LMFDB - Embedded newform 336.2.u.a.139.2

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			139.2
Character	$\chi$	$=$	336.139
Dual form			336.2.u.a.307.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.38346 + 0.293324i) q^{2} +(0.707107 - 0.707107i) q^{3} +(1.82792 - 0.811604i) q^{4} +(-2.49549 + 2.49549i) q^{5} +(-0.770842 + 1.18567i) q^{6} +(0.134305 - 2.64234i) q^{7} +(-2.29079 + 1.65899i) q^{8} -1.00000i q^{9} +O(q^{10})$	\(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} +(0.589256 + 3.69497i) 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} +(-1.77345 - 1.96338i) 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} +(-1.89903 - 4.93899i) 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} +(6.25878 + 6.92910i) 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} +(3.02940 + 2.19607i) 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} +(4.07596 + 6.27587i) 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} +(-10.6912 - 7.75028i) 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} +(-9.38565 - 10.3909i) 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} +(-4.83522 - 2.14958i) 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} +(9.56582 - 8.64043i) 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} +(9.84250 - 1.06076i) 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	$0.539476\pi$
$5$	−2.49549	+	2.49549i	−1.11602	+	1.11602i	−0.992320	+	0.123699i	$0.960524\pi$
$6$	−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	0.999051	−	0.0435523i	$-0.0138675\pi$
$13$	3.44510	+	3.44510i	0.955499	+	0.955499i	−0.0435523	+	0.999051i	$0.513868\pi$
$14$	0.589256	+	3.69497i	0.157485	+	0.987521i
$15$			3.52916i			0.911225i
$16$	2.68260	−	2.96710i	0.670650	−	0.741774i
$17$		−	0.279408i		−	0.0677664i	−0.999426	−	0.0338832i	$-0.989213\pi$
$17$		−	0.279408i		−	0.0677664i	0.999426	−	0.0338832i	$-0.0107874\pi$
$18$	0.293324	+	1.38346i	0.0691371	+	0.326085i
$19$	2.51552	−	2.51552i	0.577101	−	0.577101i	−0.357003	−	0.934103i	$-0.616201\pi$
$19$	2.51552	−	2.51552i	0.577101	−	0.577101i	0.934103	+	0.357003i	$0.116201\pi$
$20$	−2.53622	+	6.58692i	−0.567115	+	1.47288i
$21$	−1.77345	−	1.96338i	−0.386998	−	0.428446i
$22$	−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
$28$	−1.89903	−	4.93899i	−0.358884	−	0.933382i
$29$	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	$-0.685089\pi$
$31$	−6.11626			−1.09851			−0.549257	+	0.835654i	$0.685089\pi$
$32$	−2.84095	+	4.89173i	−0.502213	+	0.864744i
$33$		−	5.29232i		−	0.921274i
$34$	0.0819571	+	0.386550i	0.0140555	+	0.0662927i
$35$	6.25878	+	6.92910i	1.05793	+	1.17123i
$36$	−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	$-0.525501\pi$
$41$	−1.02484			−0.160053			−0.0800267	+	0.996793i	$0.525501\pi$
$42$	3.02940	+	2.19607i	0.467447	+	0.338861i
$43$	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	$-0.367144\pi$
$47$	5.55809			0.810731			0.405365	+	0.914155i	$0.367144\pi$
$48$	−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
$56$	4.07596	+	6.27587i	0.544673	+	0.838648i
$57$		−	3.55749i		−	0.471201i
$58$	−5.70475	+	8.77472i	−0.749070	+	1.15218i
$59$	1.85379	+	1.85379i	0.241343	+	0.241343i	0.817406	−	0.576062i	$-0.195411\pi$
$59$	1.85379	+	1.85379i	0.241343	+	0.241343i	−0.576062	+	0.817406i	$0.695411\pi$
$60$	2.86428	+	6.45103i	0.369777	+	0.832824i
$61$	−7.02125	−	7.02125i	−0.898979	−	0.898979i	0.0963664	−	0.995346i	$-0.469278\pi$
$61$	−7.02125	−	7.02125i	−0.898979	−	0.898979i	−0.995346	+	0.0963664i	$0.969278\pi$
$62$	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
$70$	−10.6912	−	7.75028i	−1.27785	−	0.926336i
$71$	−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	$-0.402815\pi$
$73$	5.13655			0.601188			0.300594	+	0.953752i	$0.402815\pi$
$74$	−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
$77$	−9.38565	−	10.3909i	−1.06959	−	1.18415i
$78$	−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	−0.773874	−	0.633339i	$-0.781684\pi$
$83$	−1.28033	+	1.28033i	−0.140535	+	0.140535i	0.633339	+	0.773874i	$0.281684\pi$
$84$	−4.83522	−	2.14958i	−0.527565	−	0.234538i
$85$	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	$-0.547087\pi$
$89$	−2.78092			−0.294777			−0.147389	+	0.989079i	$0.547087\pi$
$90$	−4.18440	−	2.72043i	−0.441075	−	0.286758i
$91$	9.56582	−	8.64043i	1.00277	−	0.905763i
$92$	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	$0.237351\pi$
$97$			13.3640i			1.35691i	−0.734641	+	0.678456i	$0.762649\pi$
$98$	9.84250	−	1.06076i	0.994243	−	0.107153i
$99$	−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	−0.855410	−	0.517952i	$-0.826694\pi$
$101$	−3.39140	+	3.39140i	−0.337457	+	0.337457i	0.517952	+	0.855410i	$0.326694\pi$
$102$	0.331284	+	0.215380i	0.0328020	+	0.0213258i
$103$		−	8.83485i		−	0.870523i	−0.900304	−	0.435262i	$-0.856656\pi$
$103$		−	8.83485i		−	0.870523i	0.900304	−	0.435262i	$-0.143344\pi$
$104$	−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
$112$	−7.47979	−	7.48683i	−0.706774	−	0.707439i
$113$	−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
$126$	3.69497	−	0.589256i	0.329174	−	0.0524951i
$127$			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	−0.0732839	−	0.997311i	$-0.523348\pi$
$131$	10.5760	−	10.5760i	0.924027	−	0.924027i	0.997311	+	0.0732839i	$0.0233479\pi$
$132$	−4.29526	−	9.67394i	−0.373855	−	0.842009i
$133$	−6.30902	−	6.98472i	−0.547061	−	0.605652i
$134$	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	0.912977	−	0.408010i	$-0.133777\pi$
$139$	5.95347	+	5.95347i	0.504967	+	0.504967i	−0.408010	+	0.912977i	$0.633777\pi$
$140$	17.0643	+	7.58620i	1.44219	+	0.641151i
$141$	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
$147$	−5.42611	+	4.42236i	−0.447538	+	0.364750i
$148$	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
$154$	16.0326	+	11.6223i	1.29194	+	0.936551i
$155$	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	0.775078	−	0.631865i	$-0.217710\pi$
$157$	1.79445	+	1.79445i	0.143213	+	0.143213i	−0.631865	+	0.775078i	$0.717710\pi$
$158$	−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	$-0.867540\pi$
$167$		−	10.4475i		−	0.808455i	0.914658	−	0.404228i	$-0.132460\pi$
$168$	7.31985	+	1.55557i	0.564739	+	0.120015i
$169$			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	0.851004	−	0.525159i	$-0.175994\pi$
$173$	4.28582	+	4.28582i	0.325845	+	0.325845i	−0.525159	+	0.851004i	$0.675994\pi$
$174$	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	$-0.366566\pi$
$181$	17.7647	−	17.7647i	1.32044	−	1.32044i	0.913417	−	0.407026i	$-0.133434\pi$
$182$	−10.6995	+	14.7596i	−0.793099	+	1.09405i
$183$	−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
$189$	−1.96338	+	1.77345i	−0.142815	+	0.128999i
$190$	−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
$196$	−13.3056	+	4.35456i	−0.950397	+	0.311040i
$197$	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	$-0.919689\pi$
$199$		−	7.04311i		−	0.499273i	0.968340	−	0.249636i	$-0.0803111\pi$
$200$	12.3678	+	17.0778i	0.874532	+	1.20758i
$201$	−0.959329			−0.0676659
$202$	3.69709	−	5.68665i	0.260126	−	0.400111i
$203$	−13.1247	−	14.5304i	−0.921174	−	1.01983i
$204$	−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
$210$	−13.0401	+	2.07958i	−0.899854	+	0.143505i
$211$	−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	$-0.733061\pi$
$223$	−19.9655			−1.33699			−0.668495	+	0.743717i	$0.733061\pi$
$224$	12.5441	+	8.16373i	0.838135	+	0.545462i
$225$	−7.45497			−0.496998
$226$	2.35428	−	0.499158i	0.156604	−	0.0332035i
$227$	0.926757	−	0.926757i	0.0615110	−	0.0615110i	−0.675682	−	0.737193i	$-0.736151\pi$
$227$	0.926757	−	0.926757i	0.0615110	−	0.0615110i	0.737193	+	0.675682i	$0.236151\pi$
$228$	−2.88727	−	6.50281i	−0.191214	−	0.430659i
$229$	−14.2225	+	14.2225i	−0.939847	+	0.939847i	−0.998291	−	0.0584437i	$-0.981386\pi$
$229$	−14.2225	+	14.2225i	−0.939847	+	0.939847i	0.0584437	+	0.998291i	$0.481386\pi$
$230$	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
$238$	1.03240	−	0.164643i	0.0669208	−	0.0106722i
$239$			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	$-0.879194\pi$
$241$		−	11.5027i		−	0.740954i	0.928842	−	0.370477i	$-0.120806\pi$
$242$	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
$245$	19.1496	−	15.6072i	1.22342	−	0.997109i
$246$	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	$0.127733\pi$
$251$	20.7727	+	20.7727i	1.31116	+	1.31116i	0.390602	+	0.920560i	$0.372267\pi$
$252$	−4.93899	+	1.89903i	−0.311127	+	0.119628i
$253$	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	$0.0236159\pi$
$257$			2.37658i			0.148247i	−0.997249	+	0.0741235i	$0.976384\pi$
$258$	0.984711	+	4.64438i	0.0613055	+	0.289147i
$259$	18.0124	−	16.2699i	1.11924	−	1.01096i
$260$	−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
$266$	10.7771	+	7.81249i	0.660784	+	0.479014i
$267$	−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	0.731006	−	0.682371i	$-0.239051\pi$
$269$	0.797673	+	0.797673i	0.0486350	+	0.0486350i	−0.682371	+	0.731006i	$0.739051\pi$
$270$	−4.88245	+	1.03519i	−0.297137	+	0.0629995i
$271$	5.41192			0.328751			0.164375	−	0.986398i	$-0.447439\pi$
$271$	5.41192			0.328751			0.164375	+	0.986398i	$0.447439\pi$
$272$	−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
$280$	−25.8329	−	5.48985i	−1.54381	−	0.328081i
$281$			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	0.931194	−	0.364524i	$-0.118768\pi$
$283$	9.53287	+	9.53287i	0.566671	+	0.566671i	−0.364524	+	0.931194i	$0.618768\pi$
$284$	−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	$0.701654\pi$
$293$	−23.9288	+	23.9288i	−1.39793	+	1.39793i	−0.805952	+	0.591981i	$0.798346\pi$
$294$	6.20963	−	7.70977i	0.362153	−	0.449643i
$295$	−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
$301$	−5.95361	−	6.59124i	−0.343160	−	0.379913i
$302$	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	−0.795765	−	0.605606i	$-0.792931\pi$
$307$	−3.33186	+	3.33186i	−0.190159	+	0.190159i	0.605606	+	0.795765i	$0.292931\pi$
$308$	−25.5895	−	11.3762i	−1.45810	−	0.648221i
$309$	−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	$-0.750182\pi$
$311$		−	24.9257i		−	1.41340i	0.707511	−	0.706702i	$-0.249818\pi$
$312$	−11.1610	+	8.08280i	−0.631867	+	0.457598i
$313$	2.83693			0.160353			0.0801764	−	0.996781i	$-0.474452\pi$
$313$	2.83693			0.160353			0.0801764	+	0.996781i	$0.474452\pi$
$314$	−3.00891	−	1.95619i	−0.169802	−	0.110394i
$315$	6.92910	−	6.25878i	0.390411	−	0.352643i
$316$	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
$322$	2.30246	+	14.4377i	0.128311	+	0.804584i
$323$	−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
$336$	−10.5830	−	0.00497852i	−0.577350	−	0.000271600i
$337$	−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	0.608452	−	0.793591i	$-0.291791\pi$
$349$	−3.45869	−	3.45869i	−0.185139	−	0.185139i	−0.793591	+	0.608452i	$0.791791\pi$
$350$	27.5459	−	4.39289i	1.47239	−	0.234810i
$351$		−	4.87211i		−	0.260054i
$352$	7.67451	+	28.9375i	0.409053	+	1.54237i
$353$			4.93908i			0.262881i	0.991324	+	0.131440i	$0.0419602\pi$
$353$			4.93908i			0.262881i	−0.991324	+	0.131440i	$0.958040\pi$
$354$	−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
$357$	−0.548585	+	0.495516i	−0.0290342	+	0.0262255i
$358$	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
$364$	10.4730	−	23.5577i	0.548933	−	1.23476i
$365$	−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	$-0.764681\pi$
$367$	−28.3127			−1.47791			−0.738956	+	0.673754i	$0.764681\pi$
$368$	10.4820	−	11.5937i	0.546412	−	0.604361i
$369$			1.02484i			0.0533511i
$370$	44.7923	−	9.49696i	2.32864	−	0.493724i
$371$	−8.42366	+	7.60876i	−0.437334	+	0.395027i
$372$	−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
$378$	2.19607	−	3.02940i	0.112954	−	0.155816i
$379$	−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	$-0.451285\pi$
$383$	5.96681			0.304890			0.152445	+	0.988312i	$0.451285\pi$
$384$	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
$392$	17.1304	−	9.92720i	0.865216	−	0.501399i
$393$		−	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	$-0.907675\pi$
$397$	−24.7911	−	24.7911i	−1.24423	−	1.24423i	−0.285997	−	0.958231i	$-0.592325\pi$
$398$	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
$406$	22.4196	+	16.2524i	1.11267	+	0.806592i
$407$	48.5525			2.40666
$408$	0.780365	+	0.124825i	0.0386338	+	0.00617978i
$409$	−8.21692			−0.406300			−0.203150	−	0.979148i	$-0.565118\pi$
$409$	−8.21692			−0.406300			−0.203150	+	0.979148i	$0.565118\pi$
$410$	−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
$413$	5.14733	−	4.64938i	0.253284	−	0.228781i
$414$	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	$0.628506\pi$
$419$	−26.8651	+	26.8651i	−1.31244	+	1.31244i	−0.919608	+	0.392836i	$0.871494\pi$
$420$	17.4305	−	6.70200i	0.850521	−	0.327024i
$421$	−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
$427$	−19.4955	+	17.6096i	−0.943455	+	0.852186i
$428$	−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	$-0.908607\pi$
$433$		−	11.7857i		−	0.566383i	0.959063	−	0.283192i	$-0.0913933\pi$
$434$	−3.60404	−	22.5994i	−0.173000	−	1.08481i
$435$	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	$-0.983235\pi$
$439$		−	2.20601i		−	0.105287i	0.998613	−	0.0526435i	$-0.0167647\pi$
$440$	−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
$448$	−19.7488	−	7.61472i	−0.933044	−	0.359762i
$449$	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	0.699546	−	0.714587i	$-0.253386\pi$
$461$	−0.322947	−	0.322947i	−0.0150412	−	0.0150412i	−0.714587	+	0.699546i	$0.753386\pi$
$462$	19.5549	−	3.11853i	0.909778	−	0.145087i
$463$		−	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	−0.500034	−	0.866006i	$-0.666679\pi$
$467$	7.90873	−	7.90873i	0.365973	−	0.365973i	0.866006	+	0.500034i	$0.166679\pi$
$468$	3.50132	−	9.09343i	0.161848	−	0.420344i
$469$	−1.88353	+	1.70132i	−0.0869734	+	0.0785597i
$470$	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
$476$	−1.37999	+	0.530605i	−0.0632520	+	0.0243203i
$477$	−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	$-0.279364\pi$
$479$	27.9688			1.27793			0.638963	+	0.769237i	$0.279364\pi$
$480$	−17.2637	−	10.0262i	−0.787976	−	0.457629i
$481$			44.6974i			2.03803i
$482$	3.37402	+	15.9135i	0.153682	+	0.724841i
$483$	−6.92959	−	7.67174i	−0.315307	−	0.349076i
$484$	−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
$490$	−21.9148	+	27.2090i	−0.990008	+	1.22918i
$491$	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	$0.0899819\pi$
$503$			12.5118i			0.557873i	−0.960310	+	0.278937i	$0.910018\pi$
$504$	6.27587	−	4.07596i	0.279549	−	0.181558i
$505$		−	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	0.309262	−	0.950977i	$-0.399918\pi$
$509$	−14.4777	−	14.4777i	−0.641715	−	0.641715i	−0.950977	+	0.309262i	$0.899918\pi$
$510$	−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
$518$	−20.1471	+	27.7922i	−0.885211	+	1.22112i
$519$	6.06107			0.266051
$520$	39.3889	−	28.5255i	1.72732	−	1.25093i
$521$	−28.9916			−1.27015			−0.635073	−	0.772452i	$-0.719030\pi$
$521$	−28.9916			−1.27015			−0.635073	+	0.772452i	$0.719030\pi$
$522$	8.77472	+	5.70475i	0.384059	+	0.249690i
$523$	14.1402	+	14.1402i	0.618307	+	0.618307i	0.945097	−	0.326790i	$-0.105967\pi$
$523$	14.1402	+	14.1402i	0.618307	+	0.618307i	−0.326790	+	0.945097i	$0.605967\pi$
$524$	10.7486	−	27.9156i	0.469553	−	1.21950i
$525$	−14.6370	+	13.2210i	−0.638810	+	0.577012i
$526$	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
$532$	−17.2012	−	7.64709i	−0.745767	−	0.331543i
$533$	−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
$539$	−28.7167	+	23.4045i	−1.23692	+	1.00810i
$540$	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
$546$	2.87092	+	18.0023i	0.122864	+	0.770426i
$547$	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
$560$	37.3491	+	0.0175700i	1.57829	+	0.000742467i
$561$	−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	$0.510078\pi$
$563$	−24.4668	+	24.4668i	−1.03115	+	1.03115i	−0.999499	+	0.0316557i	$0.989922\pi$
$564$	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
$574$	−0.603894	−	3.78675i	−0.0252060	−	0.158056i
$575$		−	29.1296i		−	1.21479i
$576$	−7.60083	−	2.49547i	−0.316701	−	0.103978i
$577$		−	18.9614i		−	0.789372i	−0.918816	−	0.394686i	$-0.870853\pi$
$577$		−	18.9614i		−	0.789372i	0.918816	−	0.394686i	$-0.129147\pi$
$578$	−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
$581$	3.21112	+	3.55503i	0.133220	+	0.147488i
$582$	−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	$0.0521691\pi$
$587$	27.8565	+	27.8565i	1.14976	+	1.14976i	0.163161	+	0.986599i	$0.447831\pi$
$588$	−6.32931	+	12.4876i	−0.261016	+	0.514979i
$589$	−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	$0.0737487\pi$
$593$			11.1833i			0.459242i	−0.973280	+	0.229621i	$0.926251\pi$
$594$	7.32171	−	1.55236i	0.300413	−	0.0636942i
$595$	1.93605	−	1.74875i	0.0793701	−	0.0716919i
$596$	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	$-0.632646\pi$
$601$	−19.8458			−0.809525			−0.404763	+	0.914422i	$0.632646\pi$
$602$	10.1699	+	7.37237i	0.414496	+	0.300476i
$603$	−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	$-0.566688\pi$
$607$	−10.2481			−0.415956			−0.207978	+	0.978133i	$0.566688\pi$
$608$	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
$616$	38.7390	+	8.23256i	1.56084	+	0.331699i
$617$			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	0.727425	−	0.686187i	$-0.240717\pi$
$619$	1.02599	+	1.02599i	0.0412378	+	0.0412378i	−0.686187	+	0.727425i	$0.740717\pi$
$620$	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
$630$	−7.75028	+	10.6912i	−0.308779	+	0.425949i
$631$	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
$637$	−21.5462	−	26.4366i	−0.853692	−	1.04746i
$638$	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	−0.920381	−	0.391023i	$-0.872121\pi$
$643$	−13.4232	+	13.4232i	−0.529358	+	0.529358i	0.391023	+	0.920381i	$0.372121\pi$
$644$	−7.42030	−	19.2987i	−0.292401	−	0.760474i
$645$	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	$0.0331687\pi$
$647$			5.29145i			0.208028i	−0.994576	+	0.104014i	$0.966831\pi$
$648$	2.29079	−	1.65899i	0.0899909	−	0.0651715i
$649$	13.8747			0.544628
$650$	−27.9981	+	43.0650i	−1.09818	+	1.68915i
$651$	10.8469	+	12.0086i	0.425123	+	0.470653i
$652$	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
$658$	3.27514	+	20.5370i	0.127678	+	0.800614i
$659$	−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	−0.997062	−	0.0766003i	$-0.975593\pi$
$661$	−23.6650	+	23.6650i	−0.920462	+	0.920462i	0.0766003	+	0.997062i	$0.475593\pi$
$662$	−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
$672$	14.6426	−	3.09736i	0.564851	−	0.119483i
$673$	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	−0.794519	−	0.607239i	$-0.792277\pi$
$677$	−4.87288	+	4.87288i	−0.187280	+	0.187280i	0.607239	+	0.794519i	$0.292277\pi$
$678$	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
$686$	−1.48099	−	26.1497i	−0.0565446	−	0.998400i
$687$			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	$-0.462575\pi$
$691$	29.1889	−	29.1889i	1.11040	−	1.11040i	0.993096	−	0.117303i	$-0.0374248\pi$
$692$	11.3125	+	4.35576i	0.430038	+	0.165581i
$693$	−10.3909	+	9.38565i	−0.394716	+	0.356531i
$694$	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
$700$	−36.8201	+	14.1572i	−1.39167	+	0.535094i
$701$	−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
$707$	8.50576	+	9.41673i	0.319892	+	0.354152i
$708$	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
$714$	0.613599	−	0.846439i	0.0229634	−	0.0316772i
$715$	−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	$-0.737573\pi$
$719$	−36.4120			−1.35794			−0.678969	+	0.734167i	$0.737573\pi$
$720$	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	$-0.891088\pi$
$727$		−	18.0933i		−	0.671042i	0.942033	−	0.335521i	$-0.108912\pi$
$728$	−7.57890	+	35.6631i	−0.280893	+	1.32176i
$729$			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	0.863051	−	0.505117i	$-0.168551\pi$
$733$	9.69069	+	9.69069i	0.357934	+	0.357934i	−0.505117	+	0.863051i	$0.668551\pi$
$734$	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
$742$	9.42196	−	12.9973i	0.345891	−	0.477145i
$743$	−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
$749$	17.1372	+	18.9726i	0.626179	+	0.693242i
$750$	−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
$756$	−2.14958	+	4.83522i	−0.0781794	+	0.175855i
$757$	−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	$-0.378429\pi$
$761$	20.5632			0.745415			0.372708	+	0.927949i	$0.378429\pi$
$762$	−12.7933	−	8.31740i	−0.463454	−	0.301308i
$763$	17.4422	+	19.3103i	0.631451	+	0.699080i
$764$	−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	$0.112158\pi$
$769$			19.1403i			0.690219i	−0.938563	+	0.345109i	$0.887842\pi$
$770$	−69.0125	+	11.0058i	−2.48704	+	0.396621i
$771$	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	−0.388982	−	0.921246i	$-0.627173\pi$
$773$	14.7985	−	14.7985i	0.532264	−	0.532264i	0.921246	+	0.388982i	$0.127173\pi$
$774$	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
$784$	−20.7873	+	18.7586i	−0.742405	+	0.669951i
$785$	−8.95608			−0.319656
$786$	4.38715	+	20.6920i	0.156485	+	0.738058i
$787$	20.6147	−	20.6147i	0.734836	−	0.734836i	−0.236738	−	0.971574i	$-0.576078\pi$
$787$	20.6147	−	20.6147i	0.734836	−	0.734836i	0.971574	+	0.236738i	$0.0760783\pi$
$788$	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	$0.182785\pi$
$797$	39.0381	+	39.0381i	1.38280	+	1.38280i	0.543192	+	0.839608i	$0.317215\pi$
$798$	13.1448	−	2.09627i	0.465321	−	0.0742072i
$799$		−	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
$805$	24.4556	+	27.0748i	0.861947	+	0.954262i
$806$	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	0.929470	−	0.368898i	$-0.120265\pi$
$811$	15.9640	+	15.9640i	0.560571	+	0.560571i	−0.368898	+	0.929470i	$0.620265\pi$
$812$	−35.7838	−	15.9083i	−1.25577	−	0.558272i
$813$	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
$819$	−8.64043	−	9.56582i	−0.301921	−	0.334257i
$820$	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
$826$	−5.75735	+	7.94207i	−0.200324	+	0.276340i
$827$	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	0.948914	−	0.315536i	$-0.102184\pi$
$829$	18.2365	+	18.2365i	0.633378	+	0.633378i	−0.315536	+	0.948914i	$0.602184\pi$
$830$	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	$-0.874197\pi$
$839$		−	22.3042i		−	0.770027i	0.922911	−	0.385014i	$-0.125803\pi$
$840$	−22.1485	+	14.3847i	−0.764197	+	0.496320i
$841$		−	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	−0.803435	−	0.595392i	$-0.796997\pi$
$853$	−6.07615	+	6.07615i	−0.208043	+	0.208043i	0.595392	+	0.803435i	$0.296997\pi$
$854$	21.8060	−	30.0806i	0.746185	−	1.02934i
$855$	12.5549			0.429370
$856$	4.31703	−	26.9885i	0.147553	−	0.922449i
$857$	20.1963			0.689894			0.344947	−	0.938622i	$-0.387897\pi$
$857$	20.1963			0.689894			0.344947	+	0.938622i	$0.387897\pi$
$858$	−19.8760	+	30.5721i	−0.678554	+	1.04371i
$859$	−11.3242	−	11.3242i	−0.386376	−	0.386376i	0.487016	−	0.873393i	$-0.338085\pi$
$859$	−11.3242	−	11.3242i	−0.386376	−	0.386376i	−0.873393	+	0.487016i	$0.838085\pi$
$860$	9.61561	+	21.6566i	0.327890	+	0.738484i
$861$	1.81750	+	2.01216i	0.0619403	+	0.0685741i
$862$	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
$868$	11.6150	+	30.2082i	0.394239	+	1.02533i
$869$	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
$875$	17.0107	−	15.3651i	0.575068	−	0.519436i
$876$	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	$-0.898563\pi$
$881$		−	18.5990i		−	0.626616i	0.949652	−	0.313308i	$-0.101437\pi$
$882$	−1.06076	−	9.84250i	−0.0357177	−	0.331414i
$883$	−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	$0.0291975\pi$
$887$			5.45605i			0.183196i	−0.995796	+	0.0915981i	$0.970803\pi$
$888$	−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
$896$	29.5553	+	4.74186i	0.987373	+	0.158414i
$897$	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
$910$	−10.1319	−	63.5329i	−0.335870	−	2.10610i
$911$		−	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
$917$	−26.5249	−	29.3657i	−0.875930	−	0.969742i
$918$	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
$924$	−26.1387	+	10.0503i	−0.859901	+	0.330630i
$925$	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	$-0.922049\pi$
$929$		−	14.7795i		−	0.484899i	0.970164	−	0.242450i	$-0.0779509\pi$
$930$	6.33148	+	29.8624i	0.207617	+	0.979225i
$931$	−19.3033	+	15.7325i	−0.632641	+	0.515612i
$932$	−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	$-0.686594\pi$
$937$	−33.8675			−1.10640			−0.553201	+	0.833048i	$0.686594\pi$
$938$	2.10675	−	2.90619i	0.0687879	−	0.0948906i
$939$	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	0.476233	−	0.879319i	$-0.342002\pi$
$941$	−12.3650	−	12.3650i	−0.403087	−	0.403087i	−0.879319	+	0.476233i	$0.842002\pi$
$942$	−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
$952$	1.75353	−	1.13886i	0.0568322	−	0.0369106i
$953$		−	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
$966$	11.8371	+	8.58094i	0.380853	+	0.276087i
$967$	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	0.651630	−	0.758537i	$-0.274085\pi$
$971$	−3.33131	−	3.33131i	−0.106907	−	0.106907i	−0.758537	+	0.651630i	$0.774085\pi$
$972$	−0.718646	+	1.86643i	−0.0230506	+	0.0598657i
$973$	16.5307	−	14.9315i	0.529949	−	0.478683i
$974$	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
$980$	22.3371	−	44.0707i	0.713534	−	1.40779i
$981$	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	$-0.810791\pi$
$983$		−	35.1168i		−	1.12005i	0.828475	−	0.560027i	$-0.189209\pi$
$984$	0.457847	−	2.86230i	0.0145956	−	0.0912468i
$985$	−61.7631			−1.96794
$986$	2.45173	+	1.59395i	0.0780789	+	0.0507618i
$987$	−9.85699	−	10.9127i	−0.313751	−	0.347354i
$988$	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
$994$	−8.48375	−	53.1979i	−0.269088	−	1.68734i
$995$	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	$0.600404\pi$
$997$	−39.8129	+	39.8129i	−1.26089	+	1.26089i	−0.950663	+	0.310225i	$0.899596\pi$
$998$	−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.139.2	yes	64
4.3	odd	2		1344.2.u.a.1231.16		64
7.6	odd	2	inner	336.2.u.a.139.1	✓	64
16.3	odd	4	inner	336.2.u.a.307.1	yes	64
16.13	even	4		1344.2.u.a.559.17		64
28.27	even	2		1344.2.u.a.1231.17		64
112.13	odd	4		1344.2.u.a.559.16		64
112.83	even	4	inner	336.2.u.a.307.2	yes	64

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

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
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} +(0.589256 + 3.69497i) 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} +(-1.77345 - 1.96338i) 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} +(-1.89903 - 4.93899i) 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} +(6.25878 + 6.92910i) 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} +(3.02940 + 2.19607i) 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} +(4.07596 + 6.27587i) 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} +(-10.6912 - 7.75028i) 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} +(-9.38565 - 10.3909i) 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} +(-4.83522 - 2.14958i) 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} +(9.56582 - 8.64043i) 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} +(9.84250 - 1.06076i) 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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