LMFDB - Embedded newform 252.2.ba.a.155.2

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			155.2
Character	$\chi$	$=$	252.155
Dual form			252.2.ba.a.239.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.40378 + 0.171499i) q^{2} +(-1.10270 - 1.33569i) q^{3} +(1.94118 - 0.481494i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.77701 + 1.68589i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +O(q^{10})$	\(q+(-1.40378 + 0.171499i) q^{2} +(-1.10270 - 1.33569i) q^{3} +(1.94118 - 0.481494i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.77701 + 1.68589i) 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} +(-2.78365 - 2.06186i) q^{12} +(1.14629 + 1.98544i) q^{13} +(-1.30146 - 0.553365i) q^{14} +(-6.82394 - 2.54568i) q^{15} +(3.53633 - 1.86933i) q^{16} -3.74182i q^{17} +(0.292323 - 4.23256i) q^{18} +4.90288i q^{19} +(6.05675 - 5.83478i) q^{20} +(-0.287120 - 1.70809i) q^{21} +(-1.23278 + 2.89936i) q^{22} +(-2.71771 - 4.70721i) q^{23} +(4.26123 + 2.41700i) 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} +(10.0159 + 2.40326i) q^{30} +(1.45004 - 0.837182i) q^{31} +(-4.64362 + 3.23060i) q^{32} +(-3.80524 + 0.639641i) q^{33} +(0.641719 + 5.25267i) q^{34} +4.20502 q^{35} +(0.315525 + 5.99170i) q^{36} -11.8022 q^{37} +(-0.840841 - 6.88255i) q^{38} +(1.38791 - 3.72043i) q^{39} +(-7.50166 + 9.22945i) q^{40} +(-2.39482 + 1.38265i) q^{41} +(0.695988 + 2.34853i) 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} +(-6.39633 - 2.66213i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-7.01789 + 16.5053i) q^{50} +(-4.99790 + 4.12609i) q^{51} +(3.18114 + 3.30216i) q^{52} +4.61318i q^{53} +(-5.97572 + 4.27678i) q^{54} -9.36786i q^{55} +(-2.79280 - 0.447537i) q^{56} +(6.54871 - 5.40639i) q^{57} +(-1.48104 - 0.629721i) q^{58} +(1.12516 + 1.94884i) q^{59} +(-14.4722 - 1.65593i) 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} +(5.23201 - 1.55051i) q^{66} +(11.4941 - 6.63610i) q^{67} +(-1.80166 - 7.26353i) q^{68} +(-3.29055 + 8.82064i) q^{69} +(-5.90291 + 0.721159i) q^{70} +1.00681 q^{71} +(-1.47050 - 8.35689i) q^{72} -5.14489 q^{73} +(16.5676 - 2.02407i) q^{74} +(-21.6623 + 3.64132i) q^{75} +(2.36070 + 9.51735i) q^{76} +(1.92931 - 1.11389i) q^{77} +(-1.31027 + 5.46068i) 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} +(-1.37978 - 3.17745i) q^{84} +(-7.86721 - 13.6264i) q^{85} +(-0.625544 - 0.265975i) q^{86} +(-0.326738 - 1.94378i) q^{87} +(-0.997014 + 6.22174i) q^{88} +12.3797i q^{89} +(-7.83446 - 16.0281i) q^{90} +2.29259i q^{91} +(-7.54205 - 7.82897i) q^{92} +(-2.71717 - 1.01364i) q^{93} +(1.63139 - 3.83684i) q^{94} +(10.3084 + 17.8546i) q^{95} +(9.43558 + 2.64006i) 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 $

$2$	−1.40378	+	0.171499i	−0.992620	+	0.121268i
$2$	−1.40378	+	0.171499i	−0.992620	+	0.121268i
$3$	−1.10270	−	1.33569i	−0.636642	−	0.771159i
$3$	−1.10270	−	1.33569i	−0.636642	−	0.771159i
$4$	1.94118	−	0.481494i	0.970588	−	0.240747i
$5$	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	$-0.0560955\pi$
$6$	1.77701	+	1.68589i	0.725461	+	0.688263i
$7$	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	−0.647797	−	0.761813i	$-0.724310\pi$
$11$	1.11389	−	1.92931i	0.335850	−	0.581710i	0.983648	+	0.180103i	$0.0576430\pi$
$12$	−2.78365	−	2.06186i	−0.803572	−	0.595208i
$13$	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	$0.730347\pi$
$14$	−1.30146	−	0.553365i	−0.347829	−	0.147893i
$15$	−6.82394	−	2.54568i	−1.76193	−	0.657292i
$16$	3.53633	−	1.86933i	0.884082	−	0.467332i
$17$		−	3.74182i		−	0.907524i	−0.891123	−	0.453762i	$-0.850082\pi$
$17$		−	3.74182i		−	0.907524i	0.891123	−	0.453762i	$-0.149918\pi$
$18$	0.292323	−	4.23256i	0.0689013	−	0.997623i
$19$			4.90288i			1.12480i	0.826866	+	0.562399i	$0.190121\pi$
$19$			4.90288i			1.12480i	−0.826866	+	0.562399i	$0.809879\pi$
$20$	6.05675	−	5.83478i	1.35433	−	1.30470i
$21$	−0.287120	−	1.70809i	−0.0626548	−	0.372735i
$22$	−1.23278	+	2.89936i	−0.262829	+	0.618145i
$23$	−2.71771	−	4.70721i	−0.566682	−	0.981522i	−0.996891	−	0.0787925i	$-0.974894\pi$
$23$	−2.71771	−	4.70721i	−0.566682	−	0.981522i	0.430209	−	0.902729i	$-0.358440\pi$
$24$	4.26123	+	2.41700i	0.869821	+	0.493368i
$25$	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	$0.632971\pi$
$30$	10.0159	+	2.40326i	1.82864	+	0.438774i
$31$	1.45004	−	0.837182i	0.260435	−	0.150362i	−0.364098	−	0.931361i	$-0.618623\pi$
$31$	1.45004	−	0.837182i	0.260435	−	0.150362i	0.624533	+	0.780998i	$0.285289\pi$
$32$	−4.64362	+	3.23060i	−0.820885	+	0.571094i
$33$	−3.80524	+	0.639641i	−0.662408	+	0.111347i
$34$	0.641719	+	5.25267i	0.110054	+	0.900826i
$35$	4.20502			0.710778
$36$	0.315525	+	5.99170i	0.0525874	+	0.998616i
$37$	−11.8022			−1.94026			−0.970132	−	0.242576i	$-0.922008\pi$
$37$	−11.8022			−1.94026			−0.970132	+	0.242576i	$0.922008\pi$
$38$	−0.840841	−	6.88255i	−0.136402	−	1.11650i
$39$	1.38791	−	3.72043i	0.222244	−	0.595746i
$40$	−7.50166	+	9.22945i	−1.18612	+	1.45930i
$41$	−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	$0.402613\pi$
$42$	0.695988	+	2.34853i	0.107393	+	0.362386i
$43$	0.416255	+	0.240325i	0.0634783	+	0.0366492i	0.531403	−	0.847119i	$-0.321665\pi$
$43$	0.416255	+	0.240325i	0.0634783	+	0.0366492i	−0.467925	+	0.883768i	$0.654998\pi$
$44$	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	−0.953277	−	0.302098i	$-0.902313\pi$
$47$	−1.47406	+	2.55314i	−0.215014	+	0.372414i	0.738263	+	0.674513i	$0.235646\pi$
$48$	−6.39633	−	2.66213i	−0.923231	−	0.384245i
$49$	0.500000	+	0.866025i	0.0714286	+	0.123718i
$50$	−7.01789	+	16.5053i	−0.992480	+	2.33421i
$51$	−4.99790	+	4.12609i	−0.699845	+	0.577768i
$52$	3.18114	+	3.30216i	0.441144	+	0.457927i
$53$			4.61318i			0.633670i	0.948481	+	0.316835i	$0.102620\pi$
$53$			4.61318i			0.633670i	−0.948481	+	0.316835i	$0.897380\pi$
$54$	−5.97572	+	4.27678i	−0.813192	+	0.581996i
$55$		−	9.36786i		−	1.26316i
$56$	−2.79280	−	0.447537i	−0.373203	−	0.0598046i
$57$	6.54871	−	5.40639i	0.867398	−	0.716094i
$58$	−1.48104	−	0.629721i	−0.194469	−	0.0826864i
$59$	1.12516	+	1.94884i	0.146484	+	0.253718i	0.929926	−	0.367748i	$-0.119871\pi$
$59$	1.12516	+	1.94884i	0.146484	+	0.253718i	−0.783442	+	0.621465i	$0.786538\pi$
$60$	−14.4722	−	1.65593i	−1.86835	−	0.213779i
$61$	−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
$66$	5.23201	−	1.55051i	0.644016	−	0.190854i
$67$	11.4941	−	6.63610i	1.40422	−	0.810729i	0.409401	−	0.912355i	$-0.365738\pi$
$67$	11.4941	−	6.63610i	1.40422	−	0.810729i	0.994823	+	0.101626i	$0.0324045\pi$
$68$	−1.80166	−	7.26353i	−0.218483	−	0.880832i
$69$	−3.29055	+	8.82064i	−0.396136	+	1.06188i
$70$	−5.90291	+	0.721159i	−0.705533	+	0.0861949i
$71$	1.00681			0.119486			0.0597431	−	0.998214i	$-0.480972\pi$
$71$	1.00681			0.119486			0.0597431	+	0.998214i	$0.480972\pi$
$72$	−1.47050	−	8.35689i	−0.173300	−	0.984869i
$73$	−5.14489			−0.602163			−0.301082	−	0.953598i	$-0.597348\pi$
$73$	−5.14489			−0.602163			−0.301082	+	0.953598i	$0.597348\pi$
$74$	16.5676	−	2.02407i	1.92595	−	0.235293i
$75$	−21.6623	+	3.64132i	−2.50135	+	0.420463i
$76$	2.36070	+	9.51735i	0.270791	+	1.09172i
$77$	1.92931	−	1.11389i	0.219866	−	0.126940i
$78$	−1.31027	+	5.46068i	−0.148358	+	0.618300i
$79$	11.6396	+	6.72012i	1.30956	+	0.756073i	0.982022	−	0.188766i	$-0.0604489\pi$
$79$	11.6396	+	6.72012i	1.30956	+	0.756073i	0.327535	+	0.944839i	$0.393782\pi$
$80$	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	$0.427489\pi$
$83$	−6.65730	+	11.5308i	−0.730734	+	1.26567i	−0.956570	+	0.291503i	$0.905845\pi$
$84$	−1.37978	−	3.17745i	−0.150547	−	0.346688i
$85$	−7.86721	−	13.6264i	−0.853319	−	1.47799i
$86$	−0.625544	−	0.265975i	−0.0674542	−	0.0286808i
$87$	−0.326738	−	1.94378i	−0.0350300	−	0.208395i
$88$	−0.997014	+	6.22174i	−0.106282	+	0.663239i
$89$			12.3797i			1.31225i	0.754652	+	0.656125i	$0.227806\pi$
$89$			12.3797i			1.31225i	−0.754652	+	0.656125i	$0.772194\pi$
$90$	−7.83446	−	16.0281i	−0.825824	−	1.68951i
$91$			2.29259i			0.240329i
$92$	−7.54205	−	7.82897i	−0.786313	−	0.816226i
$93$	−2.71717	−	1.01364i	−0.281757	−	0.105110i
$94$	1.63139	−	3.83684i	0.168265	−	0.395740i
$95$	10.3084	+	17.8546i	1.05762	+	1.83184i
$96$	9.43558	+	2.64006i	0.963014	+	0.269450i
$97$	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	$0.559632\pi$
$102$	6.30831	−	6.64924i	0.624615	−	0.658373i
$103$	3.08323	−	1.78010i	0.303799	−	0.175399i	−0.340349	−	0.940299i	$-0.610545\pi$
$103$	3.08323	−	1.78010i	0.303799	−	0.175399i	0.644148	+	0.764901i	$0.277212\pi$
$104$	−5.03192	−	4.08993i	−0.493421	−	0.401050i
$105$	−4.63686	−	5.61659i	−0.452512	−	0.548123i
$106$	−0.791158	−	6.47588i	−0.0768441	−	0.628993i
$107$	−5.03423			−0.486678			−0.243339	−	0.969941i	$-0.578243\pi$
$107$	−5.03423			−0.486678			−0.243339	+	0.969941i	$0.578243\pi$
$108$	7.65510	−	7.02847i	0.736613	−	0.676315i
$109$	4.77634			0.457491			0.228745	−	0.973486i	$-0.426538\pi$
$109$	4.77634			0.457491			0.228745	+	0.973486i	$0.426538\pi$
$110$	1.60658	+	13.1504i	0.153182	+	1.25384i
$111$	13.0142	+	15.7640i	1.23525	+	1.49625i
$112$	3.99721	+	0.149279i	0.377701	+	0.0141055i
$113$	−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	$0.412938\pi$
$114$	−8.26573	+	8.71246i	−0.774157	+	0.815997i
$115$	−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
$120$	20.5997	−	0.157419i	1.88049	−	0.0143703i
$121$	3.01850	+	5.22819i	0.274409	+	0.475290i
$122$	2.60599	−	6.12900i	0.235935	−	0.554893i
$123$	4.48755	+	1.67409i	0.404629	+	0.150947i
$124$	2.41169	−	2.32330i	0.216576	−	0.208639i
$125$		−	32.3038i		−	2.88934i
$126$	2.36944	−	3.51934i	0.211086	−	0.313528i
$127$			8.20958i			0.728482i	0.931305	+	0.364241i	$0.118672\pi$
$127$			8.20958i			0.728482i	−0.931305	+	0.364241i	$0.881328\pi$
$128$	−7.45858	+	8.50703i	−0.659252	+	0.751922i
$129$	−0.138004	−	0.820992i	−0.0121506	−	0.0722843i
$130$	−12.5465	−	5.33466i	−1.10040	−	0.467880i
$131$	−0.563287	−	0.975641i	−0.0492146	−	0.0852422i	0.840369	−	0.542015i	$-0.182338\pi$
$131$	−0.563287	−	0.975641i	−0.0492146	−	0.0852422i	−0.889583	+	0.456773i	$0.849005\pi$
$132$	−7.07866	+	3.07385i	−0.616119	+	0.267545i
$133$	−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	$0.722729\pi$
$138$	3.10646	−	12.9465i	0.264440	−	1.10208i
$139$	−4.91308	+	2.83657i	−0.416722	+	0.240595i	−0.693674	−	0.720289i	$-0.744009\pi$
$139$	−4.91308	+	2.83657i	−0.416722	+	0.240595i	0.276952	+	0.960884i	$0.410676\pi$
$140$	8.16269	−	2.02469i	0.689873	−	0.171118i
$141$	5.03564	−	0.846464i	0.424078	−	0.0712851i
$142$	−1.41333	+	0.172667i	−0.118604	+	0.0144899i
$143$	5.10739			0.427101
$144$	3.49745	+	11.4790i	0.291454	+	0.956585i
$145$	4.78525			0.397393
$146$	7.22227	−	0.882345i	0.597719	−	0.0730234i
$147$	0.605390	−	1.62281i	0.0499317	−	0.133847i
$148$	−22.9101	+	5.68267i	−1.88320	+	0.467113i
$149$	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	$0.103910\pi$
$150$	29.7846	−	8.82667i	2.43190	−	0.720694i
$151$	−11.1164	−	6.41803i	−0.904637	−	0.522292i	−0.0259350	−	0.999664i	$-0.508256\pi$
$151$	−11.1164	−	6.41803i	−0.904637	−	0.522292i	−0.878702	+	0.477371i	$0.841590\pi$
$152$	−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
$156$	0.902817	−	7.89028i	0.0722832	−	0.631728i
$157$	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	$0.635604\pi$
$158$	−17.4919	−	7.43737i	−1.39158	−	0.591685i
$159$	6.16177	−	5.08694i	0.488660	−	0.403421i
$160$	−10.1181	+	21.5280i	−0.799908	+	1.70194i
$161$		−	5.43542i		−	0.428371i
$162$	12.3018	+	3.26570i	0.966524	+	0.256577i
$163$			14.4179i			1.12930i	0.825330	+	0.564650i	$0.190989\pi$
$163$			14.4179i			1.12930i	−0.825330	+	0.564650i	$0.809011\pi$
$164$	−3.98303	+	3.83706i	−0.311022	+	0.299624i
$165$	−12.5125	+	10.3299i	−0.974099	+	0.804183i
$166$	7.36784	−	17.3284i	0.571855	−	1.34494i
$167$	0.239831	+	0.415400i	0.0185587	+	0.0321446i	0.875156	−	0.483842i	$-0.160759\pi$
$167$	0.239831	+	0.415400i	0.0185587	+	0.0321446i	−0.856597	+	0.515986i	$0.827426\pi$
$168$	2.48184	+	4.22380i	0.191478	+	0.325873i
$169$	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	$0.527908\pi$
$174$	0.792024	+	2.67259i	0.0600432	+	0.202609i
$175$	10.9831	−	6.34110i	0.830245	−	0.479342i
$176$	0.332561	−	8.90491i	0.0250677	−	0.671233i
$177$	1.36233	−	3.65185i	0.102399	−	0.274490i
$178$	−2.12312	−	17.3784i	−0.159134	−	1.30256i
$179$	−18.9784			−1.41851			−0.709257	−	0.704950i	$-0.750969\pi$
$179$	−18.9784			−1.41851			−0.709257	+	0.704950i	$0.750969\pi$
$180$	13.7466	+	21.1563i	1.02461	+	1.57690i
$181$	−12.0972			−0.899177			−0.449588	−	0.893236i	$-0.648429\pi$
$181$	−12.0972			−0.899177			−0.449588	+	0.893236i	$0.648429\pi$
$182$	−0.393178	−	3.21828i	−0.0291443	−	0.238555i
$183$	8.04396	−	1.35215i	0.594627	−	0.0999535i
$184$	11.9300	+	9.69666i	0.879492	+	0.714848i
$185$	−42.9794	+	24.8142i	−3.15991	+	1.82438i
$186$	3.98814	+	0.956936i	0.292424	+	0.0701660i
$187$	−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	−0.780182	−	0.625553i	$-0.784873\pi$
$191$	2.09590	−	3.63021i	0.151654	−	0.262672i	0.931836	+	0.362881i	$0.118207\pi$
$192$	−13.6982	−	2.08786i	−0.988583	−	0.150678i
$193$	−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	$0.990476\pi$
$194$	−2.79413	+	6.57150i	−0.200607	+	0.471806i
$195$	−2.76795	−	16.4666i	−0.198217	−	1.17920i
$196$	1.38757	+	1.44036i	0.0991124	+	0.102883i
$197$		−	7.04171i		−	0.501701i	−0.968026	−	0.250851i	$-0.919290\pi$
$197$		−	7.04171i		−	0.501701i	0.968026	−	0.250851i	$-0.0807103\pi$
$198$	−7.84032	−	5.27859i	−0.557187	−	0.375133i
$199$		−	2.66860i		−	0.189172i	−0.995517	−	0.0945859i	$-0.969847\pi$
$199$		−	2.66860i		−	0.189172i	0.995517	−	0.0945859i	$-0.0301527\pi$
$200$	−5.67576	+	35.4188i	−0.401337	+	2.50449i
$201$	−21.5382	−	8.03486i	−1.51919	−	0.566735i
$202$	−8.63132	−	3.66995i	−0.607298	−	0.258217i
$203$	0.568992	+	0.985523i	0.0399354	+	0.0691702i
$204$	−7.71511	+	10.4159i	−0.540166	+	0.729260i
$205$	−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
$210$	7.47236	+	7.08922i	0.515642	+	0.489203i
$211$	−2.44886	+	1.41385i	−0.168587	+	0.0973335i	−0.581919	−	0.813247i	$-0.697698\pi$
$211$	−2.44886	+	1.41385i	−0.168587	+	0.0973335i	0.413333	+	0.910580i	$0.364365\pi$
$212$	2.22122	+	8.95500i	0.152554	+	0.615032i
$213$	−1.11021	−	1.34478i	−0.0760700	−	0.0921429i
$214$	7.06694	−	0.863368i	0.483086	−	0.0590186i
$215$	2.02114			0.137841
$216$	−9.54068	+	11.1792i	−0.649161	+	0.760651i
$217$	1.67436			0.113663
$218$	−6.70492	+	0.819140i	−0.454114	+	0.0554791i
$219$	5.67325	+	6.87196i	0.383363	+	0.464364i
$220$	−4.51057	−	18.1847i	−0.304102	−	1.22601i
$221$	7.42916	−	4.28923i	0.499739	−	0.288525i
$222$	−20.9726	−	19.8972i	−1.40759	−	1.33541i
$223$	5.39092	+	3.11245i	0.361003	+	0.208425i	0.669521	−	0.742794i	$-0.266500\pi$
$223$	5.39092	+	3.11245i	0.361003	+	0.208425i	−0.308518	+	0.951219i	$0.599833\pi$
$224$	−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	$0.435171\pi$
$227$	−11.2546	+	19.4936i	−0.746995	+	1.29383i	−0.949257	+	0.314501i	$0.898163\pi$
$228$	10.1091	−	13.6479i	0.669489	−	0.903855i
$229$	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	$0.592989\pi$
$230$	29.7462	+	12.6478i	1.96140	+	0.833968i
$231$	−3.61526	−	1.34868i	−0.237866	−	0.0887364i
$232$	−3.17816	−	0.509290i	−0.208656	−	0.0334365i
$233$		−	4.33562i		−	0.284036i	−0.989864	−	0.142018i	$-0.954641\pi$
$233$		−	4.33562i		−	0.284036i	0.989864	−	0.142018i	$-0.0453591\pi$
$234$	8.73858	−	4.27137i	0.571259	−	0.279228i
$235$			12.3969i			0.808685i
$236$	3.12250	+	3.24129i	0.203257	+	0.210990i
$237$	−3.85897	−	22.9571i	−0.250667	−	1.49122i
$238$	−2.07059	+	4.86981i	−0.134217	+	0.315663i
$239$	3.20026	+	5.54301i	0.207008	+	0.358548i	0.950771	−	0.309896i	$-0.100294\pi$
$239$	3.20026	+	5.54301i	0.207008	+	0.358548i	−0.743763	+	0.668444i	$0.766961\pi$
$240$	−28.8904	+	3.75382i	−1.86487	+	0.242308i
$241$	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
$246$	−6.58662	−	1.58043i	−0.419947	−	0.100765i
$247$	−9.73438	+	5.62015i	−0.619384	+	0.357601i
$248$	−2.98703	+	3.67500i	−0.189676	+	0.233363i
$249$	22.7425	−	3.82289i	1.44125	−	0.242266i
$250$	5.54009	+	45.3474i	0.350386	+	2.86802i
$251$	−19.1515			−1.20883			−0.604416	−	0.796669i	$-0.706594\pi$
$251$	−19.1515			−1.20883			−0.604416	+	0.796669i	$0.706594\pi$
$252$	−2.72260	+	5.34672i	−0.171507	+	0.336812i
$253$	−12.1089			−0.761282
$254$	−1.40794	−	11.5244i	−0.0883419	−	0.723106i
$255$	−9.52547	+	25.5339i	−0.596508	+	1.59900i
$256$	9.01123	−	13.2211i	0.563202	−	0.826319i
$257$	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	$0.225363\pi$
$258$	0.334527	+	1.12882i	0.0208267	+	0.0702773i
$259$	−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	$-0.587105\pi$
$263$	11.3306	−	19.6253i	0.698678	−	1.21015i	0.968925	−	0.247354i	$-0.0795612\pi$
$264$	9.40969	−	5.52899i	0.579127	−	0.340286i
$265$	9.69927	+	16.7996i	0.595821	+	1.03199i
$266$	2.71308	−	6.38088i	0.166350	−	0.391237i
$267$	16.5355	−	13.6511i	1.01195	−	0.835434i
$268$	19.1168	−	18.4162i	1.16774	−	1.12495i
$269$			25.6002i			1.56087i	0.625235	+	0.780436i	$0.285003\pi$
$269$			25.6002i			1.56087i	−0.625235	+	0.780436i	$0.714997\pi$
$270$	−12.7695	+	28.1386i	−0.777129	+	1.71246i
$271$		−	30.6496i		−	1.86183i	−0.365237	−	0.930914i	$-0.619012\pi$
$271$		−	30.6496i		−	1.86183i	0.365237	−	0.930914i	$-0.380988\pi$
$272$	−6.99468	−	13.2323i	−0.424115	−	0.802326i
$273$	3.06218	−	2.52803i	0.185332	−	0.153003i
$274$	5.33813	+	2.26972i	0.322488	+	0.137119i
$275$	−14.1266	−	24.4680i	−0.851865	−	1.47547i
$276$	−2.14046	+	18.7068i	−0.128840	+	1.12602i
$277$	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	$0.901307\pi$
$282$	−6.92375	+	2.05186i	−0.412303	+	0.122186i
$283$	16.5283	−	9.54263i	0.982507	−	0.567251i	0.0794809	−	0.996836i	$-0.474674\pi$
$283$	16.5283	−	9.54263i	0.982507	−	0.567251i	0.903026	+	0.429586i	$0.141340\pi$
$284$	1.95439	−	0.484772i	0.115972	−	0.0287659i
$285$	12.4812	−	33.4569i	0.739320	−	1.98182i
$286$	−7.16963	+	0.875914i	−0.423949	+	0.0517939i
$287$	−2.76530			−0.163230
$288$	−6.87829	−	15.5142i	−0.405307	−	0.914181i
$289$	2.99880			0.176400
$290$	−6.71742	+	0.820667i	−0.394460	+	0.0481912i
$291$	−8.62472	+	1.44977i	−0.505590	+	0.0849869i
$292$	−9.98713	+	2.47723i	−0.584453	+	0.144969i
$293$	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	$0.268767\pi$
$294$	−0.571522	+	2.38188i	−0.0333318	+	0.138914i
$295$	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
$300$	−40.2971	+	17.4987i	−2.32655	+	1.01029i
$301$	0.240325	+	0.416255i	0.0138521	+	0.0239925i
$302$	16.7056	+	7.10303i	0.961298	+	0.408734i
$303$	−1.90420	−	11.3281i	−0.109393	−	0.650784i
$304$	9.16509	+	17.3382i	0.525654	+	0.994413i
$305$			19.8029i			1.13391i
$306$	−15.8375	−	1.09382i	−0.905367	−	0.0625295i
$307$			23.7896i			1.35775i	0.734255	+	0.678873i	$0.237532\pi$
$307$			23.7896i			1.35775i	−0.734255	+	0.678873i	$0.762468\pi$
$308$	3.20881	−	3.09121i	0.182839	−	0.176138i
$309$	−5.77752	−	2.15531i	−0.328672	−	0.122611i
$310$	−3.89610	+	9.16321i	−0.221284	+	0.520435i
$311$	−10.2030	−	17.6722i	−0.578562	−	1.00210i	−0.995645	−	0.0932300i	$-0.970281\pi$
$311$	−10.2030	−	17.6722i	−0.578562	−	1.00210i	0.417083	−	0.908868i	$-0.363053\pi$
$312$	0.0858251	+	11.2310i	0.00485889	+	0.635831i
$313$	−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	$0.878395\pi$
$318$	−7.77734	+	8.19767i	−0.436131	+	0.459703i
$319$	2.19553	−	1.26759i	0.122926	−	0.0709714i
$320$	10.5115	−	31.9557i	0.587613	−	1.78638i
$321$	5.55123	+	6.72416i	0.309840	+	0.375306i
$322$	0.932171	+	7.63012i	0.0519479	+	0.425210i
$323$	18.3457			1.02078
$324$	−17.8291	−	2.47455i	−0.990505	−	0.137475i
$325$	29.0751			1.61280
$326$	−2.47267	−	20.2396i	−0.136948	−	1.12097i
$327$	−5.26686	−	6.37970i	−0.291258	−	0.352798i
$328$	4.93323	−	6.06946i	0.272392	−	0.335130i
$329$	−2.55314	+	1.47406i	−0.140759	+	0.0812675i
$330$	15.7932	−	16.6468i	0.869388	−	0.916375i
$331$	−29.4795	−	17.0200i	−1.62034	−	0.935504i	−0.986828	−	0.161770i	$-0.948280\pi$
$331$	−29.4795	−	17.0200i	−1.62034	−	0.935504i	−0.633511	−	0.773733i	$-0.718387\pi$
$332$	−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
$336$	−4.20833	−	5.50364i	−0.229583	−	0.300248i
$337$	−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	$0.920882\pi$
$338$	−4.28528	+	10.0785i	−0.233088	+	0.548199i
$339$	8.53864	+	3.18535i	0.463755	+	0.173004i
$340$	−21.8327	−	22.6632i	−1.18404	−	1.22909i
$341$		−	3.73012i		−	0.201997i
$342$	20.7517	+	1.43323i	1.12212	+	0.0775000i
$343$			1.00000i			0.0539949i
$344$	−1.34236	−	0.215109i	−0.0723750	−	0.0115979i
$345$	6.56244	+	39.0402i	0.353310	+	2.10185i
$346$	−14.4561	−	6.14657i	−0.777164	−	0.330442i
$347$	9.75697	+	16.8996i	0.523782	+	0.907217i	0.999617	+	0.0276820i	$0.00881258\pi$
$347$	9.75697	+	16.8996i	0.523782	+	0.907217i	−0.475835	+	0.879535i	$0.657854\pi$
$348$	−1.57017	−	3.61589i	−0.0841700	−	0.193832i
$349$	−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	$0.654882\pi$
$354$	−1.28611	+	5.36002i	−0.0683561	+	0.284882i
$355$	3.66645	−	2.11683i	0.194595	−	0.112350i
$356$	5.96076	+	24.0312i	0.315920	+	1.27365i
$357$	−6.39135	+	1.07435i	−0.338266	+	0.0568607i
$358$	26.6414	−	3.25479i	1.40804	−	0.172021i
$359$	−29.0848			−1.53504			−0.767519	−	0.641026i	$-0.778509\pi$
$359$	−29.0848			−1.53504			−0.767519	+	0.641026i	$0.778509\pi$
$360$	−22.9255	−	27.3412i	−1.20828	−	1.44101i
$361$	−5.03823			−0.265170
$362$	16.9817	−	2.07466i	0.892541	−	0.109042i
$363$	3.65474	−	9.79688i	0.191824	−	0.514203i
$364$	1.10387	+	4.45032i	0.0578584	+	0.233260i
$365$	−18.7359	+	10.8172i	−0.980682	+	0.566197i
$366$	−11.0600	+	3.27765i	−0.578117	+	0.171325i
$367$	−9.75962	−	5.63472i	−0.509448	−	0.294130i	0.223159	−	0.974782i	$-0.428363\pi$
$367$	−9.75962	−	5.63472i	−0.509448	−	0.294130i	−0.732607	+	0.680652i	$0.761697\pi$
$368$	−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
$372$	−5.76257	−	0.659361i	−0.298775	−	0.0341863i
$373$	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	$0.800194\pi$
$374$	10.8489	+	4.61282i	0.560981	+	0.238523i
$375$	−43.1478	+	35.6214i	−2.22814	+	1.83948i
$376$	1.31939	−	8.23349i	0.0680424	−	0.424610i
$377$			2.60893i			0.134367i
$378$	−7.31351	+	0.715939i	−0.376166	+	0.0368239i
$379$		−	0.667011i		−	0.0342620i	−0.999853	−	0.0171310i	$-0.994547\pi$
$379$		−	0.667011i		−	0.0342620i	0.999853	−	0.0171310i	$-0.00545324\pi$
$380$	28.6072	+	29.6955i	1.46752	+	1.52335i
$381$	10.9654	−	9.05268i	0.561776	−	0.463783i
$382$	−2.31960	+	5.45544i	−0.118681	+	0.279125i
$383$	4.84288	+	8.38811i	0.247460	+	0.428613i	0.962820	−	0.270143i	$-0.0870709\pi$
$383$	4.84288	+	8.38811i	0.247460	+	0.428613i	−0.715361	+	0.698755i	$0.753738\pi$
$384$	19.5873	+	0.581654i	0.999559	+	0.0296824i
$385$	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	$0.974003\pi$
$390$	6.70960	+	22.6408i	0.339754	+	1.14646i
$391$	−17.6135	+	10.1692i	−0.890755	+	0.514277i
$392$	−2.19486	−	1.78398i	−0.110857	−	0.0901044i
$393$	−0.682017	+	1.82821i	−0.0344032	+	0.0922211i
$394$	1.20765	+	9.88499i	0.0608405	+	0.497999i
$395$	56.5165			2.84365
$396$	11.9113	+	6.06535i	0.598567	+	0.304795i
$397$	25.7154			1.29062			0.645310	−	0.763921i	$-0.276728\pi$
$397$	25.7154			1.29062			0.645310	+	0.763921i	$0.276728\pi$
$398$	0.457663	+	3.74611i	0.0229406	+	0.187776i
$399$	8.37455	−	1.40772i	0.419252	−	0.0704739i
$400$	1.89319	−	50.6935i	0.0946594	−	2.53467i
$401$	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	$0.233514\pi$
$402$	31.6128	+	7.58536i	1.57670	+	0.378323i
$403$	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
$408$	9.04396	−	15.9448i	0.447743	−	0.789383i
$409$	−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	$0.922501\pi$
$410$	6.43461	−	15.1335i	0.317783	−	0.747391i
$411$	1.17767	+	7.00600i	0.0580902	+	0.345580i
$412$	5.12798	−	4.94004i	0.252637	−	0.243378i
$413$			2.25033i			0.110731i
$414$	−20.7180	+	10.1268i	−1.01823	+	0.497707i
$415$			55.9882i			2.74835i
$416$	−11.7371	−	5.51643i	−0.575460	−	0.270465i
$417$	9.20641	+	3.43446i	0.450840	+	0.168186i
$418$	−14.2152	−	6.04415i	−0.695288	−	0.295629i
$419$	−16.0870	−	27.8635i	−0.785901	−	1.36122i	−0.928459	−	0.371434i	$-0.878866\pi$
$419$	−16.0870	−	27.8635i	−0.785901	−	1.36122i	0.142559	−	0.989786i	$-0.454467\pi$
$420$	−11.7053	−	8.67017i	−0.571161	−	0.423061i
$421$	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
$426$	1.78911	+	1.69737i	0.0866826	+	0.0822380i
$427$	−4.07841	+	2.35467i	−0.197368	+	0.113950i
$428$	−9.77233	+	2.42395i	−0.472364	+	0.117166i
$429$	−5.63190	−	6.82187i	−0.271911	−	0.329363i
$430$	−2.83723	+	0.346625i	−0.136823	+	0.0167157i
$431$	14.0003			0.674370			0.337185	−	0.941438i	$-0.390525\pi$
$431$	14.0003			0.674370			0.337185	+	0.941438i	$0.390525\pi$
$432$	11.4757	−	17.3294i	0.552127	−	0.833760i
$433$	−28.9725			−1.39233			−0.696164	−	0.717883i	$-0.745111\pi$
$433$	−28.9725			−1.39233			−0.696164	+	0.717883i	$0.745111\pi$
$434$	−2.35043	+	0.287152i	−0.112824	+	0.0137838i
$435$	−5.27668	−	6.39159i	−0.252997	−	0.306453i
$436$	9.27172	−	2.29978i	0.444035	−	0.110139i
$437$	23.0789	−	13.3246i	1.10401	−	0.637402i
$438$	−9.14251	−	8.67373i	−0.436846	−	0.414447i
$439$	26.3297	+	15.2014i	1.25665	+	0.725525i	0.972421	−	0.233232i	$-0.0749303\pi$
$439$	26.3297	+	15.2014i	1.25665	+	0.725525i	0.284225	+	0.958758i	$0.408264\pi$
$440$	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	$0.341195\pi$
$443$	−10.9707	+	19.0019i	−0.521235	+	0.902805i	−0.999695	+	0.0246960i	$0.992138\pi$
$444$	32.8532	+	24.3344i	1.55914	+	1.15486i
$445$	26.0285	+	45.0827i	1.23387	+	2.13713i
$446$	−8.10143	−	3.44464i	−0.383614	−	0.163109i
$447$	−26.1458	−	9.75374i	−1.23666	−	0.461336i
$448$	7.83117	−	1.63486i	0.369988	−	0.0772397i
$449$			21.1481i			0.998043i	0.866590	+	0.499021i	$0.166307\pi$
$449$			21.1481i			0.998043i	−0.866590	+	0.499021i	$0.833693\pi$
$450$	−44.6330	−	30.0497i	−2.10402	−	1.41656i
$451$			6.16048i			0.290086i
$452$	−7.57867	+	7.30092i	−0.356471	+	0.343406i
$453$	3.68549	+	21.9251i	0.173160	+	1.03013i
$454$	12.4558	−	29.2947i	0.584581	−	1.37487i
$455$	4.82020	+	8.34882i	0.225974	+	0.391399i
$456$	−11.8502	+	20.8923i	−0.554939	+	0.978373i
$457$	−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	$0.465759\pi$
$462$	5.30631	+	1.27323i	0.246872	+	0.0592358i
$463$	−7.18441	+	4.14792i	−0.333888	+	0.192770i	−0.657566	−	0.753397i	$-0.728414\pi$
$463$	−7.18441	+	4.14792i	−0.333888	+	0.192770i	0.323678	+	0.946167i	$0.395081\pi$
$464$	4.54876	+	0.169877i	0.211171	+	0.00788635i
$465$	−12.0262	+	2.02154i	−0.557701	+	0.0937466i
$466$	0.743557	+	6.08625i	0.0344446	+	0.281940i
$467$	23.3145			1.07887			0.539434	−	0.842028i	$-0.318638\pi$
$467$	23.3145			1.07887			0.539434	+	0.842028i	$0.318638\pi$
$468$	−11.5345	+	7.49471i	−0.533181	+	0.346443i
$469$	13.2722			0.612853
$470$	−2.12606	−	17.4025i	−0.0980679	−	0.802716i
$471$	8.82952	−	23.6684i	0.406843	−	1.09058i
$472$	−4.93917	−	4.01454i	−0.227344	−	0.184784i
$473$	0.927324	−	0.535391i	0.0426384	−	0.0246173i
$474$	9.35425	+	31.5648i	0.429655	+	1.44982i
$475$	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	$0.354639\pi$
$479$	−12.1862	+	21.1071i	−0.556802	+	0.964410i	−0.997761	+	0.0668826i	$0.978695\pi$
$480$	39.9119	−	10.2242i	1.82172	−	0.466669i
$481$	−13.5288	−	23.4325i	−0.616859	−	1.06843i
$482$	−3.97865	+	9.35737i	−0.181223	+	0.426216i
$483$	−7.26002	+	5.99362i	−0.330342	+	0.272719i
$484$	8.37678	+	8.69545i	0.380763	+	0.395248i
$485$		−	21.2326i		−	0.964123i
$486$	−9.20325	−	20.0325i	−0.417468	−	0.908692i
$487$		−	19.2798i		−	0.873652i	−0.899546	−	0.436826i	$-0.856103\pi$
$487$		−	19.2798i		−	0.873652i	0.899546	−	0.436826i	$-0.143897\pi$
$488$	2.10760	−	13.1522i	0.0954067	−	0.595373i
$489$	19.2578	−	15.8986i	0.870870	−	0.718960i
$490$	−5.47265	−	2.32691i	−0.247229	−	0.105119i
$491$	−5.83130	−	10.1001i	−0.263163	−	0.455812i	0.703918	−	0.710282i	$-0.251432\pi$
$491$	−5.83130	−	10.1001i	−0.263163	−	0.455812i	−0.967081	+	0.254470i	$0.918099\pi$
$492$	9.51718	+	1.08897i	0.429068	+	0.0490945i
$493$	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
$498$	−31.2698	+	9.26681i	−1.40123	+	0.415256i
$499$	7.81906	−	4.51434i	0.350029	−	0.202089i	−0.314669	−	0.949201i	$-0.601893\pi$
$499$	7.81906	−	4.51434i	0.350029	−	0.202089i	0.664698	+	0.747112i	$0.268560\pi$
$500$	−15.5541	−	62.7074i	−0.695600	−	2.80436i
$501$	0.290383	−	0.778399i	0.0129733	−	0.0347763i
$502$	26.8844	−	3.28447i	1.19991	−	0.146593i
$503$	31.2652			1.39405			0.697023	−	0.717049i	$-0.254508\pi$
$503$	31.2652			1.39405			0.697023	+	0.717049i	$0.254508\pi$
$504$	2.90496	−	7.97253i	0.129397	−	0.355125i
$505$	27.8879			1.24100
$506$	16.9982	−	2.07667i	0.755663	−	0.0923194i
$507$	−13.2275	+	2.22347i	−0.587453	+	0.0987477i
$508$	3.95286	+	15.9362i	0.175380	+	0.707056i
$509$	−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	$0.456445\pi$
$510$	8.99257	−	37.4775i	0.398198	−	1.65953i
$511$	−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
$516$	−0.663193	−	1.52724i	−0.0291954	−	0.0672331i
$517$	3.28388	+	5.68785i	0.144425	+	0.250151i
$518$	15.3600	+	6.53091i	0.674880	+	0.286952i
$519$	−3.18922	−	18.9728i	−0.139991	−	0.832813i
$520$	−26.9236	−	4.31443i	−1.18068	−	0.189200i
$521$		−	26.5870i		−	1.16480i	−0.812904	−	0.582398i	$-0.802115\pi$
$521$		−	26.5870i		−	1.16480i	0.812904	−	0.582398i	$-0.197885\pi$
$522$	2.69638	−	4.00495i	0.118017	−	0.175292i
$523$		−	10.3523i		−	0.452675i	−0.974049	−	0.226338i	$-0.927325\pi$
$523$		−	10.3523i		−	0.452675i	0.974049	−	0.226338i	$-0.0726753\pi$
$524$	−1.56320	−	1.62267i	−0.0682889	−	0.0708868i
$525$	−20.5808	−	7.67768i	−0.898219	−	0.335082i
$526$	−12.5400	+	29.4927i	−0.546769	+	1.28594i
$527$	−3.13258	−	5.42579i	−0.136457	−	0.236351i
$528$	−12.2609	+	9.37522i	−0.533587	+	0.408004i
$529$	−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
$534$	−20.8709	+	21.9989i	−0.903173	+	0.951986i
$535$	−18.3329	+	10.5845i	−0.792602	+	0.457609i
$536$	−23.6773	+	29.1307i	−1.02270	+	1.25825i
$537$	20.9274	+	25.3492i	0.903086	+	1.09390i
$538$	−4.39042	−	35.9370i	−0.189284	−	1.54935i
$539$	2.22778			0.0959573
$540$	13.0998	−	41.6902i	0.563726	−	1.79406i
$541$	−10.3163			−0.443534			−0.221767	−	0.975100i	$-0.571182\pi$
$541$	−10.3163			−0.443534			−0.221767	+	0.975100i	$0.571182\pi$
$542$	5.25638	+	43.0251i	0.225781	+	1.84809i
$543$	13.3395	+	16.1581i	0.572454	+	0.693408i
$544$	12.0883	+	17.3756i	0.518282	+	0.744973i
$545$	17.3938	−	10.0423i	0.745068	−	0.430165i
$546$	−3.86506	+	4.07395i	−0.165409	+	0.174349i
$547$	−33.4294	−	19.3005i	−1.42934	−	0.825229i	−0.432270	−	0.901744i	$-0.642287\pi$
$547$	−33.4294	−	19.3005i	−1.42934	−	0.825229i	−0.997068	+	0.0765150i	$0.975621\pi$
$548$	−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
$552$	−0.203480	−	26.6272i	−0.00866067	−	1.13333i
$553$	6.72012	+	11.6396i	0.285769	+	0.494966i
$554$	−3.98574	+	9.37404i	−0.169338	+	0.398265i
$555$	80.5373	+	30.0445i	3.41862	+	1.27532i
$556$	−8.17137	+	7.87190i	−0.346543	+	0.333843i
$557$			33.9277i			1.43756i	0.695236	+	0.718781i	$0.255300\pi$
$557$			33.9277i			1.43756i	−0.695236	+	0.718781i	$0.744700\pi$
$558$	−3.11954	−	6.38211i	−0.132061	−	0.270176i
$559$			1.10193i			0.0466068i
$560$	14.8703	−	7.86056i	0.628386	−	0.332169i
$561$	2.39342	+	14.2385i	0.101050	+	0.601151i
$562$	29.3289	+	12.4703i	1.23716	+	0.526029i
$563$	−11.2520	−	19.4890i	−0.474216	−	0.821366i	0.525349	−	0.850887i	$-0.323935\pi$
$563$	−11.2520	−	19.4890i	−0.474216	−	0.821366i	−0.999564	+	0.0295216i	$0.990602\pi$
$564$	9.36750	−	4.06776i	0.394443	−	0.171284i
$565$	−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	$0.789058\pi$
$570$	−11.7829	+	49.1066i	−0.493532	+	2.05685i
$571$	−24.0060	+	13.8599i	−1.00462	+	0.580017i	−0.909612	−	0.415459i	$-0.863621\pi$
$571$	−24.0060	+	13.8599i	−1.00462	+	0.580017i	−0.0950074	+	0.995477i	$0.530287\pi$
$572$	9.91434	−	2.45917i	0.414539	−	0.102823i
$573$	−7.15996	+	1.20355i	−0.299112	+	0.0502790i
$574$	3.88186	−	0.474247i	0.162026	−	0.0197947i
$575$	−68.9331			−2.87471
$576$	12.3162	+	20.5988i	0.513177	+	0.858283i
$577$	−42.5735			−1.77236			−0.886179	−	0.463344i	$-0.846650\pi$
$577$	−42.5735			−1.77236			−0.886179	+	0.463344i	$0.846650\pi$
$578$	−4.20965	+	0.514293i	−0.175098	+	0.0213918i
$579$	−7.97078	+	21.3664i	−0.331254	+	0.887959i
$580$	9.28901	−	2.30407i	0.385705	−	0.0956711i
$581$	−11.5308	+	6.65730i	−0.478378	+	0.276191i
$582$	11.8585	−	3.51428i	0.491552	−	0.145672i
$583$	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	$0.599950\pi$
$587$	−23.6978	+	41.0459i	−0.978115	+	1.69414i	−0.669248	+	0.743039i	$0.733384\pi$
$588$	0.393798	−	3.44165i	0.0162400	−	0.141931i
$589$	4.10460	+	7.10938i	0.169127	+	0.292937i
$590$	−12.3153	−	5.23632i	−0.507011	−	0.215576i
$591$	−9.40553	+	7.76488i	−0.386892	+	0.319404i
$592$	−41.7363	+	22.0621i	−1.71535	+	0.906748i
$593$			9.85416i			0.404662i	0.979317	+	0.202331i	$0.0648517\pi$
$593$			9.85416i			0.404662i	−0.979317	+	0.202331i	$0.935148\pi$
$594$	1.59495	+	16.2929i	0.0654418	+	0.668505i
$595$		−	15.7344i		−	0.645048i
$596$	23.2064	−	22.3559i	0.950570	−	0.915733i
$597$	−3.56441	+	2.94265i	−0.145882	+	0.120435i
$598$	−6.89559	+	16.2177i	−0.281982	+	0.663191i
$599$	−14.3947	−	24.9324i	−0.588153	−	1.01871i	−0.994474	−	0.104980i	$-0.966522\pi$
$599$	−14.3947	−	24.9324i	−0.588153	−	1.01871i	0.406322	−	0.913730i	$-0.366811\pi$
$600$	53.5671	−	31.4752i	2.18687	−	1.28497i
$601$	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
$606$	4.61583	+	15.5756i	0.187505	+	0.632715i
$607$	0.492088	−	0.284107i	0.0199732	−	0.0115316i	−0.489980	−	0.871734i	$-0.662996\pi$
$607$	0.492088	−	0.284107i	0.0199732	−	0.0115316i	0.509953	+	0.860202i	$0.329663\pi$
$608$	−15.8392	−	22.7671i	−0.642365	−	0.923329i
$609$	0.688924	−	1.84673i	0.0279166	−	0.0748332i
$610$	−3.39618	−	27.7988i	−0.137507	−	1.12554i
$611$	−6.75883			−0.273433
$612$	22.4198	−	1.18064i	0.906268	−	0.0477244i
$613$	−43.0269			−1.73784			−0.868919	−	0.494953i	$-0.835185\pi$
$613$	−43.0269			−1.73784			−0.868919	+	0.494953i	$0.835185\pi$
$614$	−4.07991	−	33.3953i	−0.164652	−	1.34773i
$615$	19.8619	−	3.33868i	0.800909	−	0.134628i
$616$	−3.97431	+	4.88967i	−0.160129	+	0.197011i
$617$	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	$0.183749\pi$
$618$	8.47998	+	2.03473i	0.341115	+	0.0818490i
$619$	37.3543	+	21.5665i	1.50139	+	0.866830i	0.999999	+	0.00161224i	$0.000513192\pi$
$619$	37.3543	+	21.5665i	1.50139	+	0.866830i	0.501396	+	0.865218i	$0.332820\pi$
$620$	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
$624$	−2.04659	−	15.7511i	−0.0819293	−	0.630550i
$625$	−36.2137	−	62.7239i	−1.44855	−	2.50896i
$626$	0.764338	−	1.79764i	0.0305491	−	0.0718482i
$627$	−3.13608	−	18.6566i	−0.125243	−	0.745075i
$628$	20.2375	+	21.0074i	0.807566	+	0.838288i
$629$			44.1616i			1.76084i
$630$	1.22923	−	17.7980i	0.0489735	−	0.709089i
$631$		−	2.16073i		−	0.0860171i	−0.999075	−	0.0430086i	$-0.986306\pi$
$631$		−	2.16073i		−	0.0860171i	0.999075	−	0.0430086i	$-0.0136943\pi$
$632$	−37.5359	−	6.01501i	−1.49310	−	0.239264i
$633$	4.58882	+	1.71186i	0.182389	+	0.0680405i
$634$	28.6027	+	12.1616i	1.13596	+	0.482997i
$635$	17.2607	+	29.8965i	0.684971	+	1.18641i
$636$	9.51175	−	12.8415i	0.377165	−	0.509199i
$637$	−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	$0.651140\pi$
$642$	−8.94588	−	8.48718i	−0.353066	−	0.334962i
$643$	25.6821	−	14.8276i	1.01280	−	0.584742i	0.100792	−	0.994908i	$-0.467862\pi$
$643$	25.6821	−	14.8276i	1.01280	−	0.584742i	0.912011	+	0.410166i	$0.134529\pi$
$644$	−2.61712	−	10.5511i	−0.103129	−	0.415772i
$645$	−2.22871	−	2.69961i	−0.0877553	−	0.106297i
$646$	−25.7532	+	3.14627i	−1.01325	+	0.123788i
$647$	18.8904			0.742656			0.371328	−	0.928502i	$-0.378902\pi$
$647$	18.8904			0.742656			0.371328	+	0.928502i	$0.378902\pi$
$648$	25.4524	+	0.416036i	0.999866	+	0.0163435i
$649$	5.01324			0.196787
$650$	−40.8149	+	4.98636i	−1.60089	+	0.195581i
$651$	−1.84632	−	2.23643i	−0.0723628	−	0.0876525i
$652$	6.94214	+	27.9878i	0.271875	+	1.09608i
$653$	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	$0.0845906\pi$
$654$	8.48760	+	8.05241i	0.331892	+	0.314874i
$655$	−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	$-0.587263\pi$
$659$	17.9267	−	31.0499i	0.698324	−	1.20953i	0.969047	−	0.246876i	$-0.0794039\pi$
$660$	−19.3152	+	26.0769i	−0.751845	+	1.01504i
$661$	−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	$0.850894\pi$
$662$	44.3015	+	18.8366i	1.72183	+	0.732103i
$663$	−13.9212	−	5.19331i	−0.540654	−	0.201692i
$664$	5.95878	−	37.1850i	0.231245	−	1.44306i
$665$			20.6167i			0.799482i
$666$	−3.45005	+	49.9534i	−0.133687	+	1.93565i
$667$		−	6.18542i		−	0.239500i
$668$	0.665566	+	0.690886i	0.0257515	+	0.0267312i
$669$	−1.78729	−	10.6327i	−0.0691008	−	0.411083i
$670$	−30.8833	+	72.6341i	−1.19312	+	2.80610i
$671$	5.24569	+	9.08579i	0.202507	+	0.350753i
$672$	6.85142	+	7.00415i	0.264299	+	0.270191i
$673$	−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	$0.419248\pi$
$678$	−12.5326	−	3.00715i	−0.481312	−	0.115489i
$679$	4.37286	−	2.52467i	0.167815	−	0.0968880i
$680$	34.5349	+	28.0698i	1.32435	+	1.07643i
$681$	38.4477	−	6.46285i	1.47332	−	0.247657i
$682$	0.639712	+	5.23625i	0.0244959	+	0.200506i
$683$	1.99318			0.0762668			0.0381334	−	0.999273i	$-0.487859\pi$
$683$	1.99318			0.0762668			0.0381334	+	0.999273i	$0.487859\pi$
$684$	−29.3766	+	1.54698i	−1.12324	+	0.0591502i
$685$	−17.2476			−0.658996
$686$	−0.171499	−	1.40378i	−0.00654788	−	0.0535964i
$687$	12.5570	−	33.6602i	0.479079	−	1.28422i
$688$	1.92126	+	0.0717509i	0.0732473	+	0.00273548i
$689$	−9.15920	+	5.28807i	−0.348938	+	0.201459i
$690$	−15.9076	−	53.6782i	−0.605590	−	2.04349i
$691$	−37.5981	−	21.7073i	−1.43030	−	0.825783i	−0.433155	−	0.901319i	$-0.642600\pi$
$691$	−37.5981	−	21.7073i	−1.43030	−	0.825783i	−0.997143	+	0.0755366i	$0.975933\pi$
$692$	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
$696$	2.82429	+	4.80662i	0.107055	+	0.182194i
$697$	5.17362	+	8.96098i	0.195965	+	0.339421i
$698$	8.54970	−	20.1080i	0.323611	−	0.761098i
$699$	−5.79103	+	4.78088i	−0.219037	+	0.180829i
$700$	18.2670	−	17.5975i	0.690426	−	0.665123i
$701$		−	8.04511i		−	0.303860i	−0.988391	−	0.151930i	$-0.951451\pi$
$701$		−	8.04511i		−	0.303860i	0.988391	−	0.151930i	$-0.0485488\pi$
$702$	−15.3412	−	6.96198i	−0.579017	−	0.262763i
$703$		−	57.8646i		−	2.18241i
$704$	−3.64210	−	17.4461i	−0.137267	−	0.657526i
$705$	16.5584	−	13.6700i	0.623624	−	0.514843i
$706$	−1.81013	−	0.769647i	−0.0681250	−	0.0289660i
$707$	3.31603	+	5.74352i	0.124712	+	0.216007i
$708$	0.886175	−	7.74484i	0.0333045	−	0.291069i
$709$	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
$714$	8.78778	−	2.60426i	0.328874	−	0.0974620i
$715$	18.5993	−	10.7383i	0.695576	−	0.401591i
$716$	−36.8404	+	9.13798i	−1.37679	+	0.341502i
$717$	3.87481	−	10.3868i	0.144708	−	0.387902i
$718$	40.8286	−	4.98803i	1.52371	−	0.186152i
$719$	−11.2806			−0.420694			−0.210347	−	0.977627i	$-0.567459\pi$
$719$	−11.2806			−0.420694			−0.210347	+	0.977627i	$0.567459\pi$
$720$	36.8713	+	34.4492i	1.37411	+	1.28385i
$721$	3.56020			0.132589
$722$	7.07254	−	0.864053i	0.263213	−	0.0321567i
$723$	−12.2810	+	2.06437i	−0.456736	+	0.0767748i
$724$	−23.4828	+	5.82472i	−0.872730	+	0.216474i
$725$	12.4986	−	7.21607i	0.464187	−	0.267998i
$726$	−3.45028	+	14.3794i	−0.128052	+	0.533670i
$727$	−40.7358	−	23.5188i	−1.51081	−	0.872265i	−0.999920	−	0.0126169i	$-0.995984\pi$
$727$	−40.7358	−	23.5188i	−1.51081	−	0.872265i	−0.510887	−	0.859648i	$-0.670683\pi$
$728$	−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
$732$	14.9637	−	6.49787i	0.553074	−	0.240168i
$733$	−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	$0.840923\pi$
$734$	14.6667	+	6.23612i	0.541357	+	0.230179i
$735$	−1.20735	−	7.18254i	−0.0445336	−	0.264932i
$736$	27.8271	+	13.0787i	1.02572	+	0.482088i
$737$		−	29.5675i		−	1.08913i
$738$	5.15208	+	10.5404i	0.189651	+	0.387997i
$739$		−	40.5049i		−	1.49000i	−0.667067	−	0.744998i	$-0.732451\pi$
$739$		−	40.5049i		−	1.49000i	0.667067	−	0.744998i	$-0.267549\pi$
$740$	−71.4828	+	68.8630i	−2.62776	+	2.53146i
$741$	18.2408	+	6.80476i	0.670093	+	0.249979i
$742$	2.55278	−	6.00385i	0.0937154	−	0.220408i
$743$	17.6790	+	30.6209i	0.648580	+	1.12337i	0.983462	+	0.181113i	$0.0579701\pi$
$743$	17.6790	+	30.6209i	0.648580	+	1.12337i	−0.334882	+	0.942260i	$0.608697\pi$
$744$	8.20244	−	0.0626813i	0.300716	−	0.00229801i
$745$	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
$750$	54.4608	−	57.4042i	1.98863	−	2.09611i
$751$	43.2698	−	24.9818i	1.57894	−	0.911600i	0.583930	−	0.811804i	$-0.301514\pi$
$751$	43.2698	−	24.9818i	1.57894	−	0.911600i	0.995008	−	0.0997964i	$-0.0318191\pi$
$752$	−0.440092	+	11.7843i	−0.0160485	+	0.429728i
$753$	21.1183	+	25.5804i	0.769594	+	0.932202i
$754$	−0.447430	−	3.66235i	−0.0162944	−	0.133375i
$755$	−53.9759			−1.96439
$756$	10.1437	−	2.25928i	0.368925	−	0.0821693i
$757$	15.8751			0.576990			0.288495	−	0.957481i	$-0.406845\pi$
$757$	15.8751			0.576990			0.288495	+	0.957481i	$0.406845\pi$
$758$	0.114392	+	0.936334i	0.00415490	+	0.0340092i
$759$	13.3525	+	16.1737i	0.484664	+	0.587069i
$760$	−45.2509	−	36.7797i	−1.64142	−	1.33414i
$761$	−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	$0.350024\pi$
$762$	−13.8405	+	14.5885i	−0.501388	+	0.528486i
$763$	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
$768$	−27.5959	+	2.54269i	−0.995782	+	0.0917516i
$769$	−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	$0.876830\pi$
$770$	−5.18385	+	12.1919i	−0.186813	+	0.439364i
$771$	−17.3125	−	6.45844i	−0.623493	−	0.232595i
$772$	−18.2693	−	18.9643i	−0.657526	−	0.682540i
$773$		−	20.1829i		−	0.725928i	−0.931803	−	0.362964i	$-0.881765\pi$
$773$		−	20.1829i		−	0.725928i	0.931803	−	0.362964i	$-0.118235\pi$
$774$	1.13887	−	1.69157i	0.0409358	−	0.0608022i
$775$		−	21.2346i		−	0.762771i
$776$	−2.25977	+	14.1018i	−0.0811209	+	0.506225i
$777$	3.38864	+	20.1591i	0.121567	+	0.723205i
$778$	42.2172	+	17.9503i	1.51356	+	0.643550i
$779$	−6.77897	−	11.7415i	−0.242882	−	0.420683i
$780$	−13.3017	−	30.6319i	−0.476276	−	1.09680i
$781$	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
$786$	0.643862	−	2.68337i	0.0229658	−	0.0957125i
$787$	3.41708	−	1.97285i	0.121806	−	0.0703245i	−0.437859	−	0.899044i	$-0.644263\pi$
$787$	3.41708	−	1.97285i	0.121806	−	0.0703245i	0.559665	+	0.828719i	$0.310930\pi$
$788$	−3.39054	−	13.6692i	−0.120783	−	0.486945i
$789$	−38.7075	+	6.50652i	−1.37802	+	0.231638i
$790$	−79.3366	+	9.69255i	−2.82267	+	0.344845i
$791$	−5.26165			−0.187083
$792$	−17.7610	−	6.47160i	−0.631111	−	0.229958i
$793$	−10.7966			−0.383398
$794$	−36.0987	+	4.41018i	−1.28109	+	0.156511i
$795$	11.7437	−	31.4801i	0.416506	−	1.11648i
$796$	−1.28491	−	5.18021i	−0.0455425	−	0.183608i
$797$	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	$0.301209\pi$
$798$	−11.5146	+	3.41235i	−0.407611	+	0.120796i
$799$	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
$804$	−45.6782	−	5.22657i	−1.61095	−	0.184327i
$805$	−11.4280	−	19.7939i	−0.402785	−	0.697644i
$806$	−4.99581	−	2.12417i	−0.175970	−	0.0748205i
$807$	34.1939	−	28.2293i	1.20368	−	0.993718i
$808$	−18.5220	−	2.96809i	−0.651601	−	0.104417i
$809$		−	27.9065i		−	0.981140i	−0.871402	−	0.490570i	$-0.836789\pi$
$809$		−	27.9065i		−	0.981140i	0.871402	−	0.490570i	$-0.163211\pi$
$810$	51.6652	−	13.9722i	1.81533	−	0.490933i
$811$		−	2.79493i		−	0.0981434i	−0.998795	−	0.0490717i	$-0.984374\pi$
$811$		−	2.79493i		−	0.0981434i	0.998795	−	0.0490717i	$-0.0156263\pi$
$812$	1.57904	+	1.63911i	0.0554133	+	0.0575214i
$813$	−40.9382	+	33.7972i	−1.43577	+	1.18532i
$814$	14.5494	−	34.2187i	0.509957	−	1.19937i
$815$	30.3139	+	52.5052i	1.06185	+	1.83918i
$816$	−9.96119	+	23.9339i	−0.348711	+	0.837855i
$817$	−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	$0.246131\pi$
$822$	−2.85471	−	9.63288i	−0.0995694	−	0.335985i
$823$	−0.695088	+	0.401309i	−0.0242292	+	0.0139888i	−0.512066	−	0.858946i	$-0.671120\pi$
$823$	−0.695088	+	0.401309i	−0.0242292	+	0.0139888i	0.487836	+	0.872935i	$0.337786\pi$
$824$	−6.35132	+	7.81416i	−0.221259	+	0.272219i
$825$	−17.1042	+	45.8494i	−0.595492	+	1.59627i
$826$	−0.385930	−	3.15896i	−0.0134282	−	0.109914i
$827$	−10.7060			−0.372284			−0.186142	−	0.982523i	$-0.559598\pi$
$827$	−10.7060			−0.372284			−0.186142	+	0.982523i	$0.559598\pi$
$828$	27.3467	−	17.7689i	0.950363	−	0.617513i
$829$	37.9248			1.31718			0.658591	−	0.752501i	$-0.271153\pi$
$829$	37.9248			1.31718			0.658591	+	0.752501i	$0.271153\pi$
$830$	−9.60194	−	78.5949i	−0.333288	−	2.72807i
$831$	−12.3029	+	2.06805i	−0.426783	+	0.0717398i
$832$	17.4224	+	5.73092i	0.604012	+	0.198684i
$833$	3.24051	−	1.87091i	0.112277	−	0.0648231i
$834$	−13.5127	−	3.24232i	−0.467908	−	0.112272i
$835$	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	−0.915712	−	0.401835i	$-0.868372\pi$
$839$	−3.18205	+	5.51147i	−0.109856	+	0.190277i	0.805856	+	0.592112i	$0.201706\pi$
$840$	17.9186	+	10.1635i	0.618250	+	0.350675i
$841$	−13.8525	−	23.9932i	−0.477672	−	0.827353i
$842$	−9.17925	+	21.5886i	−0.316338	+	0.743992i
$843$	6.47038	+	38.4925i	0.222852	+	1.32575i
$844$	−4.07291	+	3.92365i	−0.140195	+	0.135057i
$845$		−	32.5638i		−	1.12023i
$846$	10.3754	+	6.98538i	0.356715	+	0.240162i
$847$			6.03700i			0.207434i
$848$	8.62355	+	16.3137i	0.296134	+	0.560216i
$849$	−30.9717	−	11.5540i	−1.06295	−	0.396533i
$850$	61.7599	+	26.2597i	2.11835	+	0.900699i
$851$	32.0749	+	55.5553i	1.09951	+	1.90441i
$852$	−2.80261	−	2.07590i	−0.0960158	−	0.0711192i
$853$	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	$0.741682\pi$
$858$	9.07587	+	8.61051i	0.309845	+	0.293958i
$859$	−23.5993	+	13.6251i	−0.805198	+	0.464881i	−0.845286	−	0.534315i	$-0.820570\pi$
$859$	−23.5993	+	13.6251i	−0.805198	+	0.464881i	0.0400874	+	0.999196i	$0.487236\pi$
$860$	3.92339	−	0.973167i	0.133787	−	0.0331847i
$861$	3.04929	+	3.69357i	0.103919	+	0.125877i
$862$	−19.6533	+	2.40104i	−0.669393	+	0.0817798i
$863$	30.3896			1.03447			0.517237	−	0.855842i	$-0.326961\pi$
$863$	30.3896			1.03447			0.517237	+	0.855842i	$0.326961\pi$
$864$	−13.1374	+	26.2947i	−0.446943	+	0.894562i
$865$	46.7078			1.58811
$866$	40.6708	−	4.96876i	1.38205	−	0.168845i
$867$	−3.30677	−	4.00546i	−0.112304	−	0.136033i
$868$	3.25024	−	0.806196i	0.110320	−	0.0273641i
$869$	25.9305	−	14.9710i	0.879630	−	0.507855i
$870$	8.50343	+	8.06742i	0.288293	+	0.273511i
$871$	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
$876$	14.3216	+	10.6080i	0.483881	+	0.358413i
$877$	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	$0.796190\pi$
$878$	−39.5680	−	16.8239i	−1.33536	−	0.567779i
$879$	−11.1919	−	4.17513i	−0.377492	−	0.140824i
$880$	−17.5116	−	33.1278i	−0.590316	−	1.11674i
$881$			4.57217i			0.154040i	0.997030	+	0.0770202i	$0.0245406\pi$
$881$			4.57217i			0.154040i	−0.997030	+	0.0770202i	$0.975459\pi$
$882$	3.81166	−	1.86312i	0.128345	−	0.0627345i
$883$		−	11.7784i		−	0.396374i	−0.980164	−	0.198187i	$-0.936495\pi$
$883$		−	11.7784i		−	0.396374i	0.980164	−	0.198187i	$-0.0635053\pi$
$884$	12.3561	−	11.9032i	0.415580	−	0.400349i
$885$	−2.71693	−	16.1631i	−0.0913285	−	0.543316i
$886$	12.1416	−	28.5558i	0.407906	−	0.959352i
$887$	−4.62869	−	8.01713i	−0.155416	−	0.269189i	0.777794	−	0.628519i	$-0.216339\pi$
$887$	−4.62869	−	8.01713i	−0.155416	−	0.269189i	−0.933211	+	0.359330i	$0.883005\pi$
$888$	−50.2918	−	28.5258i	−1.68768	−	0.957264i
$889$	−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
$894$	38.3757	+	9.20808i	1.28347	+	0.307964i
$895$	−69.1128	+	39.9023i	−2.31019	+	1.33379i
$896$	−10.7128	+	3.63801i	−0.357891	+	0.121537i
$897$	−21.2848	+	3.57786i	−0.710679	+	0.119461i
$898$	−3.62689	−	29.6873i	−0.121031	−	0.990677i
$899$	1.90540			0.0635486
$900$	67.8083	+	34.5285i	2.26028	+	1.15095i
$901$	17.2617			0.575070
$902$	−1.05652	−	8.64794i	−0.0351782	−	0.287945i
$903$	0.290981	−	0.780002i	0.00968323	−	0.0259568i
$904$	9.38665	−	11.5486i	0.312195	−	0.384101i
$905$	−44.0538	+	25.4345i	−1.46440	+	0.845470i
$906$	−8.93375	−	30.1459i	−0.296804	−	1.00153i
$907$	24.9384	+	14.3982i	0.828066	+	0.478084i	0.853190	−	0.521600i	$-0.174665\pi$
$907$	24.9384	+	14.3982i	0.828066	+	0.478084i	−0.0251243	+	0.999684i	$0.507998\pi$
$908$	−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	−0.521001	−	0.853556i	$-0.674441\pi$
$911$	14.4485	−	25.0256i	0.478701	−	0.829134i	0.999702	+	0.0244220i	$0.00777453\pi$
$912$	13.0521	−	31.3605i	0.432198	−	1.03845i
$913$	14.8310	+	25.6881i	0.490835	+	0.850151i
$914$	15.0919	−	35.4945i	0.499196	−	1.17405i
$915$	26.4504	−	21.8366i	0.874424	−	0.721895i
$916$	28.7810	+	29.8759i	0.950952	+	0.987129i
$917$		−	1.12657i		−	0.0372027i
$918$	16.0029	+	22.3600i	0.528175	+	0.737991i
$919$			32.1365i			1.06009i	0.847971	+	0.530043i	$0.177824\pi$
$919$			32.1365i			1.06009i	−0.847971	+	0.530043i	$0.822176\pi$
$920$	63.8323	+	10.2289i	2.10449	+	0.337238i
$921$	31.7755	−	26.2328i	1.04704	−	0.864399i
$922$	−32.9783	−	14.0220i	−1.08608	−	0.461790i
$923$	1.15410	+	1.99896i	0.0379877	+	0.0657966i
$924$	−7.66723	−	0.877295i	−0.252233	−	0.0288609i
$925$	−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	$0.571791\pi$
$930$	16.5354	−	4.90027i	0.542217	−	0.160686i
$931$	−4.24602	+	2.45144i	−0.139158	+	0.0803427i
$932$	−2.08757	−	8.41621i	−0.0683808	−	0.275682i
$933$	−12.3537	+	33.1152i	−0.404440	+	1.08414i
$934$	−32.7284	+	3.99843i	−1.07091	+	0.130833i
$935$	−35.0528			−1.14635
$936$	14.9065	−	12.4991i	0.487234	−	0.408544i
$937$	5.71581			0.186727			0.0933637	−	0.995632i	$-0.470238\pi$
$937$	5.71581			0.186727			0.0933637	+	0.995632i	$0.470238\pi$
$938$	−18.6312	+	2.27617i	−0.608330	+	0.0743197i
$939$	2.35930	−	0.396586i	0.0769929	−	0.0129421i
$940$	5.96903	+	24.0646i	0.194688	+	0.784899i
$941$	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	$0.198597\pi$
$942$	−8.33556	+	34.7394i	−0.271587	+	1.13187i
$943$	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	$-0.603977\pi$
$947$	20.3041	−	35.1677i	0.659794	−	1.14280i	0.980669	−	0.195675i	$-0.0626896\pi$
$948$	−18.5446	−	42.7057i	−0.602302	−	1.38702i
$949$	−5.89756	−	10.2149i	−0.191443	−	0.331589i
$950$	−80.9236	−	34.4079i	−2.62551	−	1.11634i
$951$	6.31017	+	37.5394i	0.204621	+	1.21730i
$952$	−1.67460	+	10.4501i	−0.0542742	+	0.338691i
$953$		−	7.17192i		−	0.232321i	−0.993230	−	0.116161i	$-0.962941\pi$
$953$		−	7.17192i		−	0.232321i	0.993230	−	0.116161i	$-0.0370588\pi$
$954$	19.5256	+	1.34854i	0.632164	+	0.0436606i
$955$		−	17.6266i		−	0.570384i
$956$	8.88119	+	9.21906i	0.287238	+	0.298166i
$957$	−4.11410	−	1.53477i	−0.132990	−	0.0496121i
$958$	13.4869	−	31.7196i	0.435741	−	1.02482i
$959$	−2.05083	−	3.55214i	−0.0662248	−	0.114705i
$960$	−54.2739	+	21.1974i	−1.75168	+	0.684142i
$961$	−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
$966$	9.16354	−	9.65879i	0.294832	−	0.310767i
$967$	−20.7638	+	11.9880i	−0.667717	+	0.385507i	−0.795211	−	0.606333i	$-0.792640\pi$
$967$	−20.7638	+	11.9880i	−0.667717	+	0.385507i	0.127494	+	0.991839i	$0.459307\pi$
$968$	−13.2504	−	10.7699i	−0.425883	−	0.346156i
$969$	−20.2297	−	24.5041i	−0.649872	−	0.787185i
$970$	3.64138	+	29.8058i	0.116918	+	0.957007i
$971$	49.7729			1.59729			0.798645	−	0.601803i	$-0.205551\pi$
$971$	49.7729			1.59729			0.798645	+	0.601803i	$0.205551\pi$
$972$	16.3549	+	26.5428i	0.524583	+	0.851360i
$973$	−5.67314			−0.181872
$974$	3.30648	+	27.0646i	0.105946	+	0.867204i
$975$	−32.0610	−	38.8352i	−1.02677	−	1.24372i
$976$	−0.703006	+	18.8242i	−0.0225027	+	0.602549i
$977$	−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	$0.405592\pi$
$978$	−24.3071	+	25.6208i	−0.777256	+	0.819263i
$979$	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	−0.570735	−	0.821134i	$-0.693342\pi$
$983$	13.3486	−	23.1205i	0.425756	−	0.737430i	0.996491	+	0.0837040i	$0.0266750\pi$
$984$	−13.5468	+	0.103521i	−0.431855	+	0.00330014i
$985$	−14.8053	−	25.6435i	−0.471735	−	0.817070i
$986$	−2.35630	+	5.54176i	−0.0750399	+	0.176486i
$987$	4.78423	+	1.78476i	0.152284	+	0.0568096i
$988$	−16.1901	+	15.5967i	−0.515075	+	0.496198i
$989$		−	2.61253i		−	0.0830738i
$990$	−39.6500	−	2.73844i	−1.26016	−	0.0870335i
$991$			0.190124i			0.00603949i	0.999995	+	0.00301974i	$0.000961215\pi$
$991$			0.190124i			0.00603949i	−0.999995	+	0.00301974i	$0.999039\pi$
$992$	−4.02885	+	8.57206i	−0.127916	+	0.272163i
$993$	9.77357	+	58.1433i	0.310155	+	1.84512i
$994$	−1.31032	−	0.557133i	−0.0415607	−	0.0176712i
$995$	−5.61075	−	9.71811i	−0.177873	−	0.308085i
$996$	42.3065	−	18.3713i	1.34053	−	0.582116i
$997$	−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.155.2	✓	72
3.2	odd	2		756.2.ba.a.575.35		72
4.3	odd	2	inner	252.2.ba.a.155.14	yes	72
9.4	even	3		756.2.ba.a.71.23		72
9.5	odd	6	inner	252.2.ba.a.239.14	yes	72
12.11	even	2		756.2.ba.a.575.23		72
36.23	even	6	inner	252.2.ba.a.239.2	yes	72
36.31	odd	6		756.2.ba.a.71.35		72

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

\(f(q)\)	\(=\)	\(q+(-1.40378 + 0.171499i) q^{2} +(-1.10270 - 1.33569i) q^{3} +(1.94118 - 0.481494i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.77701 + 1.68589i) q^{6} +(0.866025 + 0.500000i) q^{7} +(-2.64240 + 1.00882i) q^{8} +(-0.568119 + 2.94572i) q^{9} +O(q^{10})\)	\(q+(-1.40378 + 0.171499i) q^{2} +(-1.10270 - 1.33569i) q^{3} +(1.94118 - 0.481494i) q^{4} +(3.64166 - 2.10251i) q^{5} +(1.77701 + 1.68589i) 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} +(-2.78365 - 2.06186i) q^{12} +(1.14629 + 1.98544i) q^{13} +(-1.30146 - 0.553365i) q^{14} +(-6.82394 - 2.54568i) q^{15} +(3.53633 - 1.86933i) q^{16} -3.74182i q^{17} +(0.292323 - 4.23256i) q^{18} +4.90288i q^{19} +(6.05675 - 5.83478i) q^{20} +(-0.287120 - 1.70809i) q^{21} +(-1.23278 + 2.89936i) q^{22} +(-2.71771 - 4.70721i) q^{23} +(4.26123 + 2.41700i) 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} +(10.0159 + 2.40326i) q^{30} +(1.45004 - 0.837182i) q^{31} +(-4.64362 + 3.23060i) q^{32} +(-3.80524 + 0.639641i) q^{33} +(0.641719 + 5.25267i) q^{34} +4.20502 q^{35} +(0.315525 + 5.99170i) q^{36} -11.8022 q^{37} +(-0.840841 - 6.88255i) q^{38} +(1.38791 - 3.72043i) q^{39} +(-7.50166 + 9.22945i) q^{40} +(-2.39482 + 1.38265i) q^{41} +(0.695988 + 2.34853i) 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} +(-6.39633 - 2.66213i) q^{48} +(0.500000 + 0.866025i) q^{49} +(-7.01789 + 16.5053i) q^{50} +(-4.99790 + 4.12609i) q^{51} +(3.18114 + 3.30216i) q^{52} +4.61318i q^{53} +(-5.97572 + 4.27678i) q^{54} -9.36786i q^{55} +(-2.79280 - 0.447537i) q^{56} +(6.54871 - 5.40639i) q^{57} +(-1.48104 - 0.629721i) q^{58} +(1.12516 + 1.94884i) q^{59} +(-14.4722 - 1.65593i) 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} +(5.23201 - 1.55051i) q^{66} +(11.4941 - 6.63610i) q^{67} +(-1.80166 - 7.26353i) q^{68} +(-3.29055 + 8.82064i) q^{69} +(-5.90291 + 0.721159i) q^{70} +1.00681 q^{71} +(-1.47050 - 8.35689i) q^{72} -5.14489 q^{73} +(16.5676 - 2.02407i) q^{74} +(-21.6623 + 3.64132i) q^{75} +(2.36070 + 9.51735i) q^{76} +(1.92931 - 1.11389i) q^{77} +(-1.31027 + 5.46068i) 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} +(-1.37978 - 3.17745i) q^{84} +(-7.86721 - 13.6264i) q^{85} +(-0.625544 - 0.265975i) q^{86} +(-0.326738 - 1.94378i) q^{87} +(-0.997014 + 6.22174i) q^{88} +12.3797i q^{89} +(-7.83446 - 16.0281i) q^{90} +2.29259i q^{91} +(-7.54205 - 7.82897i) q^{92} +(-2.71717 - 1.01364i) q^{93} +(1.63139 - 3.83684i) q^{94} +(10.3084 + 17.8546i) q^{95} +(9.43558 + 2.64006i) 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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