LMFDB - Embedded newform 336.2.u.a.139.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,2,Mod(139,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 1, 0, 2]))

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

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

chi := DirichletCharacter("336.139");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	336.u (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.68297350792$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			139.1
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38346 + 0.293324i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.82792 - 0.811604i) q^{4} +(2.49549 - 2.49549i) q^{5} +(0.770842 - 1.18567i) q^{6} +(0.134305 + 2.64234i) q^{7} +(-2.29079 + 1.65899i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(q+(-1.38346 + 0.293324i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.82792 - 0.811604i) q^{4} +(2.49549 - 2.49549i) q^{5} +(0.770842 - 1.18567i) q^{6} +(0.134305 + 2.64234i) q^{7} +(-2.29079 + 1.65899i) q^{8} -1.00000i q^{9} +(-2.72043 + 4.18440i) q^{10} +(3.74223 - 3.74223i) q^{11} +(-0.718646 + 1.86643i) q^{12} +(-3.44510 - 3.44510i) q^{13} +(-0.960868 - 3.61618i) q^{14} +3.52916i q^{15} +(2.68260 - 2.96710i) q^{16} +0.279408i q^{17} +(0.293324 + 1.38346i) q^{18} +(-2.51552 + 2.51552i) q^{19} +(2.53622 - 6.58692i) q^{20} +(-1.96338 - 1.77345i) q^{21} +(-4.07954 + 6.27492i) q^{22} +3.90741 q^{23} +(0.446750 - 2.79292i) q^{24} -7.45497i q^{25} +(5.77669 + 3.75563i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.39003 + 4.72099i) q^{28} +(5.23306 - 5.23306i) q^{29} +(-1.03519 - 4.88245i) q^{30} +6.11626 q^{31} +(-2.84095 + 4.89173i) q^{32} +5.29232i q^{33} +(-0.0819571 - 0.386550i) q^{34} +(6.92910 + 6.25878i) q^{35} +(-0.811604 - 1.82792i) q^{36} +(6.48710 + 6.48710i) q^{37} +(2.74226 - 4.21799i) q^{38} +4.87211 q^{39} +(-1.57665 + 9.85667i) q^{40} +1.02484 q^{41} +(3.23646 + 1.87759i) q^{42} +(2.37381 - 2.37381i) q^{43} +(3.80330 - 9.87772i) q^{44} +(-2.49549 - 2.49549i) q^{45} +(-5.40574 + 1.14614i) q^{46} -5.55809 q^{47} +(0.201171 + 3.99494i) q^{48} +(-6.96392 + 0.709760i) q^{49} +(2.18672 + 10.3137i) q^{50} +(-0.197571 - 0.197571i) q^{51} +(-9.09343 - 3.50132i) q^{52} +(-3.03375 - 3.03375i) q^{53} +(-1.18567 - 0.770842i) q^{54} -18.6774i q^{55} +(-4.69129 - 5.83025i) q^{56} -3.55749i q^{57} +(-5.70475 + 8.77472i) q^{58} +(-1.85379 - 1.85379i) q^{59} +(2.86428 + 6.45103i) q^{60} +(7.02125 + 7.02125i) q^{61} +(-8.46161 + 1.79405i) q^{62} +(2.64234 - 0.134305i) q^{63} +(2.49547 - 7.60083i) q^{64} -17.1944 q^{65} +(-1.55236 - 7.32171i) q^{66} +(-0.678348 - 0.678348i) q^{67} +(0.226769 + 0.510736i) q^{68} +(-2.76295 + 2.76295i) q^{69} +(-11.4220 - 6.62631i) q^{70} -14.3974 q^{71} +(1.65899 + 2.29079i) q^{72} -5.13655 q^{73} +(-10.8775 - 7.07182i) q^{74} +(5.27146 + 5.27146i) q^{75} +(-2.55657 + 6.63979i) q^{76} +(10.3909 + 9.38565i) q^{77} +(-6.74036 + 1.42911i) q^{78} +12.7493i q^{79} +(-0.709965 - 14.0988i) q^{80} -1.00000 q^{81} +(-1.41783 + 0.300610i) q^{82} +(1.28033 - 1.28033i) q^{83} +(-5.02825 - 1.64824i) q^{84} +(0.697261 + 0.697261i) q^{85} +(-2.58778 + 3.98037i) q^{86} +7.40067i q^{87} +(-2.36434 + 14.7810i) q^{88} +2.78092 q^{89} +(4.18440 + 2.72043i) q^{90} +(8.64043 - 9.56582i) q^{91} +(7.14244 - 3.17127i) q^{92} +(-4.32485 + 4.32485i) q^{93} +(7.68939 - 1.63032i) q^{94} +12.5549i q^{95} +(-1.45012 - 5.46783i) q^{96} -13.3640i q^{97} +(9.42612 - 3.02461i) q^{98} +(-3.74223 - 3.74223i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) $ 64 * q - 4 * q^4 + 24 * q^8	$ 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) $ 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$-1$	$-1$

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 $

$2$	−1.38346	+	0.293324i	−0.978254	+	0.207411i
$2$	−1.38346	+	0.293324i	−0.978254	+	0.207411i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$3$	−0.707107	+	0.707107i	−0.408248	+	0.408248i
$4$	1.82792	−	0.811604i	0.913961	−	0.405802i
$5$	2.49549	−	2.49549i	1.11602	−	1.11602i	0.123699	−	0.992320i	$-0.460524\pi$
$5$	2.49549	−	2.49549i	1.11602	−	1.11602i	0.992320	−	0.123699i	$-0.0394756\pi$
$6$	0.770842	−	1.18567i	0.314695	−	0.484046i
$7$	0.134305	+	2.64234i	0.0507626	+	0.998711i
$7$	0.134305	+	2.64234i	0.0507626	+	0.998711i
$8$	−2.29079	+	1.65899i	−0.809918	+	0.586543i
$9$		−	1.00000i		−	0.333333i
$10$	−2.72043	+	4.18440i	−0.860274	+	1.32322i
$11$	3.74223	−	3.74223i	1.12833	−	1.12833i	0.137876	−	0.990449i	$-0.455972\pi$
$11$	3.74223	−	3.74223i	1.12833	−	1.12833i	0.990449	−	0.137876i	$-0.0440276\pi$
$12$	−0.718646	+	1.86643i	−0.207455	+	0.538791i
$13$	−3.44510	−	3.44510i	−0.955499	−	0.955499i	0.0435523	−	0.999051i	$-0.486132\pi$
$13$	−3.44510	−	3.44510i	−0.955499	−	0.955499i	−0.999051	+	0.0435523i	$0.986132\pi$
$14$	−0.960868	−	3.61618i	−0.256803	−	0.966464i
$15$			3.52916i			0.911225i
$16$	2.68260	−	2.96710i	0.670650	−	0.741774i
$17$			0.279408i			0.0677664i	0.999426	+	0.0338832i	$0.0107874\pi$
$17$			0.279408i			0.0677664i	−0.999426	+	0.0338832i	$0.989213\pi$
$18$	0.293324	+	1.38346i	0.0691371	+	0.326085i
$19$	−2.51552	+	2.51552i	−0.577101	+	0.577101i	−0.934103	−	0.357003i	$-0.883799\pi$
$19$	−2.51552	+	2.51552i	−0.577101	+	0.577101i	0.357003	+	0.934103i	$0.383799\pi$
$20$	2.53622	−	6.58692i	0.567115	−	1.47288i
$21$	−1.96338	−	1.77345i	−0.428446	−	0.386998i
$22$	−4.07954	+	6.27492i	−0.869761	+	1.33782i
$23$	3.90741			0.814751			0.407375	−	0.913261i	$-0.366444\pi$
$23$	3.90741			0.814751			0.407375	+	0.913261i	$0.366444\pi$
$24$	0.446750	−	2.79292i	0.0911924	−	0.570103i
$25$		−	7.45497i		−	1.49099i
$26$	5.77669	+	3.75563i	1.13290	+	0.736539i
$27$	0.707107	+	0.707107i	0.136083	+	0.136083i
$28$	2.39003	+	4.72099i	0.451674	+	0.892183i
$29$	5.23306	−	5.23306i	0.971755	−	0.971755i	−0.0278565	−	0.999612i	$-0.508868\pi$
$29$	5.23306	−	5.23306i	0.971755	−	0.971755i	0.999612	+	0.0278565i	$0.00886816\pi$
$30$	−1.03519	−	4.88245i	−0.188998	−	0.891410i
$31$	6.11626			1.09851			0.549257	−	0.835654i	$-0.314911\pi$
$31$	6.11626			1.09851			0.549257	+	0.835654i	$0.314911\pi$
$32$	−2.84095	+	4.89173i	−0.502213	+	0.864744i
$33$			5.29232i			0.921274i
$34$	−0.0819571	−	0.386550i	−0.0140555	−	0.0662927i
$35$	6.92910	+	6.25878i	1.17123	+	1.05793i
$36$	−0.811604	−	1.82792i	−0.135267	−	0.304654i
$37$	6.48710	+	6.48710i	1.06647	+	1.06647i	0.997627	+	0.0688458i	$0.0219317\pi$
$37$	6.48710	+	6.48710i	1.06647	+	1.06647i	0.0688458	+	0.997627i	$0.478068\pi$
$38$	2.74226	−	4.21799i	0.444854	−	0.684248i
$39$	4.87211			0.780162
$40$	−1.57665	+	9.85667i	−0.249290	+	1.55848i
$41$	1.02484			0.160053			0.0800267	−	0.996793i	$-0.474499\pi$
$41$	1.02484			0.160053			0.0800267	+	0.996793i	$0.474499\pi$
$42$	3.23646	+	1.87759i	0.499396	+	0.289718i
$43$	2.37381	−	2.37381i	0.362003	−	0.362003i	−0.502547	−	0.864550i	$-0.667604\pi$
$43$	2.37381	−	2.37381i	0.362003	−	0.362003i	0.864550	+	0.502547i	$0.167604\pi$
$44$	3.80330	−	9.87772i	0.573369	−	1.48912i
$45$	−2.49549	−	2.49549i	−0.372006	−	0.372006i
$46$	−5.40574	+	1.14614i	−0.797033	+	0.168989i
$47$	−5.55809			−0.810731			−0.405365	−	0.914155i	$-0.632856\pi$
$47$	−5.55809			−0.810731			−0.405365	+	0.914155i	$0.632856\pi$
$48$	0.201171	+	3.99494i	0.0290365	+	0.576620i
$49$	−6.96392	+	0.709760i	−0.994846	+	0.101394i
$50$	2.18672	+	10.3137i	0.309249	+	1.45857i
$51$	−0.197571	−	0.197571i	−0.0276655	−	0.0276655i
$52$	−9.09343	−	3.50132i	−1.26103	−	0.485545i
$53$	−3.03375	−	3.03375i	−0.416718	−	0.416718i	0.467353	−	0.884071i	$-0.345208\pi$
$53$	−3.03375	−	3.03375i	−0.416718	−	0.416718i	−0.884071	+	0.467353i	$0.845208\pi$
$54$	−1.18567	−	0.770842i	−0.161349	−	0.104898i
$55$		−	18.6774i		−	2.51846i
$56$	−4.69129	−	5.83025i	−0.626901	−	0.779099i
$57$		−	3.55749i		−	0.471201i
$58$	−5.70475	+	8.77472i	−0.749070	+	1.15218i
$59$	−1.85379	−	1.85379i	−0.241343	−	0.241343i	0.576062	−	0.817406i	$-0.304589\pi$
$59$	−1.85379	−	1.85379i	−0.241343	−	0.241343i	−0.817406	+	0.576062i	$0.804589\pi$
$60$	2.86428	+	6.45103i	0.369777	+	0.832824i
$61$	7.02125	+	7.02125i	0.898979	+	0.898979i	0.995346	−	0.0963664i	$-0.0307221\pi$
$61$	7.02125	+	7.02125i	0.898979	+	0.898979i	−0.0963664	+	0.995346i	$0.530722\pi$
$62$	−8.46161	+	1.79405i	−1.07462	+	0.227844i
$63$	2.64234	−	0.134305i	0.332904	−	0.0169209i
$64$	2.49547	−	7.60083i	0.311934	−	0.950104i
$65$	−17.1944			−2.13271
$66$	−1.55236	−	7.32171i	−0.191083	−	0.901240i
$67$	−0.678348	−	0.678348i	−0.0828734	−	0.0828734i	0.664455	−	0.747328i	$-0.268664\pi$
$67$	−0.678348	−	0.678348i	−0.0828734	−	0.0828734i	−0.747328	+	0.664455i	$0.768664\pi$
$68$	0.226769	+	0.510736i	0.0274997	+	0.0619358i
$69$	−2.76295	+	2.76295i	−0.332621	+	0.332621i
$70$	−11.4220	−	6.62631i	−1.36519	−	0.791995i
$71$	−14.3974			−1.70866			−0.854329	−	0.519733i	$-0.826031\pi$
$71$	−14.3974			−1.70866			−0.854329	+	0.519733i	$0.826031\pi$
$72$	1.65899	+	2.29079i	0.195514	+	0.269973i
$73$	−5.13655			−0.601188			−0.300594	−	0.953752i	$-0.597185\pi$
$73$	−5.13655			−0.601188			−0.300594	+	0.953752i	$0.597185\pi$
$74$	−10.8775	−	7.07182i	−1.26448	−	0.822083i
$75$	5.27146	+	5.27146i	0.608696	+	0.608696i
$76$	−2.55657	+	6.63979i	−0.293259	+	0.761636i
$77$	10.3909	+	9.38565i	1.18415	+	1.06959i
$78$	−6.74036	+	1.42911i	−0.763196	+	0.161814i
$79$			12.7493i			1.43441i	0.696861	+	0.717206i	$0.254579\pi$
$79$			12.7493i			1.43441i	−0.696861	+	0.717206i	$0.745421\pi$
$80$	−0.709965	−	14.0988i	−0.0793765	−	1.57629i
$81$	−1.00000			−0.111111
$82$	−1.41783	+	0.300610i	−0.156573	+	0.0331969i
$83$	1.28033	−	1.28033i	0.140535	−	0.140535i	−0.633339	−	0.773874i	$-0.718316\pi$
$83$	1.28033	−	1.28033i	0.140535	−	0.140535i	0.773874	+	0.633339i	$0.218316\pi$
$84$	−5.02825	−	1.64824i	−0.548627	−	0.179837i
$85$	0.697261	+	0.697261i	0.0756285	+	0.0756285i
$86$	−2.58778	+	3.98037i	−0.279047	+	0.429214i
$87$			7.40067i			0.793435i
$88$	−2.36434	+	14.7810i	−0.252039	+	1.57566i
$89$	2.78092			0.294777			0.147389	−	0.989079i	$-0.452913\pi$
$89$	2.78092			0.294777			0.147389	+	0.989079i	$0.452913\pi$
$90$	4.18440	+	2.72043i	0.441075	+	0.286758i
$91$	8.64043	−	9.56582i	0.905763	−	1.00277i
$92$	7.14244	−	3.17127i	0.744650	−	0.330627i
$93$	−4.32485	+	4.32485i	−0.448466	+	0.448466i
$94$	7.68939	−	1.63032i	0.793101	−	0.168155i
$95$			12.5549i			1.28811i
$96$	−1.45012	−	5.46783i	−0.148003	−	0.558058i
$97$		−	13.3640i		−	1.35691i	−0.734641	−	0.678456i	$-0.762649\pi$
$97$		−	13.3640i		−	1.35691i	0.734641	−	0.678456i	$-0.237351\pi$
$98$	9.42612	−	3.02461i	0.952182	−	0.305532i
$99$	−3.74223	−	3.74223i	−0.376109	−	0.376109i
$100$	−6.05048	−	13.6271i	−0.605048	−	1.36271i
$101$	3.39140	−	3.39140i	0.337457	−	0.337457i	−0.517952	−	0.855410i	$-0.673306\pi$
$101$	3.39140	−	3.39140i	0.337457	−	0.337457i	0.855410	+	0.517952i	$0.173306\pi$
$102$	0.331284	+	0.215380i	0.0328020	+	0.0213258i
$103$			8.83485i			0.870523i	0.900304	+	0.435262i	$0.143344\pi$
$103$			8.83485i			0.870523i	−0.900304	+	0.435262i	$0.856656\pi$
$104$	13.6074	+	2.17661i	1.33432	+	0.213434i
$105$	−9.32524	+	0.473985i	−0.910050	+	0.0462562i
$106$	5.08695	+	3.30720i	0.494088	+	0.321224i
$107$	−6.83291	+	6.83291i	−0.660562	+	0.660562i	−0.955513	−	0.294950i	$-0.904697\pi$
$107$	−6.83291	+	6.83291i	−0.660562	+	0.660562i	0.294950	+	0.955513i	$0.404697\pi$
$108$	1.86643	+	0.718646i	0.179597	+	0.0691517i
$109$	−6.95454	+	6.95454i	−0.666124	+	0.666124i	−0.956817	−	0.290692i	$-0.906114\pi$
$109$	−6.95454	+	6.95454i	−0.666124	+	0.666124i	0.290692	+	0.956817i	$0.406114\pi$
$110$	5.47854	+	25.8395i	0.522358	+	2.46370i
$111$	−9.17415			−0.870772
$112$	8.20037	+	6.68984i	0.774862	+	0.632131i
$113$	−1.70173			−0.160085			−0.0800427	−	0.996791i	$-0.525506\pi$
$113$	−1.70173			−0.160085			−0.0800427	+	0.996791i	$0.525506\pi$
$114$	1.04350	+	4.92164i	0.0977324	+	0.460954i
$115$	9.75091	−	9.75091i	0.909277	−	0.909277i
$116$	5.31846	−	13.8128i	0.493806	−	1.28249i
$117$	−3.44510	+	3.44510i	−0.318500	+	0.318500i
$118$	3.10841	+	2.02089i	0.286153	+	0.186038i
$119$	−0.738291	+	0.0375259i	−0.0676790	+	0.00344000i
$120$	−5.85486	−	8.08458i	−0.534473	−	0.738018i
$121$		−	17.0086i		−	1.54624i
$122$	−11.7731	−	7.65412i	−1.06589	−	0.692972i
$123$	−0.724672	+	0.724672i	−0.0653415	+	0.0653415i
$124$	11.1801	−	4.96398i	1.00400	−	0.445779i
$125$	−6.12636	−	6.12636i	−0.547958	−	0.547958i
$126$	−3.61618	+	0.960868i	−0.322155	+	0.0856009i
$127$			10.7900i			0.957459i	0.877962	+	0.478730i	$0.158903\pi$
$127$			10.7900i			0.957459i	−0.877962	+	0.478730i	$0.841097\pi$
$128$	−1.22288	+	11.2474i	−0.108088	+	0.994141i
$129$			3.35708i			0.295574i
$130$	23.7878	−	5.04354i	2.08633	−	0.442348i
$131$	−10.5760	+	10.5760i	−0.924027	+	0.924027i	−0.997311	−	0.0732839i	$-0.976652\pi$
$131$	−10.5760	+	10.5760i	−0.924027	+	0.924027i	0.0732839	+	0.997311i	$0.476652\pi$
$132$	4.29526	+	9.67394i	0.373855	+	0.842009i
$133$	−6.98472	−	6.30902i	−0.605652	−	0.547061i
$134$	1.13744	+	0.739492i	0.0982601	+	0.0638823i
$135$	3.52916			0.303742
$136$	−0.463536	−	0.640066i	−0.0397479	−	0.0548852i
$137$			1.09451i			0.0935104i	0.998906	+	0.0467552i	$0.0148881\pi$
$137$			1.09451i			0.0935104i	−0.998906	+	0.0467552i	$0.985112\pi$
$138$	3.01200	−	4.63288i	0.256398	−	0.394377i
$139$	−5.95347	−	5.95347i	−0.504967	−	0.504967i	0.408010	−	0.912977i	$-0.366223\pi$
$139$	−5.95347	−	5.95347i	−0.504967	−	0.504967i	−0.912977	+	0.408010i	$0.866223\pi$
$140$	17.7455	+	5.81689i	1.49977	+	0.491617i
$141$	3.93016	−	3.93016i	0.330979	−	0.330979i
$142$	19.9182	−	4.22310i	1.67150	−	0.354395i
$143$	−25.7847			−2.15623
$144$	−2.96710	−	2.68260i	−0.247258	−	0.223550i
$145$		−	26.1181i		−	2.16899i
$146$	7.10622	−	1.50667i	0.588115	−	0.124693i
$147$	4.42236	−	5.42611i	0.364750	−	0.447538i
$148$	17.1229	+	6.59296i	1.40749	+	0.541938i
$149$	8.93319	+	8.93319i	0.731836	+	0.731836i	0.970983	−	0.239148i	$-0.0768680\pi$
$149$	8.93319	+	8.93319i	0.731836	+	0.731836i	−0.239148	+	0.970983i	$0.576868\pi$
$150$	−8.83910	−	5.74661i	−0.721709	−	0.469209i
$151$	−9.78462			−0.796261			−0.398130	−	0.917329i	$-0.630341\pi$
$151$	−9.78462			−0.796261			−0.398130	+	0.917329i	$0.630341\pi$
$152$	1.58931	−	9.93578i	0.128910	−	0.805899i
$153$	0.279408			0.0225888
$154$	−17.1284	−	9.93678i	−1.38024	−	0.800729i
$155$	15.2631	−	15.2631i	1.22596	−	1.22596i
$156$	8.90583	−	3.95422i	0.713037	−	0.316591i
$157$	−1.79445	−	1.79445i	−0.143213	−	0.143213i	0.631865	−	0.775078i	$-0.282290\pi$
$157$	−1.79445	−	1.79445i	−0.143213	−	0.143213i	−0.775078	+	0.631865i	$0.782290\pi$
$158$	−3.73968	−	17.6382i	−0.297513	−	1.40322i
$159$	4.29037			0.340249
$160$	5.11772	+	19.2968i	0.404591	+	1.52555i
$161$	0.524785	+	10.3247i	0.0413589	+	0.813700i
$162$	1.38346	−	0.293324i	0.108695	−	0.0230457i
$163$	1.56969	+	1.56969i	0.122948	+	0.122948i	0.765903	−	0.642956i	$-0.222292\pi$
$163$	1.56969	+	1.56969i	0.122948	+	0.122948i	−0.642956	+	0.765903i	$0.722292\pi$
$164$	1.87333	−	0.831765i	0.146282	−	0.0649499i
$165$	13.2069	+	13.2069i	1.02816	+	1.02816i
$166$	−1.39574	+	2.14684i	−0.108330	+	0.166627i
$167$			10.4475i			0.808455i	0.914658	+	0.404228i	$0.132460\pi$
$167$			10.4475i			0.808455i	−0.914658	+	0.404228i	$0.867540\pi$
$168$	7.43985	+	0.805360i	0.573997	+	0.0621349i
$169$			10.7374i			0.825956i
$170$	−1.16916	−	0.760109i	−0.0896701	−	0.0582977i
$171$	2.51552	+	2.51552i	0.192367	+	0.192367i
$172$	2.41255	−	6.26574i	0.183955	−	0.477758i
$173$	−4.28582	−	4.28582i	−0.325845	−	0.325845i	0.525159	−	0.851004i	$-0.324006\pi$
$173$	−4.28582	−	4.28582i	−0.325845	−	0.325845i	−0.851004	+	0.525159i	$0.824006\pi$
$174$	−2.17079	−	10.2385i	−0.164567	−	0.776181i
$175$	19.6986	−	1.00124i	1.48907	−	0.0756867i
$176$	−1.06466	−	21.1425i	−0.0802518	−	1.59367i
$177$	2.62166			0.197056
$178$	−3.84729	+	0.815711i	−0.288367	+	0.0611401i
$179$	−0.760959	−	0.760959i	−0.0568768	−	0.0568768i	0.678096	−	0.734973i	$-0.262805\pi$
$179$	−0.760959	−	0.760959i	−0.0568768	−	0.0568768i	−0.734973	+	0.678096i	$0.762805\pi$
$180$	−6.58692	−	2.53622i	−0.490960	−	0.189038i
$181$	−17.7647	+	17.7647i	−1.32044	+	1.32044i	−0.407026	+	0.913417i	$0.633434\pi$
$181$	−17.7647	+	17.7647i	−1.32044	+	1.32044i	−0.913417	+	0.407026i	$0.866566\pi$
$182$	−9.14781	+	15.7684i	−0.678080	+	1.16883i
$183$	−9.92955			−0.734014
$184$	−8.95106	+	6.48237i	−0.659881	+	0.477886i
$185$	32.3770			2.38041
$186$	4.71468	−	7.25184i	0.345697	−	0.531731i
$187$	1.04561	+	1.04561i	0.0764626	+	0.0764626i
$188$	−10.1598	+	4.51097i	−0.740976	+	0.328996i
$189$	−1.77345	+	1.96338i	−0.128999	+	0.142815i
$190$	−3.68267	−	17.3693i	−0.267169	−	1.26010i
$191$		−	17.3849i		−	1.25793i	−0.777435	−	0.628963i	$-0.783480\pi$
$191$		−	17.3849i		−	1.25793i	0.777435	−	0.628963i	$-0.216520\pi$
$192$	3.61003	+	7.13916i	0.260532	+	0.515225i
$193$	−12.1767			−0.876499			−0.438249	−	0.898853i	$-0.644401\pi$
$193$	−12.1767			−0.876499			−0.438249	+	0.898853i	$0.644401\pi$
$194$	3.91999	+	18.4886i	0.281439	+	1.32741i
$195$	12.1583	−	12.1583i	0.870675	−	0.870675i
$196$	−12.1535	+	6.94933i	−0.868105	+	0.496381i
$197$	12.3749	+	12.3749i	0.881678	+	0.881678i	0.993705	−	0.112027i	$-0.0357345\pi$
$197$	12.3749	+	12.3749i	0.881678	+	0.881678i	−0.112027	+	0.993705i	$0.535734\pi$
$198$	6.27492	+	4.07954i	0.445939	+	0.289920i
$199$			7.04311i			0.499273i	0.968340	+	0.249636i	$0.0803111\pi$
$199$			7.04311i			0.499273i	−0.968340	+	0.249636i	$0.919689\pi$
$200$	12.3678	+	17.0778i	0.874532	+	1.20758i
$201$	0.959329			0.0676659
$202$	−3.69709	+	5.68665i	−0.260126	+	0.400111i
$203$	14.5304	+	13.1247i	1.01983	+	0.921174i
$204$	−0.521495	−	0.200795i	−0.0365119	−	0.0140585i
$205$	2.55748	−	2.55748i	0.178622	−	0.178622i
$206$	−2.59147	−	12.2227i	−0.180556	−	0.851593i
$207$		−	3.90741i		−	0.271584i
$208$	−19.4638	+	0.980127i	−1.34957	+	0.0679596i
$209$			18.8273i			1.30231i
$210$	12.7621	−	3.39106i	0.880666	−	0.234005i
$211$	−3.82693	−	3.82693i	−0.263457	−	0.263457i	0.563000	−	0.826457i	$-0.309647\pi$
$211$	−3.82693	−	3.82693i	−0.263457	−	0.263457i	−0.826457	+	0.563000i	$0.809647\pi$
$212$	−8.00767	−	3.08326i	−0.549969	−	0.211759i
$213$	10.1805	−	10.1805i	0.697556	−	0.697556i
$214$	7.44880	−	11.4573i	0.509189	−	0.783205i
$215$		−	11.8477i		−	0.808004i
$216$	−2.79292	−	0.446750i	−0.190034	−	0.0303975i
$217$	0.821446	+	16.1613i	0.0557634	+	1.09710i
$218$	7.58140	−	11.6613i	0.513477	−	0.789801i
$219$	3.63209	−	3.63209i	0.245434	−	0.245434i
$220$	−15.1587	−	34.1409i	−1.02200	−	2.30178i
$221$	0.962589	−	0.962589i	0.0647507	−	0.0647507i
$222$	12.6921	−	2.69100i	0.851836	−	0.180608i
$223$	19.9655			1.33699			0.668495	−	0.743717i	$-0.266939\pi$
$223$	19.9655			1.33699			0.668495	+	0.743717i	$0.266939\pi$
$224$	−13.3072	−	6.84976i	−0.889123	−	0.457669i
$225$	−7.45497			−0.496998
$226$	2.35428	−	0.499158i	0.156604	−	0.0332035i
$227$	−0.926757	+	0.926757i	−0.0615110	+	0.0615110i	−0.737193	−	0.675682i	$-0.763849\pi$
$227$	−0.926757	+	0.926757i	−0.0615110	+	0.0615110i	0.675682	+	0.737193i	$0.263849\pi$
$228$	−2.88727	−	6.50281i	−0.191214	−	0.430659i
$229$	14.2225	−	14.2225i	0.939847	−	0.939847i	−0.0584437	−	0.998291i	$-0.518614\pi$
$229$	14.2225	−	14.2225i	0.939847	−	0.939847i	0.998291	+	0.0584437i	$0.0186138\pi$
$230$	−10.6298	+	16.3502i	−0.700909	+	1.07810i
$231$	−13.9841	+	0.710786i	−0.920086	+	0.0467663i
$232$	−3.30625	+	20.6695i	−0.217066	+	1.35702i
$233$		−	21.4717i		−	1.40666i	−0.710864	−	0.703330i	$-0.751696\pi$
$233$		−	21.4717i		−	1.40666i	0.710864	−	0.703330i	$-0.248304\pi$
$234$	3.75563	−	5.77669i	0.245513	−	0.377634i
$235$	−13.8702	+	13.8702i	−0.904791	+	0.904791i
$236$	−4.89314	−	1.88404i	−0.318516	−	0.122641i
$237$	−9.01514	−	9.01514i	−0.585596	−	0.585596i
$238$	1.01039	−	0.268474i	0.0654938	−	0.0174026i
$239$			8.84921i			0.572408i	0.958169	+	0.286204i	$0.0923934\pi$
$239$			8.84921i			0.572408i	−0.958169	+	0.286204i	$0.907607\pi$
$240$	10.4714	+	9.46732i	0.675923	+	0.611113i
$241$			11.5027i			0.740954i	0.928842	+	0.370477i	$0.120806\pi$
$241$			11.5027i			0.740954i	−0.928842	+	0.370477i	$0.879194\pi$
$242$	4.98903	+	23.5307i	0.320707	+	1.51261i
$243$	0.707107	−	0.707107i	0.0453609	−	0.0453609i
$244$	18.5328	+	7.13583i	1.18644	+	0.456825i
$245$	−15.6072	+	19.1496i	−0.997109	+	1.22342i
$246$	0.789991	−	1.21512i	0.0503680	−	0.0774731i
$247$	17.3325			1.10284
$248$	−14.0111	+	10.1468i	−0.889706	+	0.644326i
$249$			1.81067i			0.114746i
$250$	10.2726	+	6.67857i	0.649695	+	0.422390i
$251$	−20.7727	−	20.7727i	−1.31116	−	1.31116i	−0.920560	−	0.390602i	$-0.872267\pi$
$251$	−20.7727	−	20.7727i	−1.31116	−	1.31116i	−0.390602	−	0.920560i	$-0.627733\pi$
$252$	4.72099	−	2.39003i	0.297394	−	0.150558i
$253$	14.6224	−	14.6224i	0.919304	−	0.919304i
$254$	−3.16497	−	14.9276i	−0.198588	−	0.936638i
$255$	−0.986076			−0.0617504
$256$	−1.60733	−	15.9191i	−0.100458	−	0.994941i
$257$		−	2.37658i		−	0.148247i	−0.997249	−	0.0741235i	$-0.976384\pi$
$257$		−	2.37658i		−	0.148247i	0.997249	−	0.0741235i	$-0.0236159\pi$
$258$	−0.984711	−	4.64438i	−0.0613055	−	0.289147i
$259$	−16.2699	+	18.0124i	−1.01096	+	1.11924i
$260$	−31.4301	+	13.9551i	−1.94921	+	0.865457i
$261$	−5.23306	−	5.23306i	−0.323918	−	0.323918i
$262$	11.5292	−	17.7336i	0.712279	−	1.09559i
$263$	−10.3071			−0.635562			−0.317781	−	0.948164i	$-0.602938\pi$
$263$	−10.3071			−0.635562			−0.317781	+	0.948164i	$0.602938\pi$
$264$	−8.77992	−	12.1236i	−0.540367	−	0.746156i
$265$	−15.1414			−0.930130
$266$	11.5137	+	6.67949i	0.705948	+	0.409546i
$267$	−1.96641	+	1.96641i	−0.120342	+	0.120342i
$268$	−1.79052	−	0.689418i	−0.109373	−	0.0421129i
$269$	−0.797673	−	0.797673i	−0.0486350	−	0.0486350i	0.682371	−	0.731006i	$-0.260949\pi$
$269$	−0.797673	−	0.797673i	−0.0486350	−	0.0486350i	−0.731006	+	0.682371i	$0.760949\pi$
$270$	−4.88245	+	1.03519i	−0.297137	+	0.0629995i
$271$	−5.41192			−0.328751			−0.164375	−	0.986398i	$-0.552561\pi$
$271$	−5.41192			−0.328751			−0.164375	+	0.986398i	$0.552561\pi$
$272$	0.829031	+	0.749539i	0.0502674	+	0.0454475i
$273$	0.654349	+	12.8738i	0.0396030	+	0.779156i
$274$	−0.321046	−	1.51421i	−0.0193951	−	0.0914769i
$275$	−27.8982	−	27.8982i	−1.68233	−	1.68233i
$276$	−2.80804	+	7.29289i	−0.169024	+	0.438980i
$277$	6.22699	+	6.22699i	0.374143	+	0.374143i	0.868984	−	0.494840i	$-0.164774\pi$
$277$	6.22699	+	6.22699i	0.374143	+	0.374143i	−0.494840	+	0.868984i	$0.664774\pi$
$278$	9.98269	+	6.49009i	0.598722	+	0.389250i
$279$		−	6.11626i		−	0.366171i
$280$	−26.2564	−	2.84225i	−1.56912	−	0.169857i
$281$			28.1356i			1.67843i	0.543802	+	0.839214i	$0.316984\pi$
$281$			28.1356i			1.67843i	−0.543802	+	0.839214i	$0.683016\pi$
$282$	−4.28441	+	6.59003i	−0.255133	+	0.392431i
$283$	−9.53287	−	9.53287i	−0.566671	−	0.566671i	0.364524	−	0.931194i	$-0.381232\pi$
$283$	−9.53287	−	9.53287i	−0.566671	−	0.566671i	−0.931194	+	0.364524i	$0.881232\pi$
$284$	−26.3173	+	11.6850i	−1.56165	+	0.693376i
$285$	−8.87768	−	8.87768i	−0.525869	−	0.525869i
$286$	35.6721	−	7.56328i	2.10934	−	0.447226i
$287$	0.137641	+	2.70798i	0.00812472	+	0.159847i
$288$	4.89173	+	2.84095i	0.288248	+	0.167404i
$289$	16.9219			0.995408
$290$	7.66108	+	36.1334i	0.449874	+	2.12183i
$291$	9.44980	+	9.44980i	0.553957	+	0.553957i
$292$	−9.38922	+	4.16885i	−0.549463	+	0.243963i
$293$	23.9288	−	23.9288i	1.39793	−	1.39793i	0.591981	−	0.805952i	$-0.298346\pi$
$293$	23.9288	−	23.9288i	1.39793	−	1.39793i	0.805952	−	0.591981i	$-0.201654\pi$
$294$	−4.52655	+	8.80400i	−0.263994	+	0.513459i
$295$	−9.25226			−0.538687
$296$	−25.6227	−	4.09855i	−1.48929	−	0.238223i
$297$	5.29232			0.307091
$298$	−14.9790	−	9.73839i	−0.867712	−	0.564130i
$299$	−13.4614	−	13.4614i	−0.778493	−	0.778493i
$300$	13.9142	+	5.35748i	0.803334	+	0.309314i
$301$	6.59124	+	5.95361i	0.379913	+	0.343160i
$302$	13.5366	−	2.87006i	0.778945	−	0.165154i
$303$			4.79617i			0.275533i
$304$	0.715663	+	14.2119i	0.0410461	+	0.815111i
$305$	35.0430			2.00656
$306$	−0.386550	+	0.0819571i	−0.0220976	+	0.00468517i
$307$	3.33186	−	3.33186i	0.190159	−	0.190159i	−0.605606	−	0.795765i	$-0.707069\pi$
$307$	3.33186	−	3.33186i	0.190159	−	0.190159i	0.795765	+	0.605606i	$0.207069\pi$
$308$	26.6111	+	8.72298i	1.51631	+	0.497038i
$309$	−6.24718	−	6.24718i	−0.355390	−	0.355390i
$310$	−16.6388	+	25.5929i	−0.945023	+	1.45358i
$311$			24.9257i			1.41340i	0.707511	+	0.706702i	$0.249818\pi$
$311$			24.9257i			1.41340i	−0.707511	+	0.706702i	$0.750182\pi$
$312$	−11.1610	+	8.08280i	−0.631867	+	0.457598i
$313$	−2.83693			−0.160353			−0.0801764	−	0.996781i	$-0.525548\pi$
$313$	−2.83693			−0.160353			−0.0801764	+	0.996781i	$0.525548\pi$
$314$	3.00891	+	1.95619i	0.169802	+	0.110394i
$315$	6.25878	−	6.92910i	0.352643	−	0.390411i
$316$	10.3474	+	23.3048i	0.582087	+	1.31100i
$317$	−17.3384	+	17.3384i	−0.973822	+	0.973822i	−0.999666	−	0.0258438i	$-0.991773\pi$
$317$	−17.3384	+	17.3384i	−0.973822	+	0.973822i	0.0258438	+	0.999666i	$0.491773\pi$
$318$	−5.93556	+	1.25847i	−0.332850	+	0.0705715i
$319$		−	39.1667i		−	2.19291i
$320$	−12.7404	−	25.1953i	−0.712209	−	1.40846i
$321$		−	9.66319i		−	0.539347i
$322$	−3.75450	−	14.1299i	−0.209230	−	0.787427i
$323$	−0.702857	−	0.702857i	−0.0391080	−	0.0391080i
$324$	−1.82792	+	0.811604i	−0.101551	+	0.0450891i
$325$	−25.6831	+	25.6831i	−1.42464	+	1.42464i
$326$	−2.63203	−	1.71118i	−0.145775	−	0.0947732i
$327$		−	9.83521i		−	0.543888i
$328$	−2.34770	+	1.70021i	−0.129630	+	0.0938782i
$329$	−0.746480	−	14.6864i	−0.0411548	−	0.809686i
$330$	−22.1452	−	14.3974i	−1.21905	−	0.792548i
$331$	14.1730	−	14.1730i	0.779021	−	0.779021i	−0.200643	−	0.979664i	$-0.564303\pi$
$331$	14.1730	−	14.1730i	0.779021	−	0.779021i	0.979664	+	0.200643i	$0.0643032\pi$
$332$	1.30123	−	3.37948i	0.0714141	−	0.185473i
$333$	6.48710	−	6.48710i	0.355491	−	0.355491i
$334$	−3.06451	−	14.4538i	−0.167683	−	0.790874i
$335$	−3.38563			−0.184977
$336$	−10.5290	+	1.06810i	−0.574402	+	0.0582698i
$337$	−24.5029			−1.33476			−0.667379	−	0.744719i	$-0.732584\pi$
$337$	−24.5029			−1.33476			−0.667379	+	0.744719i	$0.732584\pi$
$338$	−3.14955	−	14.8548i	−0.171313	−	0.807995i
$339$	1.20331	−	1.20331i	0.0653546	−	0.0653546i
$340$	1.84044	+	0.708639i	0.0998118	+	0.0384313i
$341$	22.8885	−	22.8885i	1.23948	−	1.23948i
$342$	−4.21799	−	2.74226i	−0.228083	−	0.148285i
$343$	−2.81072	−	18.3057i	−0.151765	−	0.988417i
$344$	−1.49977	+	9.37606i	−0.0808623	+	0.505523i
$345$			13.7899i			0.742421i
$346$	7.18640	+	4.67213i	0.386343	+	0.251175i
$347$	−1.61394	+	1.61394i	−0.0866408	+	0.0866408i	−0.749099	−	0.662458i	$-0.769513\pi$
$347$	−1.61394	+	1.61394i	−0.0866408	+	0.0866408i	0.662458	+	0.749099i	$0.269513\pi$
$348$	6.00641	+	13.5278i	0.321977	+	0.725169i
$349$	3.45869	+	3.45869i	0.185139	+	0.185139i	0.793591	−	0.608452i	$-0.208209\pi$
$349$	3.45869	+	3.45869i	0.185139	+	0.185139i	−0.608452	+	0.793591i	$0.708209\pi$
$350$	−26.9585	+	7.16324i	−1.44099	+	0.382891i
$351$		−	4.87211i		−	0.260054i
$352$	7.67451	+	28.9375i	0.409053	+	1.54237i
$353$		−	4.93908i		−	0.262881i	−0.991324	−	0.131440i	$-0.958040\pi$
$353$		−	4.93908i		−	0.262881i	0.991324	−	0.131440i	$-0.0419602\pi$
$354$	−3.62696	+	0.768996i	−0.192771	+	0.0408717i
$355$	−35.9286	+	35.9286i	−1.90689	+	1.90689i
$356$	5.08331	−	2.25701i	0.269415	−	0.119621i
$357$	0.495516	−	0.548585i	0.0262255	−	0.0290342i
$358$	1.27596	+	0.829549i	0.0674368	+	0.0438430i
$359$	1.22033			0.0644067			0.0322033	−	0.999481i	$-0.489748\pi$
$359$	1.22033			0.0644067			0.0322033	+	0.999481i	$0.489748\pi$
$360$	9.85667	+	1.57665i	0.519492	+	0.0830968i
$361$			6.34429i			0.333910i
$362$	19.3660	−	29.7876i	1.01785	−	1.56560i
$363$	12.0269	+	12.0269i	0.631249	+	0.631249i
$364$	8.03038	−	24.4982i	0.420906	−	1.28405i
$365$	−12.8182	+	12.8182i	−0.670937	+	0.670937i
$366$	13.7371	−	2.91258i	0.718052	−	0.152243i
$367$	28.3127			1.47791			0.738956	−	0.673754i	$-0.235319\pi$
$367$	28.3127			1.47791			0.738956	+	0.673754i	$0.235319\pi$
$368$	10.4820	−	11.5937i	0.546412	−	0.604361i
$369$		−	1.02484i		−	0.0533511i
$370$	−44.7923	+	9.49696i	−2.32864	+	0.493724i
$371$	7.60876	−	8.42366i	0.395027	−	0.437334i
$372$	−4.39543	+	11.4156i	−0.227892	+	0.591869i
$373$	19.3199	+	19.3199i	1.00035	+	1.00035i	1.00000		0.000345348i	$0.000109928\pi$
$373$	19.3199	+	19.3199i	1.00035	+	1.00035i	0.000345348		1.00000i	$0.499890\pi$
$374$	−1.75326	−	1.13986i	−0.0906590	−	0.0589406i
$375$	8.66398			0.447406
$376$	12.7324	−	9.22084i	0.656625	−	0.475529i
$377$	−36.0569			−1.85702
$378$	1.87759	−	3.23646i	0.0965727	−	0.166465i
$379$	−1.08467	+	1.08467i	−0.0557156	+	0.0557156i	−0.734416	−	0.678700i	$-0.762544\pi$
$379$	−1.08467	+	1.08467i	−0.0557156	+	0.0557156i	0.678700	+	0.734416i	$0.262544\pi$
$380$	10.1896	+	22.9495i	0.522717	+	1.17728i
$381$	−7.62970	−	7.62970i	−0.390881	−	0.390881i
$382$	5.09940	+	24.0513i	0.260908	+	1.23057i
$383$	−5.96681			−0.304890			−0.152445	−	0.988312i	$-0.548715\pi$
$383$	−5.96681			−0.304890			−0.152445	+	0.988312i	$0.548715\pi$
$384$	−7.08842	−	8.81784i	−0.361730	−	0.449983i
$385$	49.3521	−	2.50848i	2.51522	−	0.127844i
$386$	16.8460	−	3.57172i	0.857438	−	0.181796i
$387$	−2.37381	−	2.37381i	−0.120668	−	0.120668i
$388$	−10.8463	−	24.4284i	−0.550638	−	1.24017i
$389$	−1.04147	−	1.04147i	−0.0528046	−	0.0528046i	0.680211	−	0.733016i	$-0.261888\pi$
$389$	−1.04147	−	1.04147i	−0.0528046	−	0.0528046i	−0.733016	+	0.680211i	$0.761888\pi$
$390$	−13.2542	+	20.3869i	−0.671153	+	1.03233i
$391$			1.09176i			0.0552127i
$392$	14.7754	−	13.1790i	0.746272	−	0.665641i
$393$		−	14.9567i		−	0.754465i
$394$	−20.7501	−	13.4904i	−1.04537	−	0.679635i
$395$	31.8159	+	31.8159i	1.60083	+	1.60083i
$396$	−9.87772	−	3.80330i	−0.496374	−	0.191123i
$397$	24.7911	+	24.7911i	1.24423	+	1.24423i	0.958231	+	0.285997i	$0.0923247\pi$
$397$	24.7911	+	24.7911i	1.24423	+	1.24423i	0.285997	+	0.958231i	$0.407675\pi$
$398$	−2.06591	−	9.74386i	−0.103555	−	0.488416i
$399$	9.40009	−	0.477789i	0.470593	−	0.0239194i
$400$	−22.1196	−	19.9987i	−1.10598	−	0.999935i
$401$	−1.92520			−0.0961401			−0.0480701	−	0.998844i	$-0.515307\pi$
$401$	−1.92520			−0.0961401			−0.0480701	+	0.998844i	$0.515307\pi$
$402$	−1.32719	+	0.281394i	−0.0661944	+	0.0140347i
$403$	−21.0711	−	21.0711i	−1.04963	−	1.04963i
$404$	3.44675	−	8.95170i	0.171482	−	0.445364i
$405$	−2.49549	+	2.49549i	−0.124002	+	0.124002i
$406$	−23.9520	−	13.8954i	−1.18872	−	0.689617i
$407$	48.5525			2.40666
$408$	0.780365	+	0.124825i	0.0386338	+	0.00617978i
$409$	8.21692			0.406300			0.203150	−	0.979148i	$-0.434882\pi$
$409$	8.21692			0.406300			0.203150	+	0.979148i	$0.434882\pi$
$410$	−2.78801	+	4.28835i	−0.137690	+	0.211786i
$411$	−0.773936	−	0.773936i	−0.0381755	−	0.0381755i
$412$	7.17040	+	16.1494i	0.353260	+	0.795624i
$413$	4.64938	−	5.14733i	0.228781	−	0.253284i
$414$	1.14614	+	5.40574i	0.0563295	+	0.265678i
$415$		−	6.39013i		−	0.313679i
$416$	26.6398	−	7.06516i	1.30613	−	0.346398i
$417$	8.41948			0.412304
$418$	−5.52251	−	26.0469i	−0.270115	−	1.27399i
$419$	26.8651	−	26.8651i	1.31244	−	1.31244i	0.392836	−	0.919608i	$-0.371494\pi$
$419$	26.8651	−	26.8651i	1.31244	−	1.31244i	0.919608	−	0.392836i	$-0.128506\pi$
$420$	−16.6611	+	8.43481i	−0.812980	+	0.411577i
$421$	−17.0268	−	17.0268i	−0.829836	−	0.829836i	0.157658	−	0.987494i	$-0.449606\pi$
$421$	−17.0268	−	17.0268i	−0.829836	−	0.829836i	−0.987494	+	0.157658i	$0.949606\pi$
$422$	6.41693	+	4.17187i	0.312371	+	0.203084i
$423$			5.55809i			0.270244i
$424$	11.9827	+	1.91672i	0.581931	+	0.0930843i
$425$	2.08298			0.101039
$426$	−11.0981	+	17.0705i	−0.537706	+	0.827068i
$427$	−17.6096	+	19.4955i	−0.852186	+	0.943455i
$428$	−6.94441	+	18.0356i	−0.335671	+	0.871785i
$429$	18.2326	−	18.2326i	0.880276	−	0.880276i
$430$	3.47520	+	16.3908i	0.167589	+	0.790433i
$431$		−	3.65902i		−	0.176249i	−0.996109	−	0.0881245i	$-0.971913\pi$
$431$		−	3.65902i		−	0.176249i	0.996109	−	0.0881245i	$-0.0280873\pi$
$432$	3.99494	−	0.201171i	0.192207	−	0.00967885i
$433$			11.7857i			0.566383i	0.959063	+	0.283192i	$0.0913933\pi$
$433$			11.7857i			0.566383i	−0.959063	+	0.283192i	$0.908607\pi$
$434$	−5.87692	−	22.1175i	−0.282101	−	1.06167i
$435$	18.4683	+	18.4683i	0.885488	+	0.885488i
$436$	−7.06803	+	18.3567i	−0.338497	+	0.879126i
$437$	−9.82917	+	9.82917i	−0.470193	+	0.470193i
$438$	−3.95947	+	6.09023i	−0.189191	+	0.291003i
$439$			2.20601i			0.105287i	0.998613	+	0.0526435i	$0.0167647\pi$
$439$			2.20601i			0.105287i	−0.998613	+	0.0526435i	$0.983235\pi$
$440$	30.9858	+	42.7861i	1.47719	+	2.03975i
$441$	0.709760	+	6.96392i	0.0337981	+	0.331615i
$442$	−1.04935	+	1.61405i	−0.0499126	+	0.0767727i
$443$	−12.4137	+	12.4137i	−0.589792	+	0.589792i	−0.937575	−	0.347783i	$-0.886935\pi$
$443$	−12.4137	+	12.4137i	−0.589792	+	0.589792i	0.347783	+	0.937575i	$0.386935\pi$
$444$	−16.7696	+	7.44577i	−0.795851	+	0.353361i
$445$	6.93977	−	6.93977i	0.328977	−	0.328977i
$446$	−27.6215	+	5.85636i	−1.30792	+	0.277307i
$447$	−12.6334			−0.597541
$448$	20.4191	+	5.57306i	0.964713	+	0.263302i
$449$	12.5409			0.591840			0.295920	−	0.955213i	$-0.404374\pi$
$449$	12.5409			0.591840			0.295920	+	0.955213i	$0.404374\pi$
$450$	10.3137	−	2.18672i	0.486190	−	0.103083i
$451$	3.83519	−	3.83519i	0.180592	−	0.180592i
$452$	−3.11063	+	1.38113i	−0.146312	+	0.0649629i
$453$	6.91877	−	6.91877i	0.325072	−	0.325072i
$454$	1.01029	−	1.55397i	0.0474153	−	0.0729315i
$455$	−2.30930	−	45.4336i	−0.108262	−	2.12996i
$456$	5.90185	+	8.14947i	0.276380	+	0.381634i
$457$			28.8831i			1.35110i	0.737316	+	0.675548i	$0.236093\pi$
$457$			28.8831i			1.35110i	−0.737316	+	0.675548i	$0.763907\pi$
$458$	−15.5044	+	23.8480i	−0.724474	+	1.11434i
$459$	−0.197571	+	0.197571i	−0.00922184	+	0.00922184i
$460$	9.91002	−	25.7378i	0.462057	−	1.20003i
$461$	0.322947	+	0.322947i	0.0150412	+	0.0150412i	0.714587	−	0.699546i	$-0.246614\pi$
$461$	0.322947	+	0.322947i	0.0150412	+	0.0150412i	−0.699546	+	0.714587i	$0.746614\pi$
$462$	19.1380	−	5.08522i	0.890378	−	0.236586i
$463$		−	1.56052i		−	0.0725234i	−0.999342	−	0.0362617i	$-0.988455\pi$
$463$		−	1.56052i		−	0.0725234i	0.999342	−	0.0362617i	$-0.0115450\pi$
$464$	−1.48880	−	29.5652i	−0.0691158	−	1.37253i
$465$			21.5853i			1.00099i
$466$	6.29817	+	29.7053i	0.291757	+	1.37607i
$467$	−7.90873	+	7.90873i	−0.365973	+	0.365973i	−0.866006	−	0.500034i	$-0.833321\pi$
$467$	−7.90873	+	7.90873i	−0.365973	+	0.365973i	0.500034	+	0.866006i	$0.333321\pi$
$468$	−3.50132	+	9.09343i	−0.161848	+	0.420344i
$469$	1.70132	−	1.88353i	0.0785597	−	0.0869734i
$470$	15.1204	−	23.2573i	0.697451	−	1.07278i
$471$	2.53774			0.116933
$472$	7.32209	+	1.17123i	0.337027	+	0.0539100i
$473$		−	17.7667i		−	0.816915i
$474$	15.1164	+	9.82772i	0.694321	+	0.451402i
$475$	18.7532	+	18.7532i	0.860454	+	0.860454i
$476$	−1.31908	+	0.667794i	−0.0604600	+	0.0306083i
$477$	−3.03375	+	3.03375i	−0.138906	+	0.138906i
$478$	−2.59568	−	12.2425i	−0.118724	−	0.559960i
$479$	−27.9688			−1.27793			−0.638963	−	0.769237i	$-0.720636\pi$
$479$	−27.9688			−1.27793			−0.638963	+	0.769237i	$0.720636\pi$
$480$	−17.2637	−	10.0262i	−0.787976	−	0.457629i
$481$		−	44.6974i		−	2.03803i
$482$	−3.37402	−	15.9135i	−0.153682	−	0.724841i
$483$	−7.67174	−	6.92959i	−0.349076	−	0.315307i
$484$	−13.8043	−	31.0904i	−0.627466	−	1.41320i
$485$	−33.3499	−	33.3499i	−1.51434	−	1.51434i
$486$	−0.770842	+	1.18567i	−0.0349661	+	0.0537829i
$487$	−17.3498			−0.786192			−0.393096	−	0.919497i	$-0.628596\pi$
$487$	−17.3498			−0.786192			−0.393096	+	0.919497i	$0.628596\pi$
$488$	−27.7325	−	4.43602i	−1.25539	−	0.200809i
$489$	−2.21988			−0.100386
$490$	15.9749	−	31.0707i	0.721673	−	1.40363i
$491$	4.01880	−	4.01880i	0.181366	−	0.181366i	−0.610585	−	0.791951i	$-0.709066\pi$
$491$	4.01880	−	4.01880i	0.181366	−	0.181366i	0.791951	+	0.610585i	$0.209066\pi$
$492$	−0.736498	+	1.91279i	−0.0332039	+	0.0862353i
$493$	1.46216	+	1.46216i	0.0658524	+	0.0658524i
$494$	−23.9788	+	5.08403i	−1.07886	+	0.228741i
$495$	−18.6774			−0.839488
$496$	16.4075	−	18.1475i	0.736718	−	0.814849i
$497$	−1.93365	−	38.0428i	−0.0867359	−	1.70645i
$498$	−0.531112	−	2.50498i	−0.0237997	−	0.112251i
$499$	26.7221	+	26.7221i	1.19624	+	1.19624i	0.975282	+	0.220962i	$0.0709197\pi$
$499$	26.7221	+	26.7221i	1.19624	+	1.19624i	0.220962	+	0.975282i	$0.429080\pi$
$500$	−16.1707	−	6.22633i	−0.723175	−	0.278450i
$501$	−7.38753	−	7.38753i	−0.330050	−	0.330050i
$502$	34.8313	+	22.6451i	1.55460	+	1.01070i
$503$		−	12.5118i		−	0.557873i	−0.960310	−	0.278937i	$-0.910018\pi$
$503$		−	12.5118i		−	0.557873i	0.960310	−	0.278937i	$-0.0899819\pi$
$504$	−5.83025	+	4.69129i	−0.259700	+	0.208967i
$505$		−	16.9264i		−	0.753217i
$506$	−15.9404	+	24.5186i	−0.708639	+	1.08999i
$507$	−7.59251	−	7.59251i	−0.337195	−	0.337195i
$508$	8.75722	+	19.7233i	0.388539	+	0.875081i
$509$	14.4777	+	14.4777i	0.641715	+	0.641715i	0.950977	−	0.309262i	$-0.100082\pi$
$509$	14.4777	+	14.4777i	0.641715	+	0.641715i	−0.309262	+	0.950977i	$0.600082\pi$
$510$	1.36420	−	0.289240i	0.0604076	−	0.0128077i
$511$	−0.689866	−	13.5725i	−0.0305179	−	0.600413i
$512$	6.89312	+	21.5519i	0.304636	+	0.952469i
$513$	−3.55749			−0.157067
$514$	0.697108	+	3.28790i	0.0307481	+	0.145023i
$515$	22.0473	+	22.0473i	0.971520	+	0.971520i
$516$	2.72462	+	6.13648i	0.119945	+	0.270143i
$517$	−20.7997	+	20.7997i	−0.914768	+	0.914768i
$518$	17.2253	−	29.6918i	0.756835	−	1.30458i
$519$	6.06107			0.266051
$520$	39.3889	−	28.5255i	1.72732	−	1.25093i
$521$	28.9916			1.27015			0.635073	−	0.772452i	$-0.280970\pi$
$521$	28.9916			1.27015			0.635073	+	0.772452i	$0.280970\pi$
$522$	8.77472	+	5.70475i	0.384059	+	0.249690i
$523$	−14.1402	−	14.1402i	−0.618307	−	0.618307i	0.326790	−	0.945097i	$-0.394033\pi$
$523$	−14.1402	−	14.1402i	−0.618307	−	0.618307i	−0.945097	+	0.326790i	$0.894033\pi$
$524$	−10.7486	+	27.9156i	−0.469553	+	1.21950i
$525$	−13.2210	+	14.6370i	−0.577012	+	0.638810i
$526$	14.2594	−	3.02331i	0.621741	−	0.131823i
$527$			1.70893i			0.0744423i
$528$	15.7028	+	14.1972i	0.683377	+	0.617852i
$529$	−7.73217			−0.336181
$530$	20.9475	−	4.44134i	0.909903	−	0.192920i
$531$	−1.85379	+	1.85379i	−0.0804478	+	0.0804478i
$532$	−17.8879	−	5.86358i	−0.775541	−	0.254218i
$533$	−3.53068	−	3.53068i	−0.152931	−	0.152931i
$534$	2.14365	−	3.29724i	0.0927649	−	0.142686i
$535$			34.1029i			1.47440i
$536$	2.67933	+	0.428580i	0.115729	+	0.0185118i
$537$	1.07616			0.0464397
$538$	1.33752	+	0.869571i	0.0576648	+	0.0374899i
$539$	−23.4045	+	28.7167i	−1.00810	+	1.23692i
$540$	6.45103	−	2.86428i	0.277608	−	0.123259i
$541$	−15.6232	+	15.6232i	−0.671694	+	0.671694i	−0.958106	−	0.286412i	$-0.907537\pi$
$541$	−15.6232	+	15.6232i	−0.671694	+	0.671694i	0.286412	+	0.958106i	$0.407537\pi$
$542$	7.48718	−	1.58745i	0.321602	−	0.0681867i
$543$		−	25.1231i		−	1.07814i
$544$	−1.36679	−	0.793783i	−0.0586006	−	0.0340332i
$545$			34.7100i			1.48681i
$546$	−4.68145	−	17.6184i	−0.200348	−	0.753998i
$547$	2.55876	+	2.55876i	0.109404	+	0.109404i	0.759690	−	0.650285i	$-0.225351\pi$
$547$	2.55876	+	2.55876i	0.109404	+	0.109404i	−0.650285	+	0.759690i	$0.725351\pi$
$548$	0.888310	+	2.00068i	0.0379467	+	0.0854649i
$549$	7.02125	−	7.02125i	0.299660	−	0.299660i
$550$	46.7793	+	30.4129i	1.99468	+	1.29681i
$551$			26.3278i			1.12160i
$552$	1.74563	−	10.9131i	0.0742990	−	0.464492i
$553$	−33.6881	+	1.71230i	−1.43256	+	0.0728145i
$554$	−10.4413	−	6.78826i	−0.443609	−	0.288406i
$555$	−22.8940	+	22.8940i	−0.971797	+	0.971797i
$556$	−15.7143	−	6.05062i	−0.666437	−	0.256604i
$557$	9.19820	−	9.19820i	0.389740	−	0.389740i	−0.484855	−	0.874595i	$-0.661127\pi$
$557$	9.19820	−	9.19820i	0.389740	−	0.389740i	0.874595	+	0.484855i	$0.161127\pi$
$558$	1.79405	+	8.46161i	0.0759481	+	0.358208i
$559$	−16.3560			−0.691787
$560$	37.1584	−	3.76951i	1.57023	−	0.159291i
$561$	−1.47872			−0.0624314
$562$	−8.25284	−	38.9244i	−0.348125	−	1.64193i
$563$	24.4668	−	24.4668i	1.03115	−	1.03115i	0.0316557	−	0.999499i	$-0.489922\pi$
$563$	24.4668	−	24.4668i	1.03115	−	1.03115i	0.999499	−	0.0316557i	$-0.0100780\pi$
$564$	3.99430	−	10.3738i	0.168190	−	0.436814i
$565$	−4.24666	+	4.24666i	−0.178658	+	0.178658i
$566$	15.9846	+	10.3921i	0.671882	+	0.436814i
$567$	−0.134305	−	2.64234i	−0.00564029	−	0.110968i
$568$	32.9815	−	23.8852i	1.38387	−	1.00220i
$569$			27.5195i			1.15368i	0.816858	+	0.576838i	$0.195714\pi$
$569$			27.5195i			1.15368i	−0.816858	+	0.576838i	$0.804286\pi$
$570$	14.8860	+	9.67788i	0.623504	+	0.405362i
$571$	10.7327	−	10.7327i	0.449151	−	0.449151i	−0.445921	−	0.895072i	$-0.647124\pi$
$571$	10.7327	−	10.7327i	0.449151	−	0.449151i	0.895072	+	0.445921i	$0.147124\pi$
$572$	−47.1325	+	20.9270i	−1.97071	+	0.875001i
$573$	12.2930	+	12.2930i	0.513546	+	0.513546i
$574$	−0.984737	−	3.70601i	−0.0411021	−	0.154686i
$575$		−	29.1296i		−	1.21479i
$576$	−7.60083	−	2.49547i	−0.316701	−	0.103978i
$577$			18.9614i			0.789372i	0.918816	+	0.394686i	$0.129147\pi$
$577$			18.9614i			0.789372i	−0.918816	+	0.394686i	$0.870853\pi$
$578$	−23.4108	+	4.96361i	−0.973761	+	0.206459i
$579$	8.61023	−	8.61023i	0.357829	−	0.357829i
$580$	−21.1976	−	47.7419i	−0.880182	−	1.98238i
$581$	3.55503	+	3.21112i	0.147488	+	0.133220i
$582$	−15.8453	−	10.3016i	−0.656808	−	0.427014i
$583$	−22.7060			−0.940387
$584$	11.7668	−	8.52152i	0.486913	−	0.352623i
$585$			17.1944i			0.710903i
$586$	−26.0856	+	40.1234i	−1.07759	+	1.65748i
$587$	−27.8565	−	27.8565i	−1.14976	−	1.14976i	−0.986599	−	0.163161i	$-0.947831\pi$
$587$	−27.8565	−	27.8565i	−1.14976	−	1.14976i	−0.163161	−	0.986599i	$-0.552169\pi$
$588$	3.67988	−	13.5077i	0.151756	−	0.557049i
$589$	−15.3856	+	15.3856i	−0.633953	+	0.633953i
$590$	12.8001	−	2.71391i	0.526973	−	0.111730i
$591$	−17.5008			−0.719887
$592$	36.6502	−	1.84557i	1.50631	−	0.0758526i
$593$		−	11.1833i		−	0.459242i	−0.973280	−	0.229621i	$-0.926251\pi$
$593$		−	11.1833i		−	0.459242i	0.973280	−	0.229621i	$-0.0737487\pi$
$594$	−7.32171	+	1.55236i	−0.300413	+	0.0636942i
$595$	−1.74875	+	1.93605i	−0.0716919	+	0.0793701i
$596$	23.5794	+	9.07897i	0.965849	+	0.371889i
$597$	−4.98023	−	4.98023i	−0.203827	−	0.203827i
$598$	22.5719	+	14.6748i	0.923032	+	0.600096i
$599$	34.2634			1.39997			0.699983	−	0.714160i	$-0.253191\pi$
$599$	34.2634			1.39997			0.699983	+	0.714160i	$0.253191\pi$
$600$	−20.8212	−	3.33050i	−0.850020	−	0.135967i
$601$	19.8458			0.809525			0.404763	−	0.914422i	$-0.367354\pi$
$601$	19.8458			0.809525			0.404763	+	0.914422i	$0.367354\pi$
$602$	−10.8650	−	6.30321i	−0.442826	−	0.256900i
$603$	−0.678348	+	0.678348i	−0.0276245	+	0.0276245i
$604$	−17.8855	+	7.94123i	−0.727751	+	0.323124i
$605$	−42.4449	−	42.4449i	−1.72563	−	1.72563i
$606$	−1.40683	−	6.63531i	−0.0571486	−	0.269541i
$607$	10.2481			0.415956			0.207978	−	0.978133i	$-0.433312\pi$
$607$	10.2481			0.415956			0.207978	+	0.978133i	$0.433312\pi$
$608$	−5.15879	−	19.4517i	−0.209217	−	0.788872i
$609$	−19.5551	+	0.993948i	−0.792412	+	0.0402768i
$610$	−48.4806	+	10.2789i	−1.96292	+	0.416182i
$611$	19.1482	+	19.1482i	0.774652	+	0.774652i
$612$	0.510736	−	0.226769i	0.0206453	−	0.00916658i
$613$	−31.8582	−	31.8582i	−1.28674	−	1.28674i	−0.936755	−	0.349987i	$-0.886186\pi$
$613$	−31.8582	−	31.8582i	−1.28674	−	1.28674i	−0.349987	−	0.936755i	$-0.613814\pi$
$614$	−3.63218	+	5.58681i	−0.146583	+	0.225465i
$615$			3.61683i			0.145845i
$616$	−39.3740	−	4.26222i	−1.58643	−	0.171730i
$617$			0.649025i			0.0261288i	0.999915	+	0.0130644i	$0.00415864\pi$
$617$			0.649025i			0.0261288i	−0.999915	+	0.0130644i	$0.995841\pi$
$618$	10.4752	+	6.81028i	0.421373	+	0.273949i
$619$	−1.02599	−	1.02599i	−0.0412378	−	0.0412378i	0.686187	−	0.727425i	$-0.259283\pi$
$619$	−1.02599	−	1.02599i	−0.0412378	−	0.0412378i	−0.727425	+	0.686187i	$0.759283\pi$
$620$	15.5122	−	40.2873i	0.622983	−	1.61798i
$621$	2.76295	+	2.76295i	0.110874	+	0.110874i
$622$	−7.31130	−	34.4837i	−0.293156	−	1.38267i
$623$	0.373492	+	7.34814i	0.0149636	+	0.294397i
$624$	13.0699	−	14.4560i	0.523215	−	0.578704i
$625$	6.69827			0.267931
$626$	3.92478	−	0.832140i	0.156866	−	0.0332590i
$627$	−13.3129	−	13.3129i	−0.531668	−	0.531668i
$628$	−4.73650	−	1.82373i	−0.189007	−	0.0727748i
$629$	−1.81255	+	1.81255i	−0.0722710	+	0.0722710i
$630$	−6.62631	+	11.4220i	−0.263998	+	0.455063i
$631$	34.9771			1.39242			0.696208	−	0.717840i	$-0.254869\pi$
$631$	34.9771			1.39242			0.696208	+	0.717840i	$0.254869\pi$
$632$	−21.1511	−	29.2061i	−0.841344	−	1.16176i
$633$	5.41210			0.215112
$634$	18.9012	−	29.0728i	0.750664	−	1.15463i
$635$	26.9264	+	26.9264i	1.06854	+	1.06854i
$636$	7.84247	−	3.48208i	0.310974	−	0.138074i
$637$	26.4366	+	21.5462i	1.04746	+	0.853692i
$638$	11.4885	+	54.1855i	0.454835	+	2.14523i
$639$			14.3974i			0.569552i
$640$	25.0162	+	31.1196i	0.988851	+	1.23011i
$641$	−10.8753			−0.429550			−0.214775	−	0.976664i	$-0.568902\pi$
$641$	−10.8753			−0.429550			−0.214775	+	0.976664i	$0.568902\pi$
$642$	2.83445	+	13.3686i	0.111867	+	0.527618i
$643$	13.4232	−	13.4232i	0.529358	−	0.529358i	−0.391023	−	0.920381i	$-0.627879\pi$
$643$	13.4232	−	13.4232i	0.529358	−	0.529358i	0.920381	+	0.391023i	$0.127879\pi$
$644$	9.33883	+	18.4468i	0.368001	+	0.726907i
$645$	8.37756	+	8.37756i	0.329866	+	0.329866i
$646$	1.17854	+	0.766210i	0.0463690	+	0.0301461i
$647$		−	5.29145i		−	0.208028i	−0.994576	−	0.104014i	$-0.966831\pi$
$647$		−	5.29145i		−	0.208028i	0.994576	−	0.104014i	$-0.0331687\pi$
$648$	2.29079	−	1.65899i	0.0899909	−	0.0651715i
$649$	−13.8747			−0.544628
$650$	27.9981	−	43.0650i	1.09818	−	1.68915i
$651$	−12.0086	−	10.8469i	−0.470653	−	0.425123i
$652$	4.14324	+	1.59530i	0.162262	+	0.0624769i
$653$	31.5939	−	31.5939i	1.23637	−	1.23637i	0.274889	−	0.961476i	$-0.411359\pi$
$653$	31.5939	−	31.5939i	1.23637	−	1.23637i	0.961476	−	0.274889i	$-0.0886412\pi$
$654$	2.88490	+	13.6066i	0.112809	+	0.532061i
$655$			52.7845i			2.06246i
$656$	2.74924	−	3.04080i	0.107340	−	0.118723i
$657$			5.13655i			0.200396i
$658$	5.34059	+	20.0990i	0.208198	+	0.783542i
$659$	−17.4610	−	17.4610i	−0.680183	−	0.680183i	0.279858	−	0.960041i	$-0.409712\pi$
$659$	−17.4610	−	17.4610i	−0.680183	−	0.680183i	−0.960041	+	0.279858i	$0.909712\pi$
$660$	34.8601	+	13.4225i	1.35693	+	0.522468i
$661$	23.6650	−	23.6650i	0.920462	−	0.920462i	−0.0766003	−	0.997062i	$-0.524407\pi$
$661$	23.6650	−	23.6650i	0.920462	−	0.920462i	0.997062	+	0.0766003i	$0.0244065\pi$
$662$	−15.4505	+	23.7651i	−0.600503	+	0.923658i
$663$			1.36131i			0.0528687i
$664$	−0.808914	+	5.05705i	−0.0313920	+	0.196252i
$665$	−33.1744	+	1.68619i	−1.28645	+	0.0653878i
$666$	−7.07182	+	10.8775i	−0.274028	+	0.421493i
$667$	20.4477	−	20.4477i	0.791738	−	0.791738i
$668$	8.47927	+	19.0973i	0.328073	+	0.738897i
$669$	−14.1178	+	14.1178i	−0.545824	+	0.545824i
$670$	4.68388	−	0.993085i	0.180954	−	0.0383662i
$671$	52.5503			2.02868
$672$	14.2531	−	4.56608i	0.549825	−	0.176140i
$673$	11.1080			0.428182			0.214091	−	0.976814i	$-0.431321\pi$
$673$	11.1080			0.428182			0.214091	+	0.976814i	$0.431321\pi$
$674$	33.8988	−	7.18728i	1.30573	−	0.276844i
$675$	5.27146	−	5.27146i	0.202899	−	0.202899i
$676$	8.71454	+	19.6272i	0.335175	+	0.754892i
$677$	4.87288	−	4.87288i	0.187280	−	0.187280i	−0.607239	−	0.794519i	$-0.707723\pi$
$677$	4.87288	−	4.87288i	0.187280	−	0.187280i	0.794519	+	0.607239i	$0.207723\pi$
$678$	−1.31177	+	2.01768i	−0.0503781	+	0.0774886i
$679$	35.3123	−	1.79486i	1.35516	−	0.0688804i
$680$	−2.75403	−	0.440529i	−0.105612	−	0.0168935i
$681$		−	1.31063i		−	0.0502236i
$682$	−24.9516	+	38.3790i	−0.955444	+	1.46961i
$683$	−28.2027	+	28.2027i	−1.07915	+	1.07915i	−0.0825613	+	0.996586i	$0.526310\pi$
$683$	−28.2027	+	28.2027i	−1.07915	+	1.07915i	−0.996586	+	0.0825613i	$0.973690\pi$
$684$	6.63979	+	2.55657i	0.253879	+	0.0977530i
$685$	2.73135	+	2.73135i	0.104359	+	0.104359i
$686$	9.25803	+	24.5008i	0.353473	+	0.935445i
$687$			20.1136i			0.767382i
$688$	−0.675347	−	13.4113i	−0.0257474	−	0.511302i
$689$			20.9032i			0.796347i
$690$	−4.04490	−	19.0777i	−0.153987	−	0.726276i
$691$	−29.1889	+	29.1889i	−1.11040	+	1.11040i	−0.117303	+	0.993096i	$0.537425\pi$
$691$	−29.1889	+	29.1889i	−1.11040	+	1.11040i	−0.993096	+	0.117303i	$0.962575\pi$
$692$	−11.3125	−	4.35576i	−0.430038	−	0.165581i
$693$	9.38565	−	10.3909i	0.356531	−	0.394716i
$694$	1.75941	−	2.70623i	0.0667864	−	0.102727i
$695$	−29.7137			−1.12710
$696$	−12.2777	−	16.9534i	−0.465384	−	0.642617i
$697$			0.286349i			0.0108462i
$698$	−5.79948	−	3.77044i	−0.219513	−	0.142713i
$699$	15.1828	+	15.1828i	0.574266	+	0.574266i
$700$	35.1948	−	17.8176i	1.33024	−	0.673443i
$701$	−21.3203	+	21.3203i	−0.805256	+	0.805256i	−0.983912	−	0.178656i	$-0.942825\pi$
$701$	−21.3203	+	21.3203i	−0.805256	+	0.805256i	0.178656	+	0.983912i	$0.442825\pi$
$702$	1.42911	+	6.74036i	0.0539381	+	0.254399i
$703$	−32.6369			−1.23092
$704$	−19.1054	−	37.7827i	−0.720063	−	1.42399i
$705$		−	19.6154i		−	0.738758i
$706$	1.44875	+	6.83302i	0.0545244	+	0.257164i
$707$	9.41673	+	8.50576i	0.354152	+	0.319892i
$708$	4.79219	−	2.12775i	0.180102	−	0.0799657i
$709$	−23.3213	−	23.3213i	−0.875849	−	0.875849i	0.117253	−	0.993102i	$-0.462591\pi$
$709$	−23.3213	−	23.3213i	−0.875849	−	0.875849i	−0.993102	+	0.117253i	$0.962591\pi$
$710$	39.1671	−	60.2445i	1.46991	−	2.26094i
$711$	12.7493			0.478137
$712$	−6.37052	+	4.61353i	−0.238745	+	0.172899i
$713$	23.8987			0.895015
$714$	−0.524613	+	0.904293i	−0.0196331	+	0.0338423i
$715$	−64.3456	+	64.3456i	−2.40639	+	2.40639i
$716$	−2.00857	−	0.773377i	−0.0750639	−	0.0289025i
$717$	−6.25733	−	6.25733i	−0.233684	−	0.233684i
$718$	−1.68828	+	0.357953i	−0.0630061	+	0.0133587i
$719$	36.4120			1.35794			0.678969	−	0.734167i	$-0.262427\pi$
$719$	36.4120			1.35794			0.678969	+	0.734167i	$0.262427\pi$
$720$	−14.0988	+	0.709965i	−0.525430	+	0.0264588i
$721$	−23.3447	+	1.18657i	−0.869401	+	0.0441900i
$722$	−1.86093	−	8.77707i	−0.0692567	−	0.326649i
$723$	−8.13364	−	8.13364i	−0.302493	−	0.302493i
$724$	−18.0546	+	46.8905i	−0.670995	+	1.74267i
$725$	−39.0123	−	39.0123i	−1.44888	−	1.44888i
$726$	−20.1665	−	13.1110i	−0.748450	−	0.486593i
$727$			18.0933i			0.671042i	0.942033	+	0.335521i	$0.108912\pi$
$727$			18.0933i			0.671042i	−0.942033	+	0.335521i	$0.891088\pi$
$728$	−3.92380	+	36.2478i	−0.145426	+	1.34343i
$729$			1.00000i			0.0370370i
$730$	13.9736	−	21.4934i	0.517187	−	0.795507i
$731$	0.663262	+	0.663262i	0.0245316	+	0.0245316i
$732$	−18.1504	+	8.05886i	−0.670860	+	0.297864i
$733$	−9.69069	−	9.69069i	−0.357934	−	0.357934i	0.505117	−	0.863051i	$-0.331449\pi$
$733$	−9.69069	−	9.69069i	−0.357934	−	0.357934i	−0.863051	+	0.505117i	$0.831449\pi$
$734$	−39.1695	+	8.30479i	−1.44577	+	0.306536i
$735$	−2.50486	−	24.5768i	−0.0923930	−	0.906529i
$736$	−11.1007	+	19.1140i	−0.409178	+	0.704551i
$737$	−5.07707			−0.187016
$738$	0.300610	+	1.41783i	0.0110656	+	0.0521909i
$739$	15.9416	+	15.9416i	0.586419	+	0.586419i	0.936660	−	0.350240i	$-0.113900\pi$
$739$	15.9416	+	15.9416i	0.586419	+	0.586419i	−0.350240	+	0.936660i	$0.613900\pi$
$740$	59.1827	−	26.2773i	2.17560	−	0.965974i
$741$	−12.2559	+	12.2559i	−0.450232	+	0.450232i
$742$	−8.05555	+	13.8856i	−0.295729	+	0.509757i
$743$	−31.1489			−1.14274			−0.571371	−	0.820692i	$-0.693588\pi$
$743$	−31.1489			−1.14274			−0.571371	+	0.820692i	$0.693588\pi$
$744$	2.73244	−	17.0822i	0.100176	−	0.626266i
$745$	44.5854			1.63348
$746$	−32.3953	−	21.0613i	−1.18607	−	0.771109i
$747$	−1.28033	−	1.28033i	−0.0468450	−	0.0468450i
$748$	2.75991	+	1.06267i	0.100912	+	0.0388551i
$749$	−18.9726	−	17.1372i	−0.693242	−	0.626179i
$750$	−11.9863	+	2.54135i	−0.437677	+	0.0927971i
$751$			4.20458i			0.153427i	0.997053	+	0.0767137i	$0.0244428\pi$
$751$			4.20458i			0.153427i	−0.997053	+	0.0767137i	$0.975557\pi$
$752$	−14.9101	+	16.4914i	−0.543716	+	0.601379i
$753$	29.3770			1.07056
$754$	49.8832	−	10.5763i	1.81664	−	0.385168i
$755$	−24.4174	+	24.4174i	−0.888642	+	0.888642i
$756$	−1.64824	+	5.02825i	−0.0599457	+	0.182876i
$757$	−34.4236	−	34.4236i	−1.25115	−	1.25115i	−0.955206	−	0.295940i	$-0.904367\pi$
$757$	−34.4236	−	34.4236i	−1.25115	−	1.25115i	−0.295940	−	0.955206i	$-0.595633\pi$
$758$	1.18243	−	1.81875i	0.0429479	−	0.0660600i
$759$			20.6792i			0.750609i
$760$	−20.8286	−	28.7608i	−0.755532	−	1.04326i
$761$	−20.5632			−0.745415			−0.372708	−	0.927949i	$-0.621571\pi$
$761$	−20.5632			−0.745415			−0.372708	+	0.927949i	$0.621571\pi$
$762$	12.7933	+	8.31740i	0.463454	+	0.301308i
$763$	−19.3103	−	17.4422i	−0.699080	−	0.631451i
$764$	−14.1096	−	31.7782i	−0.510469	−	1.14970i
$765$	0.697261	−	0.697261i	0.0252095	−	0.0252095i
$766$	8.25485	−	1.75021i	0.298260	−	0.0632376i
$767$			12.7730i			0.461207i
$768$	12.3930	+	10.1199i	0.447195	+	0.365171i
$769$		−	19.1403i		−	0.690219i	−0.938563	−	0.345109i	$-0.887842\pi$
$769$		−	19.1403i		−	0.690219i	0.938563	−	0.345109i	$-0.112158\pi$
$770$	−67.5409	+	17.9465i	−2.43400	+	0.646748i
$771$	1.68050	+	1.68050i	0.0605216	+	0.0605216i
$772$	−22.2581	+	9.88266i	−0.801086	+	0.355685i
$773$	−14.7985	+	14.7985i	−0.532264	+	0.532264i	−0.921246	−	0.388982i	$-0.872827\pi$
$773$	−14.7985	+	14.7985i	−0.532264	+	0.532264i	0.388982	+	0.921246i	$0.372827\pi$
$774$	3.98037	+	2.58778i	0.143071	+	0.0930158i
$775$		−	45.5966i		−	1.63788i
$776$	22.1709	+	30.6143i	0.795888	+	1.09899i
$777$	−1.23214	−	24.2412i	−0.0442026	−	0.869649i
$778$	1.74632	+	1.13534i	0.0626086	+	0.0407040i
$779$	−2.57801	+	2.57801i	−0.0923669	+	0.0923669i
$780$	12.3567	−	32.0922i	0.442441	−	1.14908i
$781$	−53.8784	+	53.8784i	−1.92792	+	1.92792i
$782$	−0.320240	−	1.51041i	−0.0114517	−	0.0540121i
$783$	7.40067			0.264478
$784$	−16.5755	+	22.5666i	−0.591982	+	0.805951i
$785$	−8.95608			−0.319656
$786$	4.38715	+	20.6920i	0.156485	+	0.738058i
$787$	−20.6147	+	20.6147i	−0.734836	+	0.734836i	−0.971574	−	0.236738i	$-0.923922\pi$
$787$	−20.6147	+	20.6147i	−0.734836	+	0.734836i	0.236738	+	0.971574i	$0.423922\pi$
$788$	32.6640	+	12.5769i	1.16361	+	0.448033i
$789$	7.28821	−	7.28821i	0.259467	−	0.259467i
$790$	−53.3483	−	34.6836i	−1.89805	−	1.23399i
$791$	−0.228551	−	4.49655i	−0.00812635	−	0.159879i
$792$	14.7810	+	2.36434i	0.525221	+	0.0840132i
$793$		−	48.3778i		−	1.71795i
$794$	−41.5692	−	27.0256i	−1.47524	−	0.959103i
$795$	10.7066	−	10.7066i	0.379724	−	0.379724i
$796$	5.71622	+	12.8743i	0.202606	+	0.456316i
$797$	−39.0381	−	39.0381i	−1.38280	−	1.38280i	−0.839608	−	0.543192i	$-0.817215\pi$
$797$	−39.0381	−	39.0381i	−1.38280	−	1.38280i	−0.543192	−	0.839608i	$-0.682785\pi$
$798$	−12.8645	+	3.41827i	−0.455398	+	0.121006i
$799$		−	1.55298i		−	0.0549403i
$800$	36.4677	+	21.1792i	1.28933	+	0.748797i
$801$		−	2.78092i		−	0.0982590i
$802$	2.66344	−	0.564709i	0.0940495	−	0.0199406i
$803$	−19.2222	+	19.2222i	−0.678336	+	0.678336i
$804$	1.75358	−	0.778595i	0.0618440	−	0.0274589i
$805$	27.0748	+	24.4556i	0.954262	+	0.861947i
$806$	35.3317	+	22.9704i	1.24451	+	0.809098i
$807$	1.12808			0.0397103
$808$	−2.14269	+	13.3953i	−0.0753794	+	0.471246i
$809$			24.7047i			0.868570i	0.900776	+	0.434285i	$0.142999\pi$
$809$			24.7047i			0.868570i	−0.900776	+	0.434285i	$0.857001\pi$
$810$	2.72043	−	4.18440i	0.0955860	−	0.147025i
$811$	−15.9640	−	15.9640i	−0.560571	−	0.560571i	0.368898	−	0.929470i	$-0.379735\pi$
$811$	−15.9640	−	15.9640i	−0.560571	−	0.560571i	−0.929470	+	0.368898i	$0.879735\pi$
$812$	37.2124	+	12.1980i	1.30590	+	0.428067i
$813$	3.82681	−	3.82681i	0.134212	−	0.134212i
$814$	−67.1704	+	14.2416i	−2.35432	+	0.499168i
$815$	7.83430			0.274424
$816$	−1.11622	+	0.0562088i	−0.0390754	+	0.00196770i
$817$			11.9428i			0.417824i
$818$	−11.3678	+	2.41022i	−0.397465	+	0.0842713i
$819$	−9.56582	−	8.64043i	−0.334257	−	0.301921i
$820$	2.59922	−	6.75055i	0.0907686	−	0.235739i
$821$	−7.85824	−	7.85824i	−0.274254	−	0.274254i	0.556556	−	0.830810i	$-0.312123\pi$
$821$	−7.85824	−	7.85824i	−0.274254	−	0.274254i	−0.830810	+	0.556556i	$0.812123\pi$
$822$	1.29772	+	0.843696i	0.0452633	+	0.0294273i
$823$	10.8482			0.378145			0.189073	−	0.981963i	$-0.439452\pi$
$823$	10.8482			0.378145			0.189073	+	0.981963i	$0.439452\pi$
$824$	−14.6570	−	20.2388i	−0.510600	−	0.705053i
$825$	39.4541			1.37361
$826$	−4.92240	+	8.48490i	−0.171272	+	0.295227i
$827$	24.2110	−	24.2110i	0.841900	−	0.841900i	−0.147206	−	0.989106i	$-0.547028\pi$
$827$	24.2110	−	24.2110i	0.841900	−	0.841900i	0.989106	+	0.147206i	$0.0470280\pi$
$828$	−3.17127	−	7.14244i	−0.110209	−	0.248217i
$829$	−18.2365	−	18.2365i	−0.633378	−	0.633378i	0.315536	−	0.948914i	$-0.397816\pi$
$829$	−18.2365	−	18.2365i	−0.633378	−	0.633378i	−0.948914	+	0.315536i	$0.897816\pi$
$830$	1.87438	+	8.84049i	0.0650606	+	0.306858i
$831$	−8.80629			−0.305487
$832$	−34.7828	+	17.5885i	−1.20588	+	0.609770i
$833$	−0.198313	−	1.94578i	−0.00687113	−	0.0674172i
$834$	−11.6480	+	2.46964i	−0.403338	+	0.0855165i
$835$	26.0718	+	26.0718i	0.902251	+	0.902251i
$836$	15.2803	+	34.4149i	0.528482	+	1.19026i
$837$	4.32485	+	4.32485i	0.149489	+	0.149489i
$838$	−29.2866	+	45.0469i	−1.01169	+	1.55612i
$839$			22.3042i			0.770027i	0.922911	+	0.385014i	$0.125803\pi$
$839$			22.3042i			0.770027i	−0.922911	+	0.385014i	$0.874197\pi$
$840$	20.5759	−	16.5563i	0.709935	−	0.571248i
$841$		−	25.7699i		−	0.888617i
$842$	28.5503	+	18.5615i	0.983907	+	0.639673i
$843$	−19.8948	−	19.8948i	−0.685215	−	0.685215i
$844$	−10.1013	−	3.88938i	−0.347700	−	0.133878i
$845$	26.7952	+	26.7952i	0.921782	+	0.921782i
$846$	−1.63032	−	7.68939i	−0.0560516	−	0.264367i
$847$	44.9425	−	2.28434i	1.54424	−	0.0784910i
$848$	−17.1398	+	0.863099i	−0.588582	+	0.0296389i
$849$	13.4815			0.462685
$850$	−2.88172	+	0.610988i	−0.0988421	+	0.0209567i
$851$	25.3478	+	25.3478i	0.868910	+	0.868910i
$852$	10.3466	−	26.8717i	0.354470	−	0.920609i
$853$	6.07615	−	6.07615i	0.208043	−	0.208043i	−0.595392	−	0.803435i	$-0.703003\pi$
$853$	6.07615	−	6.07615i	0.208043	−	0.208043i	0.803435	+	0.595392i	$0.203003\pi$
$854$	18.6436	−	32.1366i	0.637971	−	1.09969i
$855$	12.5549			0.429370
$856$	4.31703	−	26.9885i	0.147553	−	0.922449i
$857$	−20.1963			−0.689894			−0.344947	−	0.938622i	$-0.612103\pi$
$857$	−20.1963			−0.689894			−0.344947	+	0.938622i	$0.612103\pi$
$858$	−19.8760	+	30.5721i	−0.678554	+	1.04371i
$859$	11.3242	+	11.3242i	0.386376	+	0.386376i	0.873393	−	0.487016i	$-0.161915\pi$
$859$	11.3242	+	11.3242i	0.386376	+	0.386376i	−0.487016	+	0.873393i	$0.661915\pi$
$860$	−9.61561	−	21.6566i	−0.327890	−	0.738484i
$861$	−2.01216	−	1.81750i	−0.0685741	−	0.0619403i
$862$	1.07328	+	5.06211i	0.0365560	+	0.172416i
$863$		−	16.0535i		−	0.546469i	−0.961947	−	0.273234i	$-0.911907\pi$
$863$		−	16.0535i		−	0.546469i	0.961947	−	0.273234i	$-0.0880935\pi$
$864$	−5.46783	+	1.45012i	−0.186019	+	0.0493342i
$865$	−21.3905			−0.727298
$866$	−3.45702	−	16.3050i	−0.117474	−	0.554067i
$867$	−11.9656	+	11.9656i	−0.406373	+	0.406373i
$868$	14.6181	+	28.8748i	0.496170	+	0.980075i
$869$	47.7110	+	47.7110i	1.61848	+	1.61848i
$870$	−30.9674	−	20.1330i	−1.04989	−	0.682572i
$871$			4.67395i			0.158371i
$872$	4.39387	−	27.4690i	0.148795	−	0.930217i
$873$	−13.3640			−0.452304
$874$	10.7151	−	16.4814i	0.362445	−	0.557492i
$875$	15.3651	−	17.0107i	0.519436	−	0.575068i
$876$	3.69136	−	9.58700i	0.124720	−	0.323915i
$877$	21.2991	−	21.2991i	0.719219	−	0.719219i	−0.249227	−	0.968445i	$-0.580176\pi$
$877$	21.2991	−	21.2991i	0.719219	−	0.719219i	0.968445	+	0.249227i	$0.0801764\pi$
$878$	−0.647075	−	3.05192i	−0.0218377	−	0.102997i
$879$			33.8404i			1.14141i
$880$	−55.4178	−	50.1040i	−1.86813	−	1.68901i
$881$			18.5990i			0.626616i	0.949652	+	0.313308i	$0.101437\pi$
$881$			18.5990i			0.626616i	−0.949652	+	0.313308i	$0.898563\pi$
$882$	−3.02461	−	9.42612i	−0.101844	−	0.317394i
$883$	−30.5023	−	30.5023i	−1.02648	−	1.02648i	−0.999640	−	0.0268431i	$-0.991455\pi$
$883$	−30.5023	−	30.5023i	−1.02648	−	1.02648i	−0.0268431	−	0.999640i	$-0.508545\pi$
$884$	0.978296	−	2.54078i	0.0329037	−	0.0854556i
$885$	6.54234	−	6.54234i	0.219918	−	0.219918i
$886$	13.5326	−	20.8151i	0.454637	−	0.699296i
$887$		−	5.45605i		−	0.183196i	−0.995796	−	0.0915981i	$-0.970803\pi$
$887$		−	5.45605i		−	0.183196i	0.995796	−	0.0915981i	$-0.0291975\pi$
$888$	21.0161	−	15.2199i	0.705254	−	0.510745i
$889$	−28.5109	+	1.44916i	−0.956225	+	0.0486031i
$890$	−7.56529	+	11.6365i	−0.253589	+	0.390056i
$891$	−3.74223	+	3.74223i	−0.125370	+	0.125370i
$892$	36.4954	−	16.2041i	1.22196	−	0.542553i
$893$	13.9815	−	13.9815i	0.467873	−	0.467873i
$894$	17.4779	−	3.70569i	0.584547	−	0.123937i
$895$	−3.79794			−0.126951
$896$	−29.8838	−	1.72068i	−0.998346	−	0.0574839i
$897$	19.0373			0.635637
$898$	−17.3498	+	3.67854i	−0.578970	+	0.122754i
$899$	32.0068	−	32.0068i	1.06749	−	1.06749i
$900$	−13.6271	+	6.05048i	−0.454237	+	0.201683i
$901$	0.847655	−	0.847655i	0.0282395	−	0.0282395i
$902$	−4.18088	+	6.43079i	−0.139208	+	0.214122i
$903$	−8.87054	+	0.450873i	−0.295193	+	0.0150041i
$904$	3.89831	−	2.82316i	0.129656	−	0.0938970i
$905$			88.6636i			2.94728i
$906$	−7.54240	+	11.6013i	−0.250579	+	0.385427i
$907$	27.8668	−	27.8668i	0.925303	−	0.925303i	−0.0720945	−	0.997398i	$-0.522968\pi$
$907$	27.8668	−	27.8668i	0.925303	−	0.925303i	0.997398	+	0.0720945i	$0.0229683\pi$
$908$	−0.941880	+	2.44620i	−0.0312574	+	0.0811800i
$909$	−3.39140	−	3.39140i	−0.112486	−	0.112486i
$910$	16.5216	+	62.1782i	0.547685	+	2.06119i
$911$		−	42.7641i		−	1.41684i	−0.705792	−	0.708419i	$-0.749409\pi$
$911$		−	42.7641i		−	1.41684i	0.705792	−	0.708419i	$-0.250591\pi$
$912$	−10.5554	−	9.54331i	−0.349525	−	0.316011i
$913$		−	9.58262i		−	0.317138i
$914$	−8.47212	−	39.9587i	−0.280233	−	1.32171i
$915$	−24.7791	+	24.7791i	−0.819173	+	0.819173i
$916$	14.4546	−	37.5406i	0.477592	−	1.24038i
$917$	−29.3657	−	26.5249i	−0.969742	−	0.875930i
$918$	0.215380	−	0.331284i	0.00710858	−	0.0109340i
$919$	−16.6329			−0.548670			−0.274335	−	0.961634i	$-0.588458\pi$
$919$	−16.6329			−0.548670			−0.274335	+	0.961634i	$0.588458\pi$
$920$	−6.16062	+	38.5140i	−0.203109	+	1.26977i
$921$			4.71197i			0.155265i
$922$	−0.541513	−	0.352057i	−0.0178338	−	0.0115944i
$923$	49.6005	+	49.6005i	1.63262	+	1.63262i
$924$	−24.9850	+	12.6488i	−0.821945	+	0.416115i
$925$	48.3612	−	48.3612i	1.59011	−	1.59011i
$926$	0.457737	+	2.15891i	0.0150422	+	0.0709463i
$927$	8.83485			0.290174
$928$	10.7319	+	40.4656i	0.352291	+	1.32835i
$929$			14.7795i			0.484899i	0.970164	+	0.242450i	$0.0779509\pi$
$929$			14.7795i			0.484899i	−0.970164	+	0.242450i	$0.922049\pi$
$930$	−6.33148	−	29.8624i	−0.207617	−	0.979225i
$931$	15.7325	−	19.3033i	0.515612	−	0.632641i
$932$	−17.4265	−	39.2486i	−0.570825	−	1.28563i
$933$	−17.6251	−	17.6251i	−0.577020	−	0.577020i
$934$	8.62159	−	13.2612i	0.282107	−	0.433921i
$935$	5.21862			0.170667
$936$	2.17661	−	13.6074i	0.0711448	−	0.444772i
$937$	33.8675			1.10640			0.553201	−	0.833048i	$-0.313406\pi$
$937$	33.8675			1.10640			0.553201	+	0.833048i	$0.313406\pi$
$938$	−1.80122	+	3.10483i	−0.0588120	+	0.101376i
$939$	2.00601	−	2.00601i	0.0654637	−	0.0654637i
$940$	−14.0965	+	36.6107i	−0.459778	+	1.19411i
$941$	12.3650	+	12.3650i	0.403087	+	0.403087i	0.879319	−	0.476233i	$-0.157998\pi$
$941$	12.3650	+	12.3650i	0.403087	+	0.403087i	−0.476233	+	0.879319i	$0.657998\pi$
$942$	−3.51086	+	0.744379i	−0.114390	+	0.0242532i
$943$	4.00447			0.130404
$944$	−10.4734	+	0.527402i	−0.340879	+	0.0171655i
$945$	0.473985	+	9.32524i	0.0154187	+	0.303350i
$946$	5.21140	+	24.5795i	0.169437	+	0.799150i
$947$	−5.59948	−	5.59948i	−0.181959	−	0.181959i	0.610250	−	0.792209i	$-0.291069\pi$
$947$	−5.59948	−	5.59948i	−0.181959	−	0.181959i	−0.792209	+	0.610250i	$0.791069\pi$
$948$	−23.7957	−	9.16225i	−0.772848	−	0.297576i
$949$	17.6959	+	17.6959i	0.574435	+	0.574435i
$950$	−31.4450	−	20.4435i	−1.02021	−	0.663274i
$951$		−	24.5202i		−	0.795123i
$952$	1.62902	−	1.31079i	0.0527968	−	0.0424828i
$953$		−	7.46492i		−	0.241813i	−0.992664	−	0.120906i	$-0.961420\pi$
$953$		−	7.46492i		−	0.241813i	0.992664	−	0.120906i	$-0.0385801\pi$
$954$	3.30720	−	5.08695i	0.107075	−	0.164696i
$955$	−43.3839	−	43.3839i	−1.40387	−	1.40387i
$956$	7.18205	+	16.1757i	0.232284	+	0.523158i
$957$	27.6950	+	27.6950i	0.895253	+	0.895253i
$958$	38.6937	−	8.20391i	1.25014	−	0.265056i
$959$	−2.89207	+	0.146999i	−0.0933898	+	0.00474683i
$960$	26.8245	+	8.80692i	0.865758	+	0.284242i
$961$	6.40868			0.206732
$962$	13.1108	+	61.8371i	0.422710	+	1.99371i
$963$	6.83291	+	6.83291i	0.220187	+	0.220187i
$964$	9.33563	+	21.0260i	0.300681	+	0.677203i
$965$	−30.3869	+	30.3869i	−0.978189	+	0.978189i
$966$	12.6462	+	7.33650i	0.406884	+	0.236048i
$967$	20.4112			0.656379			0.328190	−	0.944612i	$-0.393561\pi$
$967$	20.4112			0.656379			0.328190	+	0.944612i	$0.393561\pi$
$968$	28.2172	+	38.9632i	0.906935	+	1.25233i
$969$	0.993990			0.0319316
$970$	55.9205	+	36.3559i	1.79550	+	1.16732i
$971$	3.33131	+	3.33131i	0.106907	+	0.106907i	0.758537	−	0.651630i	$-0.225915\pi$
$971$	3.33131	+	3.33131i	0.106907	+	0.106907i	−0.651630	+	0.758537i	$0.725915\pi$
$972$	0.718646	−	1.86643i	0.0230506	−	0.0598657i
$973$	14.9315	−	16.5307i	0.478683	−	0.529949i
$974$	24.0027	−	5.08910i	0.769096	−	0.163065i
$975$		−	36.3214i		−	1.16322i
$976$	39.6679	−	1.99754i	1.26974	−	0.0639397i
$977$	−39.2958			−1.25718			−0.628592	−	0.777735i	$-0.716369\pi$
$977$	−39.2958			−1.25718			−0.628592	+	0.777735i	$0.716369\pi$
$978$	3.07111	−	0.651143i	0.0982033	−	0.0208213i
$979$	10.4069	−	10.4069i	0.332605	−	0.332605i
$980$	−12.9869	+	47.6709i	−0.414851	+	1.52279i
$981$	6.95454	+	6.95454i	0.222041	+	0.222041i
$982$	−4.38104	+	6.73866i	−0.139805	+	0.215039i
$983$			35.1168i			1.12005i	0.828475	+	0.560027i	$0.189209\pi$
$983$			35.1168i			1.12005i	−0.828475	+	0.560027i	$0.810791\pi$
$984$	0.457847	−	2.86230i	0.0145956	−	0.0912468i
$985$	61.7631			1.96794
$986$	−2.45173	−	1.59395i	−0.0780789	−	0.0507618i
$987$	10.9127	+	9.85699i	0.347354	+	0.313751i
$988$	31.6824	−	14.0671i	1.00795	−	0.447534i
$989$	9.27545	−	9.27545i	0.294942	−	0.294942i
$990$	25.8395	−	5.47854i	0.821232	−	0.174119i
$991$		−	28.3936i		−	0.901953i	−0.892536	−	0.450976i	$-0.851076\pi$
$991$		−	28.3936i		−	0.901953i	0.892536	−	0.450976i	$-0.148924\pi$
$992$	−17.3760	+	29.9191i	−0.551688	+	0.949933i
$993$			20.0437i			0.636068i
$994$	13.8340	+	52.0635i	0.438788	+	1.65136i
$995$	17.5760	+	17.5760i	0.557198	+	0.557198i
$996$	1.46954	+	3.30976i	0.0465643	+	0.104874i
$997$	39.8129	−	39.8129i	1.26089	−	1.26089i	0.310225	−	0.950663i	$-0.399596\pi$
$997$	39.8129	−	39.8129i	1.26089	−	1.26089i	0.950663	−	0.310225i	$-0.100404\pi$
$998$	−44.8071	−	29.1307i	−1.41835	−	0.922116i
$999$			9.17415i			0.290257i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.2.u.a.139.1	✓	64
4.3	odd	2		1344.2.u.a.1231.17		64
7.6	odd	2	inner	336.2.u.a.139.2	yes	64
16.3	odd	4	inner	336.2.u.a.307.2	yes	64
16.13	even	4		1344.2.u.a.559.16		64
28.27	even	2		1344.2.u.a.1231.16		64
112.13	odd	4		1344.2.u.a.559.17		64
112.83	even	4	inner	336.2.u.a.307.1	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
336.2.u.a.139.1	✓	64	1.1	even	1	trivial
336.2.u.a.139.2	yes	64	7.6	odd	2	inner
336.2.u.a.307.1	yes	64	112.83	even	4	inner
336.2.u.a.307.2	yes	64	16.3	odd	4	inner
1344.2.u.a.559.16		64	16.13	even	4
1344.2.u.a.559.17		64	112.13	odd	4
1344.2.u.a.1231.16		64	28.27	even	2
1344.2.u.a.1231.17		64	4.3	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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	336.u (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38346 + 0.293324i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.82792 - 0.811604i) q^{4} +(2.49549 - 2.49549i) q^{5} +(0.770842 - 1.18567i) q^{6} +(0.134305 + 2.64234i) q^{7} +(-2.29079 + 1.65899i) q^{8} -1.00000i q^{9} +O(q^{10})\)	\(q+(-1.38346 + 0.293324i) q^{2} +(-0.707107 + 0.707107i) q^{3} +(1.82792 - 0.811604i) q^{4} +(2.49549 - 2.49549i) q^{5} +(0.770842 - 1.18567i) q^{6} +(0.134305 + 2.64234i) q^{7} +(-2.29079 + 1.65899i) q^{8} -1.00000i q^{9} +(-2.72043 + 4.18440i) q^{10} +(3.74223 - 3.74223i) q^{11} +(-0.718646 + 1.86643i) q^{12} +(-3.44510 - 3.44510i) q^{13} +(-0.960868 - 3.61618i) q^{14} +3.52916i q^{15} +(2.68260 - 2.96710i) q^{16} +0.279408i q^{17} +(0.293324 + 1.38346i) q^{18} +(-2.51552 + 2.51552i) q^{19} +(2.53622 - 6.58692i) q^{20} +(-1.96338 - 1.77345i) q^{21} +(-4.07954 + 6.27492i) q^{22} +3.90741 q^{23} +(0.446750 - 2.79292i) q^{24} -7.45497i q^{25} +(5.77669 + 3.75563i) q^{26} +(0.707107 + 0.707107i) q^{27} +(2.39003 + 4.72099i) q^{28} +(5.23306 - 5.23306i) q^{29} +(-1.03519 - 4.88245i) q^{30} +6.11626 q^{31} +(-2.84095 + 4.89173i) q^{32} +5.29232i q^{33} +(-0.0819571 - 0.386550i) q^{34} +(6.92910 + 6.25878i) q^{35} +(-0.811604 - 1.82792i) q^{36} +(6.48710 + 6.48710i) q^{37} +(2.74226 - 4.21799i) q^{38} +4.87211 q^{39} +(-1.57665 + 9.85667i) q^{40} +1.02484 q^{41} +(3.23646 + 1.87759i) q^{42} +(2.37381 - 2.37381i) q^{43} +(3.80330 - 9.87772i) q^{44} +(-2.49549 - 2.49549i) q^{45} +(-5.40574 + 1.14614i) q^{46} -5.55809 q^{47} +(0.201171 + 3.99494i) q^{48} +(-6.96392 + 0.709760i) q^{49} +(2.18672 + 10.3137i) q^{50} +(-0.197571 - 0.197571i) q^{51} +(-9.09343 - 3.50132i) q^{52} +(-3.03375 - 3.03375i) q^{53} +(-1.18567 - 0.770842i) q^{54} -18.6774i q^{55} +(-4.69129 - 5.83025i) q^{56} -3.55749i q^{57} +(-5.70475 + 8.77472i) q^{58} +(-1.85379 - 1.85379i) q^{59} +(2.86428 + 6.45103i) q^{60} +(7.02125 + 7.02125i) q^{61} +(-8.46161 + 1.79405i) q^{62} +(2.64234 - 0.134305i) q^{63} +(2.49547 - 7.60083i) q^{64} -17.1944 q^{65} +(-1.55236 - 7.32171i) q^{66} +(-0.678348 - 0.678348i) q^{67} +(0.226769 + 0.510736i) q^{68} +(-2.76295 + 2.76295i) q^{69} +(-11.4220 - 6.62631i) q^{70} -14.3974 q^{71} +(1.65899 + 2.29079i) q^{72} -5.13655 q^{73} +(-10.8775 - 7.07182i) q^{74} +(5.27146 + 5.27146i) q^{75} +(-2.55657 + 6.63979i) q^{76} +(10.3909 + 9.38565i) q^{77} +(-6.74036 + 1.42911i) q^{78} +12.7493i q^{79} +(-0.709965 - 14.0988i) q^{80} -1.00000 q^{81} +(-1.41783 + 0.300610i) q^{82} +(1.28033 - 1.28033i) q^{83} +(-5.02825 - 1.64824i) q^{84} +(0.697261 + 0.697261i) q^{85} +(-2.58778 + 3.98037i) q^{86} +7.40067i q^{87} +(-2.36434 + 14.7810i) q^{88} +2.78092 q^{89} +(4.18440 + 2.72043i) q^{90} +(8.64043 - 9.56582i) q^{91} +(7.14244 - 3.17127i) q^{92} +(-4.32485 + 4.32485i) q^{93} +(7.68939 - 1.63032i) q^{94} +12.5549i q^{95} +(-1.45012 - 5.46783i) q^{96} -13.3640i q^{97} +(9.42612 - 3.02461i) q^{98} +(-3.74223 - 3.74223i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 4 q^{4} + 24 q^{8}+O(q^{10}) \) 64 * q - 4 * q^4 + 24 * q^8	\( 64 q - 4 q^{4} + 24 q^{8} + 8 q^{11} - 16 q^{14} + 4 q^{16} - 4 q^{18} - 28 q^{22} - 16 q^{23} + 32 q^{28} + 16 q^{29} + 24 q^{35} + 16 q^{37} + 20 q^{42} - 8 q^{43} - 36 q^{44} - 40 q^{46} - 52 q^{50} + 16 q^{53} - 28 q^{56} - 92 q^{58} + 24 q^{60} - 52 q^{64} + 56 q^{67} - 40 q^{70} - 128 q^{71} + 4 q^{72} - 60 q^{74} - 64 q^{81} - 24 q^{84} + 92 q^{86} - 84 q^{88} + 8 q^{91} + 136 q^{92} - 64 q^{98} - 8 q^{99}+O(q^{100}) \) 64 * q - 4 * q^4 + 24 * q^8 + 8 * q^11 - 16 * q^14 + 4 * q^16 - 4 * q^18 - 28 * q^22 - 16 * q^23 + 32 * q^28 + 16 * q^29 + 24 * q^35 + 16 * q^37 + 20 * q^42 - 8 * q^43 - 36 * q^44 - 40 * q^46 - 52 * q^50 + 16 * q^53 - 28 * q^56 - 92 * q^58 + 24 * q^60 - 52 * q^64 + 56 * q^67 - 40 * q^70 - 128 * q^71 + 4 * q^72 - 60 * q^74 - 64 * q^81 - 24 * q^84 + 92 * q^86 - 84 * q^88 + 8 * q^91 + 136 * q^92 - 64 * q^98 - 8 * q^99

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