.394917i
$550$	24.0268	−	31.9248i	1.02451	−	1.36128i
$551$	2.78970	−	4.83190i	0.118845	−	0.205846i
$552$	−17.5934	+	19.9881i	−0.748824	+	0.850750i
$553$	6.72012	+	11.6396i	0.285769	+	0.494966i
$554$	−10.1110	−	1.23526i	−0.429576	−	0.0524813i
$555$	−80.5373	−	30.0445i	−3.41862	−	1.27532i
$556$	−2.73158	+	11.0126i	−0.115845	+	0.467037i
$557$			33.9277i			1.43756i	0.695236	+	0.718781i	$0.255300\pi$
$557$			33.9277i			1.43756i	−0.695236	+	0.718781i	$0.744700\pi$
$558$	−5.26925	+	4.76423i	−0.223065	+	0.201686i
$559$		−	1.10193i		−	0.0466068i
$560$	0.627722	+	16.8084i	0.0265261	+	0.710283i
$561$	2.39342	+	14.2385i	0.101050	+	0.601151i
$562$	−3.86481	+	31.6347i	−0.163027	+	1.33443i
$563$	11.2520	+	19.4890i	0.474216	+	0.821366i	0.999564	−	0.0295216i	$-0.00939839\pi$
$563$	11.2520	+	19.4890i	0.474216	+	0.821366i	−0.525349	+	0.850887i	$0.676065\pi$
$564$	−5.76811	+	8.42767i	−0.242881	+	0.354869i
$565$	−11.0627	+	19.1611i	−0.465410	+	0.806114i
$566$	21.5655	+	16.2303i	0.906466	+	0.682211i
$567$	5.56168	+	7.07586i	0.233568	+	0.297158i
$568$	−2.66039	−	1.01569i	−0.111628	−	0.0426174i
$569$	−15.4975	−	8.94749i	−0.649690	−	0.375098i	0.138648	−	0.990342i	$-0.455724\pi$
$569$	−15.4975	−	8.94749i	−0.649690	−	0.375098i	−0.788337	+	0.615243i	$0.789058\pi$
$570$	−50.4494	+	2.27024i	−2.11309	+	0.0950900i
$571$	24.0060	−	13.8599i	1.00462	−	0.580017i	0.0950074	−	0.995477i	$-0.469713\pi$
$571$	24.0060	−	13.8599i	1.00462	−	0.580017i	0.909612	+	0.415459i	$0.136379\pi$
$572$	7.08687	−	7.35648i	0.296317	−	0.307590i
$573$	−7.15996	+	1.20355i	−0.299112	+	0.0502790i
$574$	−1.53022	−	3.59892i	−0.0638702	−	0.150216i
$575$	68.9331			2.87471
$576$	−19.0934	+	14.5410i	−0.795559	+	0.605877i
$577$	−42.5735			−1.77236			−0.886179	−	0.463344i	$-0.846650\pi$
$577$	−42.5735			−1.77236			−0.886179	+	0.463344i	$0.846650\pi$
$578$	−1.65943	−	3.90281i	−0.0690233	−	0.162335i
$579$	7.97078	−	21.3664i	0.331254	−	0.887959i
$580$	−6.63988	+	6.89248i	−0.275706	+	0.286195i
$581$	−11.5308	+	6.65730i	−0.478378	+	0.276191i
$582$	−6.65943	−	10.4224i	−0.276042	−	0.432024i
$583$	−8.90028	−	5.13858i	−0.368612	−	0.212818i
$584$	−13.5949	−	5.19026i	−0.562559	−	0.214775i
$585$	−18.9420	+	21.8548i	−0.783157	+	0.903585i
$586$	−7.79286	−	5.86494i	−0.321920	−	0.242279i
$587$	23.6978	−	41.0459i	0.978115	−	1.69414i	0.308867	−	0.951105i	$-0.400050\pi$
$587$	23.6978	−	41.0459i	0.978115	−	1.69414i	0.669248	−	0.743039i	$-0.266616\pi$
$588$	−1.49740	−	3.12374i	−0.0617519	−	0.128821i
$589$	4.10460	+	7.10938i	0.169127	+	0.292937i
$590$	−1.62284	+	13.2835i	−0.0668115	+	0.546873i
$591$	9.40553	−	7.76488i	0.386892	−	0.319404i
$592$	1.76182	+	47.1758i	0.0724102	+	1.93891i
$593$			9.85416i			0.404662i	0.979317	+	0.202331i	$0.0648517\pi$
$593$			9.85416i			0.404662i	−0.979317	+	0.202331i	$0.935148\pi$
$594$	−15.2148	+	6.04253i	−0.624271	+	0.247928i
$595$			15.7344i			0.645048i
$596$	−7.75758	+	31.2752i	−0.317763	+	1.28108i
$597$	−3.56441	+	2.94265i	−0.145882	+	0.120435i
$598$	17.4927	+	2.13709i	0.715331	+	0.0873920i
$599$	14.3947	+	24.9324i	0.588153	+	1.01871i	0.994474	+	0.104980i	$0.0334779\pi$
$599$	14.3947	+	24.9324i	0.588153	+	1.01871i	−0.406322	+	0.913730i	$0.633189\pi$
$600$	60.9140	+	12.2315i	2.48680	+	0.499351i
$601$	11.9480	−	20.6946i	0.487370	−	0.844150i	−0.512524	−	0.858673i	$-0.671290\pi$
$601$	11.9480	−	20.6946i	0.487370	−	0.844150i	0.999895	+	0.0145229i	$0.00462295\pi$
$602$	0.408750	−	0.543113i	0.0166594	−	0.0221356i
$603$	−13.0181	−	37.6283i	−0.530137	−	1.53234i
$604$	−24.6691	+	7.10608i	−1.00377	+	0.289142i
$605$	21.9847	+	12.6928i	0.893804	+	0.516038i
$606$	13.6893	−	8.74682i	0.556091	−	0.355315i
$607$	−0.492088	+	0.284107i	−0.0199732	+	0.0115316i	−0.509953	−	0.860202i	$-0.670337\pi$
$607$	−0.492088	+	0.284107i	−0.0199732	+	0.0115316i	0.489980	+	0.871734i	$0.337004\pi$
$608$	11.7973	+	25.1007i	0.478444	+	1.01797i
$609$	0.688924	−	1.84673i	0.0279166	−	0.0748332i
$610$	25.7726	−	10.9582i	1.04350	−	0.443685i
$611$	6.75883			0.273433
$612$	−18.3562	+	12.9264i	−0.742006	+	0.522520i
$613$	−43.0269			−1.73784			−0.868919	−	0.494953i	$-0.835185\pi$
$613$	−43.0269			−1.73784			−0.868919	+	0.494953i	$0.835185\pi$
$614$	−30.9612	+	13.1644i	−1.24949	+	0.531271i
$615$	−19.8619	+	3.33868i	−0.800909	+	0.134628i
$616$	6.22174	−	0.997014i	0.250681	−	0.0401708i
$617$	19.4820	−	11.2480i	0.784317	−	0.452826i	−0.0536409	−	0.998560i	$-0.517083\pi$
$617$	19.4820	−	11.2480i	0.784317	−	0.452826i	0.837958	+	0.545735i	$0.183749\pi$
$618$	0.392037	+	8.71186i	0.0157701	+	0.350443i
$619$	−37.3543	−	21.5665i	−1.50139	−	0.866830i	−0.999999	−	0.00161224i	$-0.999487\pi$
$619$	−37.3543	−	21.5665i	−1.50139	−	0.866830i	−0.501396	−	0.865218i	$-0.667180\pi$
$620$	−3.89777	−	13.5313i	−0.156538	−	0.543429i
$621$	−24.1137	−	14.7042i	−0.967648	−	0.590059i
$622$	17.3536	−	23.0580i	0.695815	−	0.924541i
$623$	6.18987	−	10.7212i	0.247992	−	0.429534i
$624$	15.0785	+	4.99240i	0.603625	+	0.199856i
$625$	−36.2137	−	62.7239i	−1.44855	−	2.50896i
$626$	1.93897	+	0.236884i	0.0774969	+	0.00946780i
$627$	3.13608	+	18.6566i	0.125243	+	0.745075i
$628$	−28.3117	−	7.02251i	−1.12976	−	0.280229i
$629$			44.1616i			1.76084i
$630$	−17.4428	+	3.74531i	−0.694939	+	0.149217i
$631$			2.16073i			0.0860171i	0.999075	+	0.0430086i	$0.0136943\pi$
$631$			2.16073i			0.0860171i	−0.999075	+	0.0430086i	$0.986306\pi$
$632$	−23.9771	−	29.4995i	−0.953757	−	1.17343i
$633$	4.58882	+	1.71186i	0.182389	+	0.0680405i
$634$	−3.76912	+	30.8514i	−0.149691	+	1.22527i
$635$	−17.2607	−	29.8965i	−0.684971	−	1.18641i
$636$	1.22287	−	15.9337i	0.0484901	−	0.631811i
$637$	−1.14629	+	1.98544i	−0.0454179	+	0.0786660i
$638$	2.86464	+	2.15594i	0.113412	+	0.0853546i
$639$	0.571987	−	2.96577i	0.0226275	−	0.117324i
$640$	−9.27547	−	46.6614i	−0.366645	−	1.84445i
$641$	2.13825	+	1.23452i	0.0844557	+	0.0487605i	0.541633	−	0.840615i	$-0.317806\pi$
$641$	2.13825	+	1.23452i	0.0844557	+	0.0487605i	−0.457177	+	0.889376i	$0.651140\pi$
$642$	5.67934	−	10.9456i	0.224145	−	0.431988i
$643$	−25.6821	+	14.8276i	−1.01280	+	0.584742i	−0.912011	−	0.410166i	$-0.865471\pi$
$643$	−25.6821	+	14.8276i	−1.01280	+	0.584742i	−0.100792	+	0.994908i	$0.532138\pi$
$644$	7.82897	+	7.54205i	0.308505	+	0.297198i
$645$	−2.22871	−	2.69961i	−0.0877553	−	0.106297i
$646$	10.1519	+	23.8761i	0.399420	+	0.939392i
$647$	−18.8904			−0.742656			−0.371328	−	0.928502i	$-0.621098\pi$
$647$	−18.8904			−0.742656			−0.371328	+	0.928502i	$0.621098\pi$
$648$	−18.6993	−	17.2724i	−0.734579	−	0.678523i
$649$	5.01324			0.196787
$650$	−16.0892	−	37.8400i	−0.631068	−	1.48421i
$651$	1.84632	+	2.23643i	0.0723628	+	0.0876525i
$652$	20.7670	+	20.0059i	0.813300	+	0.783493i
$653$	31.1731	−	17.9978i	1.21990	−	0.704308i	0.255002	−	0.966941i	$-0.417924\pi$
$653$	31.1731	−	17.9978i	1.21990	−	0.704308i	0.964896	+	0.262632i	$0.0845906\pi$
$654$	5.38840	−	10.3849i	0.210703	−	0.406081i
$655$	4.10259	+	2.36863i	0.160302	+	0.0925502i
$656$	5.88424	+	9.36621i	0.229741	+	0.365689i
$657$	2.92291	−	15.1554i	0.114033	−	0.591267i
$658$	3.33124	+	2.50711i	0.129865	+	0.0977374i
$659$	−17.9267	+	31.0499i	−0.698324	+	1.20953i	0.270723	+	0.962657i	$0.412737\pi$
$659$	−17.9267	+	31.0499i	−0.698324	+	1.20953i	−0.969047	+	0.246876i	$0.920596\pi$
$660$	2.48325	−	32.3561i	0.0966605	−	1.25946i
$661$	−1.41764	−	2.45542i	−0.0551397	−	0.0955048i	0.837138	−	0.546992i	$-0.184227\pi$
$661$	−1.41764	−	2.45542i	−0.0551397	−	0.0955048i	−0.892278	+	0.451487i	$0.850894\pi$
$662$	5.83784	−	47.7845i	0.226894	−	1.85720i
$663$	13.9212	+	5.19331i	0.540654	+	0.201692i
$664$	29.2237	−	23.7529i	1.13410	−	0.921793i
$665$			20.6167i			0.799482i
$666$	−48.9565	+	10.5119i	−1.89703	+	0.407328i
$667$			6.18542i			0.239500i
$668$	0.931108	+	0.230954i	0.0360257	+	0.00893589i
$669$	−1.78729	−	10.6327i	−0.0691008	−	0.411083i
$670$	78.3446	+	9.57136i	3.02672	+	0.369774i
$671$	−5.24569	−	9.08579i	−0.202507	−	0.350753i
$672$	5.57994	+	8.05384i	0.215251	+	0.310684i
$673$	−0.243115	+	0.421088i	−0.00937141	+	0.0162318i	−0.870673	−	0.491862i	$-0.836316\pi$
$673$	−0.243115	+	0.421088i	−0.00937141	+	0.0162318i	0.861302	+	0.508094i	$0.169650\pi$
$674$	−8.47974	+	11.2672i	−0.326627	+	0.433996i
$675$	−1.58048	+	65.8797i	−0.0608328	+	2.53571i
$676$	4.28711	+	14.8829i	0.164889	+	0.572419i
$677$	31.6074	+	18.2485i	1.21477	+	0.701348i	0.963795	−	0.266645i	$-0.0859151\pi$
$677$	31.6074	+	18.2485i	1.21477	+	0.701348i	0.250976	+	0.967993i	$0.419248\pi$
$678$	0.579394	+	12.8753i	0.0222515	+	0.494474i
$679$	−4.37286	+	2.52467i	−0.167815	+	0.0968880i
$680$	−7.04174	−	43.9430i	−0.270038	−	1.68514i
$681$	38.4477	−	6.46285i	1.47332	−	0.247657i
$682$	−4.85458	+	2.06412i	−0.185891	+	0.0790391i
$683$	−1.99318			−0.0762668			−0.0381334	−	0.999273i	$-0.512141\pi$
$683$	−1.99318			−0.0762668			−0.0381334	+	0.999273i	$0.512141\pi$
$684$	−24.0520	+	16.9374i	−0.919652	+	0.647619i
$685$	−17.2476			−0.658996
$686$	−1.30146	+	0.553365i	−0.0496898	+	0.0211276i
$687$	−12.5570	+	33.6602i	−0.479079	+	1.28422i
$688$	−0.898492	+	1.69974i	−0.0342547	+	0.0648018i
$689$	−9.15920	+	5.28807i	−0.348938	+	0.201459i
$690$	47.1776	−	30.1442i	1.79602	−	1.14757i
$691$	37.5981	+	21.7073i	1.43030	+	0.825783i	0.997143	−	0.0755366i	$-0.0240670\pi$
$691$	37.5981	+	21.7073i	1.43030	+	0.825783i	0.433155	+	0.901319i	$0.357400\pi$
$692$	−21.3472	+	6.14921i	−0.811500	+	0.233758i
$693$	2.18512	+	6.31603i	0.0830060	+	0.239926i
$694$	−16.5949	+	22.0499i	−0.629933	+	0.837003i
$695$	11.9278	−	20.6596i	0.452449	−	0.783664i
$696$	−1.09755	+	5.46585i	−0.0416024	+	0.207183i
$697$	5.17362	+	8.96098i	0.195965	+	0.339421i
$698$	21.6889	+	2.64973i	0.820935	+	0.100294i
$699$	5.79103	−	4.78088i	0.219037	−	0.180829i
$700$	6.10640	−	24.6184i	0.230800	−	0.930488i
$701$		−	8.04511i		−	0.303860i	−0.988391	−	0.151930i	$-0.951451\pi$
$701$		−	8.04511i		−	0.303860i	0.988391	−	0.151930i	$-0.0485488\pi$
$702$	−2.44349	+	16.6689i	−0.0922237	+	0.629126i
$703$			57.8646i			2.18241i
$704$	−16.9298	+	5.56891i	−0.638067	+	0.209886i
$705$	16.5584	−	13.6700i	0.623624	−	0.514843i
$706$	0.238530	−	1.95244i	0.00897718	−	0.0734810i
$707$	−3.31603	−	5.74352i	−0.124712	−	0.216007i
$708$	3.36965	+	7.02945i	0.126639	+	0.264183i
$709$	8.65512	−	14.9911i	0.325050	−	0.563003i	−0.656473	−	0.754350i	$-0.727952\pi$
$709$	8.65512	−	14.9911i	0.325050	−	0.563003i	0.981522	+	0.191347i	$0.0612856\pi$
$710$	4.78384	+	3.60035i	0.179534	+	0.135119i
$711$	26.4082	−	30.4691i	0.990386	−	1.14268i
$712$	−12.4889	+	32.7122i	−0.468042	+	1.22594i
$713$	−7.88159	−	4.55044i	−0.295168	−	0.170415i
$714$	4.93497	+	7.72355i	0.184687	+	0.289047i
$715$	−18.5993	+	10.7383i	−0.695576	+	0.401591i
$716$	−26.3339	+	27.3358i	−0.984146	+	1.02159i
$717$	3.87481	−	10.3868i	0.144708	−	0.387902i
$718$	−16.0945	−	37.8526i	−0.600643	−	1.41265i
$719$	11.2806			0.420694			0.210347	−	0.977627i	$-0.432541\pi$
$719$	11.2806			0.420694			0.210347	+	0.977627i	$0.432541\pi$
$720$	47.0381	−	18.2662i	1.75301	−	0.680741i
$721$	3.56020			0.132589
$722$	2.78798	+	6.55703i	0.103758	+	0.244027i
$723$	12.2810	−	2.06437i	0.456736	−	0.0767748i
$724$	16.7857	−	17.4243i	0.623837	−	0.647570i
$725$	12.4986	−	7.21607i	0.464187	−	0.267998i
$726$	14.7726	−	0.664773i	0.548263	−	0.0246721i
$727$	40.7358	+	23.5188i	1.51081	+	0.872265i	0.999920	+	0.0126169i	$0.00401620\pi$
$727$	40.7358	+	23.5188i	1.51081	+	0.872265i	0.510887	+	0.859648i	$0.329317\pi$
$728$	2.31281	−	6.05794i	0.0857184	−	0.224522i
$729$	14.6057	−	22.7084i	0.540954	−	0.841052i
$730$	24.4459	+	18.3981i	0.904783	+	0.680944i
$731$	−0.899252	+	1.55755i	−0.0332600	+	0.0576081i
$732$	9.21401	−	13.4624i	0.340560	−	0.497585i
$733$	−0.645488	−	1.11802i	−0.0238416	−	0.0412949i	0.853858	−	0.520505i	$-0.174256\pi$
$733$	−0.645488	−	1.11802i	−0.0238416	−	0.0412949i	−0.877700	+	0.479210i	$0.840923\pi$
$734$	1.93270	−	15.8198i	0.0713373	−	0.583918i
$735$	1.20735	+	7.18254i	0.0445336	+	0.264932i
$736$	−25.2401	−	17.5596i	−0.930361	−	0.647257i
$737$		−	29.5675i		−	1.08913i
$738$	−8.70245	+	7.86837i	−0.320342	+	0.289639i
$739$			40.5049i			1.49000i	0.667067	+	0.744998i	$0.267549\pi$
$739$			40.5049i			1.49000i	−0.667067	+	0.744998i	$0.732451\pi$
$740$	23.8957	−	96.3374i	0.878425	−	3.54143i
$741$	18.2408	+	6.80476i	0.670093	+	0.249979i
$742$	−6.47588	−	0.791158i	−0.237737	−	0.0290443i
$743$	−17.6790	−	30.6209i	−0.648580	−	1.12337i	−0.983462	−	0.181113i	$-0.942030\pi$
$743$	−17.6790	−	30.6209i	−0.648580	−	1.12337i	0.334882	−	0.942260i	$-0.391303\pi$
$744$	−6.15727	−	5.41959i	−0.225736	−	0.198692i
$745$	33.8746	−	58.6725i	1.24107	−	2.14959i
$746$	3.41367	−	4.53580i	0.124983	−	0.166067i
$747$	30.1843	+	26.1614i	1.10438	+	0.957195i
$748$	−16.0205	+	4.61480i	−0.585767	+	0.168734i
$749$	−4.35977	−	2.51712i	−0.159303	−	0.0919735i
$750$	−70.2361	−	36.4434i	−2.56466	−	1.33072i
$751$	−43.2698	+	24.9818i	−1.57894	+	0.911600i	−0.583930	+	0.811804i	$0.698486\pi$
$751$	−43.2698	+	24.9818i	−1.57894	+	0.911600i	−0.995008	+	0.0997964i	$0.968181\pi$
$752$	−10.4255	−	5.51100i	−0.380179	−	0.200965i
$753$	21.1183	+	25.5804i	0.769594	+	0.932202i
$754$	3.39541	−	1.44369i	0.123653	−	0.0525761i
$755$	53.9759			1.96439
$756$	−7.38747	+	7.30926i	−0.268680	+	0.265835i
$757$	15.8751			0.576990			0.288495	−	0.957481i	$-0.406845\pi$
$757$	15.8751			0.576990			0.288495	+	0.957481i	$0.406845\pi$
$758$	0.868085	−	0.369101i	0.0315303	−	0.0134063i
$759$	−13.3525	−	16.1737i	−0.484664	−	0.587069i
$760$	−9.22674	−	57.5783i	−0.334689	−	2.08858i
$761$	−2.50431	+	1.44587i	−0.0907813	+	0.0524126i	−0.544703	−	0.838629i	$-0.683358\pi$
$761$	−2.50431	+	1.44587i	−0.0907813	+	0.0524126i	0.453922	+	0.891041i	$0.350024\pi$
$762$	−17.8495	−	9.26158i	−0.646621	−	0.335512i
$763$	−4.13643	−	2.38817i	−0.149749	−	0.0864576i
$764$	−2.32059	−	8.05603i	−0.0839560	−	0.291457i
$765$	44.6090	−	15.4331i	1.61284	−	0.557987i
$766$	−8.23688	+	10.9445i	−0.297610	+	0.395440i
$767$	2.57954	−	4.46790i	0.0931418	−	0.161326i
$768$	−19.1880	−	19.9955i	−0.692388	−	0.721526i
$769$	−3.77761	−	6.54301i	−0.136224	−	0.235947i	0.789840	−	0.613312i	$-0.210163\pi$
$769$	−3.77761	−	6.54301i	−0.136224	−	0.235947i	−0.926064	+	0.377366i	$0.876830\pi$
$770$	−13.1504	−	1.60658i	−0.473907	−	0.0578972i
$771$	17.3125	+	6.45844i	0.623493	+	0.232595i
$772$	25.5582	+	6.33951i	0.919860	+	0.228164i
$773$		−	20.1829i		−	0.725928i	−0.931803	−	0.362964i	$-0.881765\pi$
$773$		−	20.1829i		−	0.725928i	0.931803	−	0.362964i	$-0.118235\pi$
$774$	−1.94072	−	0.626143i	−0.0697576	−	0.0225062i
$775$			21.2346i			0.762771i
$776$	11.0826	−	9.00791i	0.397843	−	0.323365i
$777$	3.38864	+	20.1591i	0.121567	+	0.723205i
$778$	−5.56318	+	45.5364i	−0.199450	+	1.63256i
$779$	6.77897	+	11.7415i	0.242882	+	0.420683i
$780$	−27.5586	−	18.8618i	−0.986757	−	0.675361i
$781$	1.12147	−	1.94245i	0.0401295	−	0.0695064i
$782$	−22.9815	−	17.2960i	−0.821815	−	0.618502i
$783$	−5.91144	−	0.141818i	−0.211258	−	0.00506816i
$784$	3.38705	−	2.12789i	0.120966	−	0.0759959i
$785$	53.1130	+	30.6648i	1.89568	+	1.09447i
$786$	2.75674	−	0.124054i	0.0983297	−	0.00442488i
$787$	−3.41708	+	1.97285i	−0.121806	+	0.0703245i	−0.559665	−	0.828719i	$-0.689070\pi$
$787$	−3.41708	+	1.97285i	−0.121806	+	0.0703245i	0.437859	+	0.899044i	$0.355737\pi$
$788$	10.1426	+	9.77090i	0.361316	+	0.348074i
$789$	−38.7075	+	6.50652i	−1.37802	+	0.231638i
$790$	31.2743	+	73.5537i	1.11269	+	2.61692i
$791$	5.26165			0.187083
$792$	−8.92926	−	16.6615i	−0.317288	−	0.592040i
$793$	−10.7966			−0.383398
$794$	−14.2300	−	33.4675i	−0.505004	−	1.18772i
$795$	−11.7437	+	31.4801i	−0.416506	+	1.11648i
$796$	−3.84374	−	3.70287i	−0.136238	−	0.131245i
$797$	4.92647	−	2.84430i	0.174505	−	0.100750i	−0.410204	−	0.911994i	$-0.634542\pi$
$797$	4.92647	−	2.84430i	0.174505	−	0.100750i	0.584708	+	0.811244i	$0.301209\pi$
$798$	6.46626	+	10.1201i	0.228903	+	0.358248i
$799$	−9.55340	−	5.51566i	−0.337975	−	0.195130i
$800$	−6.03629	+	71.4870i	−0.213415	+	2.52745i
$801$	−36.4672	−	7.03316i	−1.28850	−	0.248505i
$802$	−13.9600	−	10.5064i	−0.492946	−	0.370994i
$803$	5.73084	−	9.92610i	0.202237	−	0.350285i
$804$	41.4590	−	19.8739i	1.46215	−	0.700897i
$805$	−11.4280	−	19.7939i	−0.402785	−	0.697644i
$806$	−0.658323	+	5.38858i	−0.0231884	+	0.189805i
$807$	−34.1939	+	28.2293i	−1.20368	+	0.993718i
$808$	11.8314	+	14.5564i	0.416228	+	0.512094i
$809$		−	27.9065i		−	0.981140i	−0.871402	−	0.490570i	$-0.836789\pi$
$809$		−	27.9065i		−	0.981140i	0.871402	−	0.490570i	$-0.163211\pi$
$810$	27.7273	+	45.7790i	0.974237	+	1.60851i
$811$			2.79493i			0.0981434i	0.998795	+	0.0490717i	$0.0156263\pi$
$811$			2.79493i			0.0981434i	−0.998795	+	0.0490717i	$0.984374\pi$
$812$	2.20903	+	0.547932i	0.0775216	+	0.0192286i
$813$	−40.9382	+	33.7972i	−1.43577	+	1.18532i
$814$	−36.9090	−	4.50917i	−1.29366	−	0.158046i
$815$	−30.3139	−	52.5052i	−1.06185	−	1.83918i
$816$	−17.2389	−	19.3617i	−0.603484	−	0.677796i
$817$	−1.17828	+	2.04085i	−0.0412229	+	0.0714002i
$818$	−9.51005	+	12.6362i	−0.332511	+	0.441814i
$819$	6.75332	+	1.30246i	0.235980	+	0.0455118i
$820$	−6.43737	−	22.3476i	−0.224803	−	0.780412i
$821$	48.0901	+	27.7648i	1.67836	+	0.969000i	0.962709	+	0.270539i	$0.0872019\pi$
$821$	48.0901	+	27.7648i	1.67836	+	0.969000i	0.715648	+	0.698461i	$0.246131\pi$
$822$	−8.46631	+	5.40956i	−0.295297	+	0.188680i
$823$	0.695088	−	0.401309i	0.0242292	−	0.0139888i	−0.487836	−	0.872935i	$-0.662214\pi$
$823$	0.695088	−	0.401309i	0.0242292	−	0.0139888i	0.512066	+	0.858946i	$0.328880\pi$
$824$	−9.94292	+	1.59332i	−0.346378	+	0.0555060i
$825$	−17.1042	+	45.8494i	−0.595492	+	1.59627i
$826$	2.92870	−	1.24525i	0.101903	−	0.0433279i
$827$	10.7060			0.372284			0.186142	−	0.982523i	$-0.440402\pi$
$827$	10.7060			0.372284			0.186142	+	0.982523i	$0.440402\pi$
$828$	13.7036	−	29.5937i	0.476232	−	1.02845i
$829$	37.9248			1.31718			0.658591	−	0.752501i	$-0.271153\pi$
$829$	37.9248			1.31718			0.658591	+	0.752501i	$0.271153\pi$
$830$	−72.8662	+	30.9819i	−2.52922	+	1.07540i
$831$	12.3029	−	2.06805i	0.426783	−	0.0717398i
$832$	−3.74805	+	17.9537i	−0.129940	+	0.622431i
$833$	3.24051	−	1.87091i	0.112277	−	0.0648231i
$834$	−0.624707	−	13.8822i	−0.0216318	−	0.480703i
$835$	−1.74676	−	1.00849i	−0.0604493	−	0.0349004i
$836$	−20.9915	+	6.04674i	−0.726007	+	0.209131i
$837$	4.52958	−	7.42814i	0.156565	−	0.256754i
$838$	27.3611	−	36.3552i	0.945174	−	1.25587i
$839$	3.18205	−	5.51147i	0.109856	−	0.190277i	−0.805856	−	0.592112i	$-0.798294\pi$
$839$	3.18205	−	5.51147i	0.109856	−	0.190277i	0.915712	+	0.401835i	$0.131628\pi$
$840$	−6.58633	−	19.5190i	−0.227250	−	0.673471i
$841$	−13.8525	−	23.9932i	−0.477672	−	0.827353i
$842$	−23.2859	−	2.84484i	−0.802485	−	0.0980396i
$843$	−6.47038	−	38.4925i	−0.222852	−	1.32575i
$844$	−1.36152	+	5.48907i	−0.0468655	+	0.188942i
$845$		−	32.5638i		−	1.12023i
$846$	3.84051	−	11.9036i	0.132040	−	0.409254i
$847$		−	6.03700i		−	0.207434i
$848$	18.4399	−	0.688652i	0.633228	−	0.0236484i
$849$	−30.9717	−	11.5540i	−1.06295	−	0.396533i
$850$	−8.13842	+	66.6155i	−0.279145	+	2.28489i
$851$	−32.0749	−	55.5553i	−1.09951	−	1.90441i
$852$	3.47746	+	0.266887i	0.119136	+	0.00914340i
$853$	9.54388	−	16.5305i	0.326776	−	0.565993i	−0.655094	−	0.755547i	$-0.727371\pi$
$853$	9.54388	−	16.5305i	0.326776	−	0.565993i	0.981870	+	0.189554i	$0.0607043\pi$
$854$	−5.32135	−	4.00487i	−0.182093	−	0.137044i
$855$	58.4509	−	20.2220i	1.99898	−	0.691576i
$856$	13.3025	+	5.07863i	0.454669	+	0.173584i
$857$	−11.8392	−	6.83538i	−0.404420	−	0.233492i	0.283969	−	0.958833i	$-0.408349\pi$
$857$	−11.8392	−	6.83538i	−0.404420	−	0.233492i	−0.688389	+	0.725341i	$0.741682\pi$
$858$	−5.76186	+	11.1047i	−0.196707	+	0.379107i
$859$	23.5993	−	13.6251i	0.805198	−	0.464881i	−0.0400874	−	0.999196i	$-0.512764\pi$
$859$	23.5993	−	13.6251i	0.805198	−	0.464881i	0.845286	+	0.534315i	$0.179430\pi$
$860$	2.80448	−	2.91117i	0.0956321	−	0.0992702i
$861$	3.04929	+	3.69357i	0.103919	+	0.125877i
$862$	7.74727	+	18.2208i	0.263873	+	0.620601i
$863$	−30.3896			−1.03447			−0.517237	−	0.855842i	$-0.673039\pi$
$863$	−30.3896			−1.03447			−0.517237	+	0.855842i	$0.673039\pi$
$864$	17.3605	−	23.7194i	0.590617	−	0.806952i
$865$	46.7078			1.58811
$866$	16.0324	+	37.7064i	0.544802	+	1.28131i
$867$	3.30677	+	4.00546i	0.112304	+	0.136033i
$868$	−2.32330	+	2.41169i	−0.0788581	+	0.0818580i
$869$	25.9305	−	14.9710i	0.879630	−	0.507855i
$870$	5.39844	−	10.4042i	0.183024	−	0.352737i
$871$	−26.3512	−	15.2139i	−0.892876	−	0.515502i
$872$	12.6210	+	4.81847i	0.427401	+	0.163174i
$873$	11.4469	+	9.92127i	0.387418	+	0.335784i
$874$	−30.1124	−	22.6628i	−1.01857	−	0.766580i
$875$	−16.1519	+	27.9759i	−0.546035	+	0.945760i
$876$	17.7702	+	1.36382i	0.600398	+	0.0460791i
$877$	3.44779	+	5.97175i	0.116424	+	0.201652i	0.918348	−	0.395774i	$-0.129524\pi$
$877$	3.44779	+	5.97175i	0.116424	+	0.201652i	−0.801924	+	0.597426i	$0.796190\pi$
$878$	−5.21407	+	42.6788i	−0.175967	+	1.44034i
$879$	11.1919	+	4.17513i	0.377492	+	0.140824i
$880$	37.4453	−	1.39843i	1.26228	−	0.0471409i
$881$			4.57217i			0.154040i	0.997030	+	0.0770202i	$0.0245406\pi$
$881$			4.57217i			0.154040i	−0.997030	+	0.0770202i	$0.975459\pi$
$882$	2.84540	+	3.14702i	0.0958095	+	0.105966i
$883$			11.7784i			0.396374i	0.980164	+	0.198187i	$0.0635053\pi$
$883$			11.7784i			0.396374i	−0.980164	+	0.198187i	$0.936495\pi$
$884$	−4.13047	+	16.6523i	−0.138923	+	0.560077i
$885$	−2.71693	−	16.1631i	−0.0913285	−	0.543316i
$886$	−30.8009	−	3.76295i	−1.03478	−	0.126419i
$887$	4.62869	+	8.01713i	0.155416	+	0.269189i	0.933211	−	0.359330i	$-0.116995\pi$
$887$	4.62869	+	8.01713i	0.155416	+	0.269189i	−0.777794	+	0.628519i	$0.783661\pi$
$888$	−18.4857	−	54.7838i	−0.620341	−	1.83842i
$889$	−4.10479	+	7.10971i	−0.137670	+	0.238452i
$890$	44.2699	−	58.8222i	1.48393	−	1.97172i
$891$	15.7635	−	12.3902i	0.528096	−	0.415087i
$892$	11.9633	−	3.44612i	0.400563	−	0.115385i
$893$	−12.5178	−	7.22713i	−0.418891	−	0.241847i
$894$	−1.77414	−	39.4250i	−0.0593362	−	1.31857i
$895$	69.1128	−	39.9023i	2.31019	−	1.33379i
$896$	−8.50703	+	7.45858i	−0.284200	+	0.249174i
$897$	−21.2848	+	3.57786i	−0.710679	+	0.119461i
$898$	27.5234	−	11.7026i	0.918467	−	0.390522i
$899$	−1.90540			−0.0635486
$900$	−75.7857	+	6.83461i	−2.52619	+	0.227820i
$901$	17.2617			0.575070
$902$	−8.01759	+	3.40900i	−0.266957	+	0.113507i
$903$	−0.290981	+	0.780002i	−0.00968323	+	0.0259568i
$904$	−14.6947	+	2.35478i	−0.488739	+	0.0783189i
$905$	−44.0538	+	25.4345i	−1.46440	+	0.845470i
$906$	26.4951	−	16.9291i	0.880242	−	0.562432i
$907$	−24.9384	−	14.3982i	−0.828066	−	0.478084i	0.0251243	−	0.999684i	$-0.492002\pi$
$907$	−24.9384	−	14.3982i	−0.828066	−	0.478084i	−0.853190	+	0.521600i	$0.825335\pi$
$908$	12.4612	+	43.2594i	0.413538	+	1.43561i
$909$	−13.0311	+	15.0349i	−0.432213	+	0.498676i
$910$	−8.19829	+	10.8932i	−0.271771	+	0.361107i
$911$	−14.4485	+	25.0256i	−0.478701	+	0.829134i	−0.999702	−	0.0244220i	$-0.992225\pi$
$911$	−14.4485	+	25.0256i	−0.478701	+	0.829134i	0.521001	+	0.853556i	$0.325559\pi$
$912$	−22.5881	−	25.3695i	−0.747966	−	0.840069i
$913$	14.8310	+	25.6881i	0.490835	+	0.850151i
$914$	38.2851	+	4.67729i	1.26636	+	0.154711i
$915$	−26.4504	+	21.8366i	−0.874424	+	0.721895i
$916$	−40.2638	−	9.98713i	−1.33035	−	0.329984i
$917$		−	1.12657i		−	0.0372027i
$918$	17.0567	−	21.5669i	0.562956	−	0.711815i
$919$		−	32.1365i		−	1.06009i	−0.847971	−	0.530043i	$-0.822176\pi$
$919$		−	32.1365i		−	1.06009i	0.847971	−	0.530043i	$-0.177824\pi$
$920$	40.7747	+	50.1660i	1.34430	+	1.65392i
$921$	31.7755	−	26.2328i	1.04704	−	0.864399i
$922$	4.34571	−	35.5710i	0.143118	−	1.17147i
$923$	−1.15410	−	1.99896i	−0.0379877	−	0.0657966i
$924$	−6.95902	+	3.33589i	−0.228935	+	0.109743i
$925$	−74.8388	+	129.625i	−2.46068	+	4.26203i
$926$	−9.37394	−	7.05488i	−0.308047	−	0.231838i
$927$	−3.49203	−	10.0936i	−0.114693	−	0.331518i
$928$	−6.41458	−	0.541641i	−0.210569	−	0.0177802i
$929$	15.5033	+	8.95081i	0.508645	+	0.293666i	0.732277	−	0.681007i	$-0.238458\pi$
$929$	15.5033	+	8.95081i	0.508645	+	0.293666i	−0.223631	+	0.974674i	$0.571791\pi$
$930$	9.28582	+	14.5329i	0.304494	+	0.476553i
$931$	4.24602	−	2.45144i	0.139158	−	0.0803427i
$932$	6.24486	+	6.01600i	0.204557	+	0.197061i
$933$	−12.3537	+	33.1152i	−0.404440	+	1.08414i
$934$	12.9014	+	30.3428i	0.422148	+	0.992847i
$935$	35.0528			1.14635
$936$	−19.4435	−	0.615155i	−0.635532	−	0.0201070i
$937$	5.71581			0.186727			0.0933637	−	0.995632i	$-0.470238\pi$
$937$	5.71581			0.186727			0.0933637	+	0.995632i	$0.470238\pi$
$938$	−7.34438	−	17.2732i	−0.239802	−	0.563989i
$939$	−2.35930	+	0.396586i	−0.0769929	+	0.0129421i
$940$	17.8560	+	17.2016i	0.582399	+	0.561055i
$941$	21.8244	−	12.6003i	0.711454	−	0.410758i	−0.100145	−	0.994973i	$-0.531931\pi$
$941$	21.8244	−	12.6003i	0.711454	−	0.410758i	0.811599	+	0.584215i	$0.198597\pi$
$942$	35.6893	−	1.60603i	1.16282	−	0.0523274i
$943$	−13.0169	−	7.51529i	−0.423887	−	0.244731i
$944$	−7.62198	+	4.78845i	−0.248074	+	0.155851i
$945$	19.1792	−	10.4680i	0.623899	−	0.340524i
$946$	−1.20994	−	0.910605i	−0.0393384	−	0.0296063i
$947$	−20.3041	+	35.1677i	−0.659794	+	1.14280i	0.320875	+	0.947121i	$0.396023\pi$
$947$	−20.3041	+	35.1677i	−0.659794	+	1.14280i	−0.980669	+	0.195675i	$0.937310\pi$
$948$	38.4211	+	26.2964i	1.24786	+	0.854067i
$949$	−5.89756	−	10.2149i	−0.191443	−	0.331589i
$950$	−10.6637	+	87.2859i	−0.345977	+	2.83193i
$951$	−6.31017	−	37.5394i	−0.204621	−	1.21730i
$952$	−8.21278	+	6.67531i	−0.266178	+	0.216348i
$953$		−	7.17192i		−	0.232321i	−0.993230	−	0.116161i	$-0.962941\pi$
$953$		−	7.17192i		−	0.232321i	0.993230	−	0.116161i	$-0.0370588\pi$
$954$	4.10885	+	19.1359i	0.133029	+	0.619549i
$955$			17.6266i			0.570384i
$956$	12.4245	+	3.08181i	0.401838	+	0.0996728i
$957$	−4.11410	−	1.53477i	−0.132990	−	0.0496121i
$958$	−34.2134	−	4.17986i	−1.10539	−	0.135045i
$959$	2.05083	+	3.55214i	0.0662248	+	0.114705i
$960$	27.1298	+	51.5651i	0.875609	+	1.66426i
$961$	−14.0983	+	24.4189i	−0.454782	+	0.787706i
$962$	−23.0100	+	30.5738i	−0.741873	+	0.985740i
$963$	−2.86004	+	14.8294i	−0.0921636	+	0.477871i
$964$	3.98036	+	13.8180i	0.128199	+	0.445047i
$965$	−47.9473	−	27.6824i	−1.54348	−	0.891128i
$966$	−11.8179	−	6.13193i	−0.380234	−	0.197292i
$967$	20.7638	−	11.9880i	0.667717	−	0.385507i	−0.127494	−	0.991839i	$-0.540693\pi$
$967$	20.7638	−	11.9880i	0.667717	−	0.385507i	0.795211	+	0.606333i	$0.207360\pi$
$968$	2.70178	+	16.8601i	0.0868385	+	0.541904i
$969$	−20.2297	−	24.5041i	−0.649872	−	0.787185i
$970$	−27.6333	+	11.7494i	−0.887251	+	0.377250i
$971$	−49.7729			−1.59729			−0.798645	−	0.601803i	$-0.794449\pi$
$971$	−49.7729			−1.59729			−0.798645	+	0.601803i	$0.794449\pi$
$972$	27.9687	+	13.7751i	0.897096	+	0.441836i
$973$	−5.67314			−0.181872
$974$	25.0918	−	10.6688i	0.803994	−	0.341850i
$975$	32.0610	+	38.8352i	1.02677	+	1.24372i
$976$	16.6538	+	8.80330i	0.533074	+	0.281787i
$977$	−12.1846	+	7.03477i	−0.389819	+	0.225062i	−0.682082	−	0.731276i	$-0.738925\pi$
$977$	−12.1846	+	7.03477i	−0.389819	+	0.225062i	0.292263	+	0.956338i	$0.405592\pi$
$978$	−31.3480	−	16.2655i	−1.00240	−	0.520113i
$979$	−23.8844	−	13.7897i	−0.763349	−	0.440720i
$980$	−8.08144	+	2.32791i	−0.258152	+	0.0743623i
$981$	−2.71353	+	14.0697i	−0.0866363	+	0.449212i
$982$	9.91801	−	13.1782i	0.316496	−	0.420534i
$983$	−13.3486	+	23.1205i	−0.425756	+	0.737430i	−0.996491	−	0.0837040i	$-0.973325\pi$
$983$	−13.3486	+	23.1205i	−0.425756	+	0.737430i	0.570735	+	0.821134i	$0.306658\pi$
$984$	−10.1691	−	8.95073i	−0.324178	−	0.285339i
$985$	−14.8053	−	25.6435i	−0.471735	−	0.817070i
$986$	−5.97746	−	0.730266i	−0.190361	−	0.0232564i
$987$	−4.78423	−	1.78476i	−0.152284	−	0.0568096i
$988$	−5.41213	+	21.8194i	−0.172183	+	0.694167i
$989$		−	2.61253i		−	0.0830738i
$990$	8.34373	+	38.8588i	0.265181	+	1.23501i
$991$		−	0.190124i		−	0.00603949i	−0.999995	−	0.00301974i	$-0.999039\pi$
$991$		−	0.190124i		−	0.00603949i	0.999995	−	0.00301974i	$-0.000961215\pi$
$992$	5.40919	−	7.77512i	0.171742	−	0.246860i
$993$	9.77357	+	58.1433i	0.310155	+	1.84512i
$994$	0.172667	−	1.41333i	0.00547667	−	0.0448283i
$995$	5.61075	+	9.71811i	0.177873	+	0.308085i
$996$	−26.0506	+	38.0620i	−0.825443	+	1.20604i
$997$	−4.35056	+	7.53539i	−0.137784	+	0.238648i	−0.926657	−	0.375907i	$-0.877331\pi$
$997$	−4.35056	+	7.53539i	−0.137784	+	0.238648i	0.788874	+	0.614555i	$0.210665\pi$
$998$	10.2020	+	7.67808i	0.322939	+	0.243045i
$999$	53.8299	−	29.3804i	1.70310	−	0.929553i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.2.ba.a.155.14	yes	72
3.2	odd	2		756.2.ba.a.575.23		72
4.3	odd	2	inner	252.2.ba.a.155.2	✓	72
9.4	even	3		756.2.ba.a.71.35		72
9.5	odd	6	inner	252.2.ba.a.239.2	yes	72
12.11	even	2		756.2.ba.a.575.35		72
36.23	even	6	inner	252.2.ba.a.239.14	yes	72
36.31	odd	6		756.2.ba.a.71.23		72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.2.ba.a.155.2	✓	72	4.3	odd	2	inner
252.2.ba.a.155.14	yes	72	1.1	even	1	trivial
252.2.ba.a.239.2	yes	72	9.5	odd	6	inner
252.2.ba.a.239.14	yes	72	36.23	even	6	inner
756.2.ba.a.71.23		72	36.31	odd	6
756.2.ba.a.71.35		72	9.4	even	3
756.2.ba.a.575.23		72	3.2	odd	2
756.2.ba.a.575.35		72	12.11	even	2

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	252.ba (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.553365 - 1.30146i) q^{2} +(1.10270 + 1.33569i) q^{3} +(-1.38757 + 1.44036i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.12814 - 2.17423i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +O(q^{10})\)	\(q+(-0.553365 - 1.30146i) q^{2} +(1.10270 + 1.33569i) q^{3} +(-1.38757 + 1.44036i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.12814 - 2.17423i) q^{6} +(-0.866025 - 0.500000i) q^{7} +(2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +(-4.75149 - 3.57600i) q^{10} +(-1.11389 + 1.92931i) q^{11} +(-3.45394 - 0.265082i) q^{12} +(1.14629 + 1.98544i) q^{13} +(-0.171499 + 1.40378i) q^{14} +(6.82394 + 2.54568i) q^{15} +(-0.149279 - 3.99721i) q^{16} -3.74182i q^{17} +(4.14810 - 0.890676i) q^{18} -4.90288i q^{19} +(-2.02469 + 8.16269i) q^{20} +(-0.287120 - 1.70809i) q^{21} +(3.12730 + 0.382063i) q^{22} +(2.71771 + 4.70721i) q^{23} +(1.56630 + 4.64184i) q^{24} +(6.34110 - 10.9831i) q^{25} +(1.94964 - 2.59053i) q^{26} +(-4.56102 + 2.48940i) q^{27} +(1.92185 - 0.553602i) q^{28} +(0.985523 + 0.568992i) q^{29} +(-0.463043 - 10.2897i) q^{30} +(-1.45004 + 0.837182i) q^{31} +(-5.11959 + 2.40620i) q^{32} +(-3.80524 + 0.639641i) q^{33} +(-4.86981 + 2.07059i) q^{34} -4.20502 q^{35} +(-3.45459 - 4.90569i) q^{36} -11.8022 q^{37} +(-6.38088 + 2.71308i) q^{38} +(-1.38791 + 3.72043i) q^{39} +(11.7438 - 1.88190i) q^{40} +(-2.39482 + 1.38265i) q^{41} +(-2.06412 + 1.31887i) q^{42} +(-0.416255 - 0.240325i) q^{43} +(-1.23330 - 4.28147i) q^{44} +(4.12451 + 11.9218i) q^{45} +(4.62234 - 6.14179i) q^{46} +(1.47406 - 2.55314i) q^{47} +(5.17442 - 4.60711i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-17.8030 - 2.17499i) q^{50} +(4.99790 - 4.12609i) q^{51} +(-4.45032 - 1.10387i) q^{52} +4.61318i q^{53} +(5.76376 + 4.55841i) q^{54} +9.36786i q^{55} +(-1.78398 - 2.19486i) q^{56} +(6.54871 - 5.40639i) q^{57} +(0.195164 - 1.59747i) q^{58} +(-1.12516 - 1.94884i) q^{59} +(-13.1354 + 6.29662i) q^{60} +(-2.35467 + 4.07841i) q^{61} +(1.89196 + 1.42390i) q^{62} +(1.96486 - 2.26701i) q^{63} +(5.96457 + 5.33141i) q^{64} +(8.34882 + 4.82020i) q^{65} +(2.93815 + 4.59840i) q^{66} +(-11.4941 + 6.63610i) q^{67} +(5.38957 + 5.19205i) q^{68} +(-3.29055 + 8.82064i) q^{69} +(2.32691 + 5.47265i) q^{70} -1.00681 q^{71} +(-4.47289 + 7.21063i) q^{72} -5.14489 q^{73} +(6.53091 + 15.3600i) q^{74} +(21.6623 - 3.64132i) q^{75} +(7.06192 + 6.80311i) q^{76} +(1.92931 - 1.11389i) q^{77} +(5.61000 - 0.252452i) q^{78} +(-11.6396 - 6.72012i) q^{79} +(-8.94781 - 14.2426i) q^{80} +(-8.35448 - 3.34703i) q^{81} +(3.12467 + 2.35164i) q^{82} +(6.65730 - 11.5308i) q^{83} +(2.85866 + 1.95654i) q^{84} +(-7.86721 - 13.6264i) q^{85} +(-0.0824311 + 0.674725i) q^{86} +(0.326738 + 1.94378i) q^{87} +(-4.88967 + 3.97431i) q^{88} +12.3797i q^{89} +(13.2333 - 11.9649i) q^{90} -2.29259i q^{91} +(-10.5511 - 2.61712i) q^{92} +(-2.71717 - 1.01364i) q^{93} +(-4.13850 - 0.505600i) q^{94} +(-10.3084 - 17.8546i) q^{95} +(-8.85929 - 4.18486i) q^{96} +(2.52467 - 4.37286i) q^{97} +(0.850411 - 1.12996i) q^{98} +(-5.05039 - 4.37728i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 6 q^{6} + 4 q^{9}+O(q^{10}) \) 72 * q + 6 * q^6 + 4 * q^9	\( 72 q + 6 q^{6} + 4 q^{9} - 12 q^{12} - 34 q^{18} - 42 q^{20} - 2 q^{24} + 36 q^{25} + 28 q^{30} + 30 q^{32} - 44 q^{33} - 12 q^{34} + 20 q^{36} - 12 q^{40} - 60 q^{41} + 20 q^{42} - 24 q^{45} - 24 q^{46} - 28 q^{48} + 36 q^{49} - 78 q^{50} - 18 q^{52} - 10 q^{54} - 4 q^{57} - 18 q^{58} - 76 q^{60} - 60 q^{64} + 24 q^{65} + 54 q^{66} + 78 q^{68} + 24 q^{69} + 74 q^{72} - 24 q^{73} + 12 q^{76} - 20 q^{78} - 4 q^{81} - 36 q^{82} + 14 q^{84} + 30 q^{86} + 24 q^{88} + 8 q^{90} - 114 q^{92} - 96 q^{93} + 42 q^{94} + 112 q^{96} - 12 q^{97}+O(q^{100}) \) 72 * q + 6 * q^6 + 4 * q^9 - 12 * q^12 - 34 * q^18 - 42 * q^20 - 2 * q^24 + 36 * q^25 + 28 * q^30 + 30 * q^32 - 44 * q^33 - 12 * q^34 + 20 * q^36 - 12 * q^40 - 60 * q^41 + 20 * q^42 - 24 * q^45 - 24 * q^46 - 28 * q^48 + 36 * q^49 - 78 * q^50 - 18 * q^52 - 10 * q^54 - 4 * q^57 - 18 * q^58 - 76 * q^60 - 60 * q^64 + 24 * q^65 + 54 * q^66 + 78 * q^68 + 24 * q^69 + 74 * q^72 - 24 * q^73 + 12 * q^76 - 20 * q^78 - 4 * q^81 - 36 * q^82 + 14 * q^84 + 30 * q^86 + 24 * q^88 + 8 * q^90 - 114 * q^92 - 96 * q^93 + 42 * q^94 + 112 * q^96 - 12 * q^97

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