LMFDB - Embedded newform 784.2.m.k.197.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(197,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(4))

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

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

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

chi := DirichletCharacter("784.197");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.m (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			197.8
Character	$\chi$	$=$	784.197
Dual form			784.2.m.k.589.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.844695 + 1.13424i) q^{2} +(-0.614312 + 0.614312i) q^{3} +(-0.572980 + 1.91617i) q^{4} +(-2.31562 - 2.31562i) q^{5} +(-1.21568 - 0.177868i) q^{6} +(-2.65738 + 0.968682i) q^{8} +2.24524i q^{9} +(0.670466 - 4.58245i) q^{10} +(-2.10128 - 2.10128i) q^{11} +(-0.825135 - 1.52911i) q^{12} +(3.63293 - 3.63293i) q^{13} +2.84503 q^{15} +(-3.34339 - 2.19585i) q^{16} -3.63712 q^{17} +(-2.54663 + 1.89654i) q^{18} +(1.17340 - 1.17340i) q^{19} +(5.76392 - 3.11031i) q^{20} +(0.608405 - 4.15828i) q^{22} -6.16261i q^{23} +(1.03739 - 2.22753i) q^{24} +5.72420i q^{25} +(7.18931 + 1.05188i) q^{26} +(-3.22221 - 3.22221i) q^{27} +(5.10266 - 5.10266i) q^{29} +(2.40318 + 3.22693i) q^{30} -2.01521 q^{31} +(-0.333530 - 5.64701i) q^{32} +2.58168 q^{33} +(-3.07226 - 4.12535i) q^{34} +(-4.30226 - 1.28648i) q^{36} +(4.07871 + 4.07871i) q^{37} +(2.32209 + 0.339748i) q^{38} +4.46350i q^{39} +(8.39658 + 3.91038i) q^{40} -3.71244i q^{41} +(-2.91640 - 2.91640i) q^{43} +(5.23039 - 2.82241i) q^{44} +(5.19913 - 5.19913i) q^{45} +(6.98986 - 5.20553i) q^{46} -10.1313 q^{47} +(3.40282 - 0.704944i) q^{48} +(-6.49259 + 4.83520i) q^{50} +(2.23433 - 2.23433i) q^{51} +(4.87970 + 9.04289i) q^{52} +(-2.69609 - 2.69609i) q^{53} +(0.932961 - 6.37654i) q^{54} +9.73153i q^{55} +1.44167i q^{57} +(10.0978 + 1.47743i) q^{58} +(-2.67184 - 2.67184i) q^{59} +(-1.63014 + 5.45154i) q^{60} +(-4.79291 + 4.79291i) q^{61} +(-1.70224 - 2.28573i) q^{62} +(6.12331 - 5.14831i) q^{64} -16.8250 q^{65} +(2.18073 + 2.92823i) q^{66} +(-4.30731 + 4.30731i) q^{67} +(2.08400 - 6.96933i) q^{68} +(3.78577 + 3.78577i) q^{69} +9.55168i q^{71} +(-2.17492 - 5.96646i) q^{72} -1.14315i q^{73} +(-1.18095 + 8.07148i) q^{74} +(-3.51644 - 3.51644i) q^{75} +(1.57610 + 2.92078i) q^{76} +(-5.06266 + 3.77030i) q^{78} -0.241393 q^{79} +(2.65726 + 12.8268i) q^{80} -2.77684 q^{81} +(4.21079 - 3.13588i) q^{82} +(0.459183 - 0.459183i) q^{83} +(8.42219 + 8.42219i) q^{85} +(0.844416 - 5.77135i) q^{86} +6.26924i q^{87} +(7.61936 + 3.54842i) q^{88} -4.35118i q^{89} +(10.2887 + 1.50536i) q^{90} +(11.8086 + 3.53106i) q^{92} +(1.23797 - 1.23797i) q^{93} +(-8.55785 - 11.4913i) q^{94} -5.43432 q^{95} +(3.67392 + 3.26414i) q^{96} -6.80176 q^{97} +(4.71788 - 4.71788i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) $ 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	0.844695	+	1.13424i	0.597290	+	0.802026i
$2$	0.844695	+	1.13424i	0.597290	+	0.802026i
$3$	−0.614312	+	0.614312i	−0.354673	+	0.354673i	−0.861845	−	0.507172i	$-0.830691\pi$
$3$	−0.614312	+	0.614312i	−0.354673	+	0.354673i	0.507172	+	0.861845i	$0.330691\pi$
$4$	−0.572980	+	1.91617i	−0.286490	+	0.958083i
$5$	−2.31562	−	2.31562i	−1.03558	−	1.03558i	−0.999343	−	0.0362338i	$-0.988464\pi$
$5$	−2.31562	−	2.31562i	−1.03558	−	1.03558i	−0.0362338	−	0.999343i	$-0.511536\pi$
$6$	−1.21568	−	0.177868i	−0.496299	−	0.0726143i
$7$		0			0
$7$		0			0
$8$	−2.65738	+	0.968682i	−0.939525	+	0.342481i
$9$			2.24524i			0.748414i
$10$	0.670466	−	4.58245i	0.212020	−	1.44910i
$11$	−2.10128	−	2.10128i	−0.633559	−	0.633559i	0.315400	−	0.948959i	$-0.397861\pi$
$11$	−2.10128	−	2.10128i	−0.633559	−	0.633559i	−0.948959	+	0.315400i	$0.897861\pi$
$12$	−0.825135	−	1.52911i	−0.238196	−	0.441417i
$13$	3.63293	−	3.63293i	1.00759	−	1.00759i	0.00762179	−	0.999971i	$-0.497574\pi$
$13$	3.63293	−	3.63293i	1.00759	−	1.00759i	0.999971	−	0.00762179i	$-0.00242611\pi$
$14$		0			0
$15$	2.84503			0.734583
$16$	−3.34339	−	2.19585i	−0.835847	−	0.548963i
$17$	−3.63712			−0.882131			−0.441066	−	0.897475i	$-0.645399\pi$
$17$	−3.63712			−0.882131			−0.441066	+	0.897475i	$0.645399\pi$
$18$	−2.54663	+	1.89654i	−0.600247	+	0.447020i
$19$	1.17340	−	1.17340i	0.269197	−	0.269197i	−0.559579	−	0.828777i	$-0.689037\pi$
$19$	1.17340	−	1.17340i	0.269197	−	0.269197i	0.828777	+	0.559579i	$0.189037\pi$
$20$	5.76392	−	3.11031i	1.28885	−	0.695486i
$21$		0			0
$22$	0.608405	−	4.15828i	0.129712	−	0.886549i
$23$		−	6.16261i		−	1.28499i	−0.766288	−	0.642497i	$-0.777899\pi$
$23$		−	6.16261i		−	1.28499i	0.766288	−	0.642497i	$-0.222101\pi$
$24$	1.03739	−	2.22753i	0.211756	−	0.454693i
$25$			5.72420i			1.14484i
$26$	7.18931	+	1.05188i	1.40994	+	0.206291i
$27$	−3.22221	−	3.22221i	−0.620115	−	0.620115i
$28$		0			0
$29$	5.10266	−	5.10266i	0.947539	−	0.947539i	−0.0511514	−	0.998691i	$-0.516289\pi$
$29$	5.10266	−	5.10266i	0.947539	−	0.947539i	0.998691	+	0.0511514i	$0.0162891\pi$
$30$	2.40318	+	3.22693i	0.438759	+	0.589154i
$31$	−2.01521			−0.361943			−0.180972	−	0.983488i	$-0.557924\pi$
$31$	−2.01521			−0.361943			−0.180972	+	0.983488i	$0.557924\pi$
$32$	−0.333530	−	5.64701i	−0.0589603	−	0.998260i
$33$	2.58168			0.449413
$34$	−3.07226	−	4.12535i	−0.526888	−	0.707492i
$35$		0			0
$36$	−4.30226	−	1.28648i	−0.717043	−	0.214413i
$37$	4.07871	+	4.07871i	0.670536	+	0.670536i	0.957839	−	0.287304i	$-0.0927590\pi$
$37$	4.07871	+	4.07871i	0.670536	+	0.670536i	−0.287304	+	0.957839i	$0.592759\pi$
$38$	2.32209	+	0.339748i	0.376692	+	0.0551144i
$39$			4.46350i			0.714732i
$40$	8.39658	+	3.91038i	1.32762	+	0.618285i
$41$		−	3.71244i		−	0.579786i	−0.957059	−	0.289893i	$-0.906380\pi$
$41$		−	3.71244i		−	0.579786i	0.957059	−	0.289893i	$-0.0936198\pi$
$42$		0			0
$43$	−2.91640	−	2.91640i	−0.444747	−	0.444747i	0.448857	−	0.893604i	$-0.351831\pi$
$43$	−2.91640	−	2.91640i	−0.444747	−	0.444747i	−0.893604	+	0.448857i	$0.851831\pi$
$44$	5.23039	−	2.82241i	0.788511	−	0.425494i
$45$	5.19913	−	5.19913i	0.775040	−	0.775040i
$46$	6.98986	−	5.20553i	1.03060	−	0.767513i
$47$	−10.1313			−1.47780			−0.738900	−	0.673815i	$-0.764655\pi$
$47$	−10.1313			−1.47780			−0.738900	+	0.673815i	$0.764655\pi$
$48$	3.40282	−	0.704944i	0.491155	−	0.101750i
$49$		0			0
$50$	−6.49259	+	4.83520i	−0.918191	+	0.683801i
$51$	2.23433	−	2.23433i	0.312868	−	0.312868i
$52$	4.87970	+	9.04289i	0.676692	+	1.25402i
$53$	−2.69609	−	2.69609i	−0.370336	−	0.370336i	0.497264	−	0.867600i	$-0.334338\pi$
$53$	−2.69609	−	2.69609i	−0.370336	−	0.370336i	−0.867600	+	0.497264i	$0.834338\pi$
$54$	0.932961	−	6.37654i	0.126960	−	0.867737i
$55$			9.73153i			1.31220i
$56$		0			0
$57$			1.44167i			0.190954i
$58$	10.0978	+	1.47743i	1.32591	+	0.193995i
$59$	−2.67184	−	2.67184i	−0.347845	−	0.347845i	0.511462	−	0.859306i	$-0.329104\pi$
$59$	−2.67184	−	2.67184i	−0.347845	−	0.347845i	−0.859306	+	0.511462i	$0.829104\pi$
$60$	−1.63014	+	5.45154i	−0.210451	+	0.703791i
$61$	−4.79291	+	4.79291i	−0.613670	+	0.613670i	−0.943900	−	0.330231i	$-0.892873\pi$
$61$	−4.79291	+	4.79291i	−0.613670	+	0.613670i	0.330231	+	0.943900i	$0.392873\pi$
$62$	−1.70224	−	2.28573i	−0.216185	−	0.290288i
$63$		0			0
$64$	6.12331	−	5.14831i	0.765414	−	0.643538i
$65$	−16.8250			−2.08688
$66$	2.18073	+	2.92823i	0.268430	+	0.360441i
$67$	−4.30731	+	4.30731i	−0.526222	+	0.526222i	−0.919444	−	0.393222i	$-0.871361\pi$
$67$	−4.30731	+	4.30731i	−0.526222	+	0.526222i	0.393222	+	0.919444i	$0.371361\pi$
$68$	2.08400	−	6.96933i	0.252722	−	0.845155i
$69$	3.78577	+	3.78577i	0.455753	+	0.455753i
$70$		0			0
$71$			9.55168i			1.13358i	0.823864	+	0.566788i	$0.191814\pi$
$71$			9.55168i			1.13358i	−0.823864	+	0.566788i	$0.808186\pi$
$72$	−2.17492	−	5.96646i	−0.256317	−	0.703154i
$73$		−	1.14315i		−	0.133796i	−0.997760	−	0.0668980i	$-0.978690\pi$
$73$		−	1.14315i		−	0.133796i	0.997760	−	0.0668980i	$-0.0213102\pi$
$74$	−1.18095	+	8.07148i	−0.137283	+	0.938291i
$75$	−3.51644	−	3.51644i	−0.406044	−	0.406044i
$76$	1.57610	+	2.92078i	0.180791	+	0.335036i
$77$		0			0
$78$	−5.06266	+	3.77030i	−0.573233	+	0.426902i
$79$	−0.241393			−0.0271588			−0.0135794	−	0.999908i	$-0.504323\pi$
$79$	−0.241393			−0.0271588			−0.0135794	+	0.999908i	$0.504323\pi$
$80$	2.65726	+	12.8268i	0.297090	+	1.43408i
$81$	−2.77684			−0.308538
$82$	4.21079	−	3.13588i	0.465004	−	0.346300i
$83$	0.459183	−	0.459183i	0.0504018	−	0.0504018i	−0.681457	−	0.731858i	$-0.738653\pi$
$83$	0.459183	−	0.459183i	0.0504018	−	0.0504018i	0.731858	+	0.681457i	$0.238653\pi$
$84$		0			0
$85$	8.42219	+	8.42219i	0.913515	+	0.913515i
$86$	0.844416	−	5.77135i	0.0910557	−	0.622341i
$87$			6.26924i			0.672133i
$88$	7.61936	+	3.54842i	0.812226	+	0.378263i
$89$		−	4.35118i		−	0.461224i	−0.973046	−	0.230612i	$-0.925927\pi$
$89$		−	4.35118i		−	0.461224i	0.973046	−	0.230612i	$-0.0740728\pi$
$90$	10.2887	+	1.50536i	1.08453	+	0.158679i
$91$		0			0
$92$	11.8086	+	3.53106i	1.23113	+	0.368138i
$93$	1.23797	−	1.23797i	0.128371	−	0.128371i
$94$	−8.55785	−	11.4913i	−0.882675	−	1.18523i
$95$	−5.43432			−0.557549
$96$	3.67392	+	3.26414i	0.374968	+	0.333144i
$97$	−6.80176			−0.690614			−0.345307	−	0.938490i	$-0.612225\pi$
$97$	−6.80176			−0.690614			−0.345307	+	0.938490i	$0.612225\pi$
$98$		0			0
$99$	4.71788	−	4.71788i	0.474165	−	0.474165i
$100$	−10.9685	−	3.27985i	−1.09685	−	0.327985i
$101$	2.25232	+	2.25232i	0.224114	+	0.224114i	0.810229	−	0.586114i	$-0.199343\pi$
$101$	2.25232	+	2.25232i	0.224114	+	0.224114i	−0.586114	+	0.810229i	$0.699343\pi$
$102$	4.42158	+	0.646928i	0.437801	+	0.0640554i
$103$			3.75921i			0.370406i	0.982700	+	0.185203i	$0.0592942\pi$
$103$			3.75921i			0.370406i	−0.982700	+	0.185203i	$0.940706\pi$
$104$	−6.13491	+	13.1732i	−0.601577	+	1.29174i
$105$		0			0
$106$	0.780626	−	5.33537i	0.0758211	−	0.518217i
$107$	0.268184	+	0.268184i	0.0259263	+	0.0259263i	0.719951	−	0.694025i	$-0.244164\pi$
$107$	0.268184	+	0.268184i	0.0259263	+	0.0259263i	−0.694025	+	0.719951i	$0.744164\pi$
$108$	8.02056	−	4.32803i	0.771779	−	0.416465i
$109$	7.06908	−	7.06908i	0.677095	−	0.677095i	−0.282247	−	0.959342i	$-0.591080\pi$
$109$	7.06908	−	7.06908i	0.677095	−	0.677095i	0.959342	+	0.282247i	$0.0910796\pi$
$110$	−11.0378	+	8.22017i	−1.05242	+	0.783763i
$111$	−5.01120			−0.475642
$112$		0			0
$113$	2.62015			0.246483			0.123242	−	0.992377i	$-0.460671\pi$
$113$	2.62015			0.246483			0.123242	+	0.992377i	$0.460671\pi$
$114$	−1.63520	+	1.21777i	−0.153150	+	0.114055i
$115$	−14.2703	+	14.2703i	−1.33071	+	1.33071i
$116$	6.85382	+	12.7013i	0.636361	+	1.17928i
$117$	8.15680	+	8.15680i	0.754097	+	0.754097i
$118$	0.773607	−	5.28739i	0.0712163	−	0.486744i
$119$		0			0
$120$	−7.56031	+	2.75592i	−0.690159	+	0.251580i
$121$		−	2.16926i		−	0.197205i
$122$	−9.48484	−	1.38774i	−0.858717	−	0.125640i
$123$	2.28060	+	2.28060i	0.205635	+	0.205635i
$124$	1.15468	−	3.86148i	0.103693	−	0.346772i
$125$	1.67697	−	1.67697i	0.149993	−	0.149993i
$126$		0			0
$127$	−12.8840			−1.14327			−0.571635	−	0.820508i	$-0.693691\pi$
$127$	−12.8840			−1.14327			−0.571635	+	0.820508i	$0.693691\pi$
$128$	11.0117	+	2.59653i	0.973308	+	0.229503i
$129$	3.58316			0.315479
$130$	−14.2120	−	19.0835i	−1.24647	−	1.67373i
$131$	−6.57048	+	6.57048i	−0.574065	+	0.574065i	−0.933262	−	0.359197i	$-0.883051\pi$
$131$	−6.57048	+	6.57048i	−0.574065	+	0.574065i	0.359197	+	0.933262i	$0.383051\pi$
$132$	−1.47925	+	4.94693i	−0.128752	+	0.430575i
$133$		0			0
$134$	−8.52388	−	1.24714i	−0.736351	−	0.107737i
$135$			14.9229i			1.28435i
$136$	9.66520	−	3.52321i	0.828784	−	0.302113i
$137$		−	11.8024i		−	1.00834i	−0.863604	−	0.504172i	$-0.831798\pi$
$137$		−	11.8024i		−	1.00834i	0.863604	−	0.504172i	$-0.168202\pi$
$138$	−1.09613	+	7.49177i	−0.0933090	+	0.637742i
$139$	−8.15708	−	8.15708i	−0.691874	−	0.691874i	0.270770	−	0.962644i	$-0.412722\pi$
$139$	−8.15708	−	8.15708i	−0.691874	−	0.691874i	−0.962644	+	0.270770i	$0.912722\pi$
$140$		0			0
$141$	6.22377	−	6.22377i	0.524136	−	0.524136i
$142$	−10.8339	+	8.06825i	−0.909157	+	0.677073i
$143$	−15.2676			−1.27674
$144$	4.93022	−	7.50671i	0.410852	−	0.625559i
$145$	−23.6316			−1.96250
$146$	1.29660	−	0.965616i	0.107308	−	0.0799149i
$147$		0			0
$148$	−10.1525	+	5.47846i	−0.834531	+	0.450327i
$149$	−8.30787	−	8.30787i	−0.680607	−	0.680607i	0.279530	−	0.960137i	$-0.409821\pi$
$149$	−8.30787	−	8.30787i	−0.680607	−	0.680607i	−0.960137	+	0.279530i	$0.909821\pi$
$150$	1.01815	−	6.95880i	0.0831318	−	0.568184i
$151$		−	19.6074i		−	1.59563i	−0.602903	−	0.797815i	$-0.705989\pi$
$151$		−	19.6074i		−	1.59563i	0.602903	−	0.797815i	$-0.294011\pi$
$152$	−1.98152	+	4.25483i	−0.160723	+	0.345113i
$153$		−	8.16622i		−	0.660199i
$154$		0			0
$155$	4.66647	+	4.66647i	0.374820	+	0.374820i
$156$	−8.55281	−	2.55750i	−0.684773	−	0.204764i
$157$	3.82384	−	3.82384i	0.305176	−	0.305176i	−0.537859	−	0.843035i	$-0.680767\pi$
$157$	3.82384	−	3.82384i	0.305176	−	0.305176i	0.843035	+	0.537859i	$0.180767\pi$
$158$	−0.203903	−	0.273796i	−0.0162217	−	0.0217821i
$159$	3.31248			0.262696
$160$	−12.3040	+	13.8487i	−0.972718	+	1.09483i
$161$		0			0
$162$	−2.34558	−	3.14959i	−0.184286	−	0.247455i
$163$	7.97599	−	7.97599i	0.624727	−	0.624727i	−0.322009	−	0.946737i	$-0.604358\pi$
$163$	7.97599	−	7.97599i	0.624727	−	0.624727i	0.946737	+	0.322009i	$0.104358\pi$
$164$	7.11366	+	2.12716i	0.555484	+	0.166103i
$165$	−5.97819	−	5.97819i	−0.465402	−	0.465402i
$166$	0.908690	+	0.132952i	0.0705280	+	0.0103191i
$167$			21.8111i			1.68779i	0.536508	+	0.843895i	$0.319743\pi$
$167$			21.8111i			1.68779i	−0.536508	+	0.843895i	$0.680257\pi$
$168$		0			0
$169$		−	13.3963i		−	1.03049i
$170$	−2.43857	+	16.6669i	−0.187029	+	1.27830i
$171$	2.63458	+	2.63458i	0.201471	+	0.201471i
$172$	7.25935	−	3.91727i	0.553520	−	0.298689i
$173$	16.0601	−	16.0601i	1.22103	−	1.22103i	0.253759	−	0.967267i	$-0.418333\pi$
$173$	16.0601	−	16.0601i	1.22103	−	1.22103i	0.967267	−	0.253759i	$-0.0816671\pi$
$174$	−7.11080	+	5.29560i	−0.539068	+	0.401458i
$175$		0			0
$176$	2.41129	+	11.6395i	0.181758	+	0.877359i
$177$	3.28269			0.246742
$178$	4.93526	−	3.67542i	0.369913	−	0.275484i
$179$	−15.2220	+	15.2220i	−1.13774	+	1.13774i	−0.148888	+	0.988854i	$0.547569\pi$
$179$	−15.2220	+	15.2220i	−1.13774	+	1.13774i	−0.988854	+	0.148888i	$0.952431\pi$
$180$	6.98340	+	12.9414i	0.520512	+	0.964595i
$181$	11.8484	+	11.8484i	0.880684	+	0.880684i	0.993604	−	0.112920i	$-0.0360205\pi$
$181$	11.8484	+	11.8484i	0.880684	+	0.880684i	−0.112920	+	0.993604i	$0.536020\pi$
$182$		0			0
$183$		−	5.88869i		−	0.435304i
$184$	5.96961	+	16.3764i	0.440086	+	1.20728i
$185$		−	18.8895i		−	1.38878i
$186$	2.44986	+	0.358442i	0.179632	+	0.0262823i
$187$	7.64260	+	7.64260i	0.558882	+	0.558882i
$188$	5.80503	−	19.4132i	0.423375	−	1.41586i
$189$		0			0
$190$	−4.59034	−	6.16380i	−0.333018	−	0.447169i
$191$	7.88799			0.570755			0.285377	−	0.958415i	$-0.407881\pi$
$191$	7.88799			0.570755			0.285377	+	0.958415i	$0.407881\pi$
$192$	−0.598958	+	6.92429i	−0.0432261	+	0.499717i
$193$	24.8808			1.79096			0.895478	−	0.445105i	$-0.146834\pi$
$193$	24.8808			1.79096			0.895478	+	0.445105i	$0.146834\pi$
$194$	−5.74541	−	7.71480i	−0.412497	−	0.553890i
$195$	10.3358	−	10.3358i	0.740160	−	0.740160i
$196$		0			0
$197$	−7.75408	−	7.75408i	−0.552455	−	0.552455i	0.374694	−	0.927149i	$-0.377748\pi$
$197$	−7.75408	−	7.75408i	−0.552455	−	0.552455i	−0.927149	+	0.374694i	$0.877748\pi$
$198$	9.33635	+	1.36602i	0.663506	+	0.0970786i
$199$			11.4472i			0.811469i	0.913991	+	0.405734i	$0.132984\pi$
$199$			11.4472i			0.811469i	−0.913991	+	0.405734i	$0.867016\pi$
$200$	−5.54493	−	15.2114i	−0.392086	−	1.07561i
$201$		−	5.29207i		−	0.373274i
$202$	−0.652139	+	4.45719i	−0.0458843	+	0.313607i
$203$		0			0
$204$	3.00112	+	5.56157i	0.210120	+	0.389387i
$205$	−8.59661	+	8.59661i	−0.600414	+	0.600414i
$206$	−4.26383	+	3.17539i	−0.297075	+	0.221240i
$207$	13.8366			0.961707
$208$	−20.1237	+	4.16891i	−1.39532	+	0.289062i
$209$	−4.93130			−0.341105
$210$		0			0
$211$	−8.69524	+	8.69524i	−0.598605	+	0.598605i	−0.939941	−	0.341336i	$-0.889120\pi$
$211$	−8.69524	+	8.69524i	−0.598605	+	0.598605i	0.341336	+	0.939941i	$0.389120\pi$
$212$	6.71096	−	3.62135i	0.460910	−	0.248715i
$213$	−5.86771	−	5.86771i	−0.402049	−	0.402049i
$214$	−0.0776500	+	0.530717i	−0.00530805	+	0.0362791i
$215$			13.5066i			0.921139i
$216$	11.6839	+	5.44134i	0.794991	+	0.370236i
$217$		0			0
$218$	13.9892	+	2.04679i	0.947470	+	0.138626i
$219$	0.702252	+	0.702252i	0.0474538	+	0.0474538i
$220$	−18.6472	−	5.57597i	−1.25720	−	0.375932i
$221$	−13.2134	+	13.2134i	−0.888829	+	0.888829i
$222$	−4.23293	−	5.68388i	−0.284096	−	0.381477i
$223$	−21.9483			−1.46976			−0.734882	−	0.678195i	$-0.762762\pi$
$223$	−21.9483			−1.46976			−0.734882	+	0.678195i	$0.762762\pi$
$224$		0			0
$225$	−12.8522			−0.856814
$226$	2.21323	+	2.97187i	0.147222	+	0.197686i
$227$	17.4436	−	17.4436i	1.15777	−	1.15777i	0.172820	−	0.984953i	$-0.444712\pi$
$227$	17.4436	−	17.4436i	1.15777	−	1.15777i	0.984953	−	0.172820i	$-0.0552878\pi$
$228$	−2.76248	−	0.826050i	−0.182950	−	0.0547065i
$229$	6.72768	+	6.72768i	0.444578	+	0.444578i	0.893547	−	0.448969i	$-0.148209\pi$
$229$	6.72768	+	6.72768i	0.444578	+	0.444578i	−0.448969	+	0.893547i	$0.648209\pi$
$230$	−28.2399	−	4.13182i	−1.86208	−	0.272444i
$231$		0			0
$232$	−8.61684	+	18.5025i	−0.565723	+	1.21475i
$233$			22.2376i			1.45684i	0.685133	+	0.728418i	$0.259744\pi$
$233$			22.2376i			1.45684i	−0.685133	+	0.728418i	$0.740256\pi$
$234$	−2.36172	+	16.1417i	−0.154391	+	1.05522i
$235$	23.4602	+	23.4602i	1.53038	+	1.53038i
$236$	6.65061	−	3.58878i	0.432918	−	0.233610i
$237$	0.148290	−	0.148290i	0.00963250	−	0.00963250i
$238$		0			0
$239$	14.9579			0.967548			0.483774	−	0.875193i	$-0.339266\pi$
$239$	14.9579			0.967548			0.483774	+	0.875193i	$0.339266\pi$
$240$	−9.51202	−	6.24726i	−0.613999	−	0.403259i
$241$	24.3500			1.56852			0.784262	−	0.620430i	$-0.213042\pi$
$241$	24.3500			1.56852			0.784262	+	0.620430i	$0.213042\pi$
$242$	2.46045	−	1.83236i	0.158164	−	0.117789i
$243$	11.3725	−	11.3725i	0.729545	−	0.729545i
$244$	−6.43777	−	11.9303i	−0.412136	−	0.763757i
$245$		0			0
$246$	−0.660325	+	4.51315i	−0.0421008	+	0.287748i
$247$		−	8.52578i		−	0.542483i
$248$	5.35518	−	1.95210i	0.340055	−	0.123958i
$249$			0.564162i			0.0357523i
$250$	3.31862	+	0.485552i	0.209888	+	0.0307090i
$251$	3.50509	+	3.50509i	0.221239	+	0.221239i	0.809020	−	0.587781i	$-0.199998\pi$
$251$	3.50509	+	3.50509i	0.221239	+	0.221239i	−0.587781	+	0.809020i	$0.699998\pi$
$252$		0			0
$253$	−12.9494	+	12.9494i	−0.814120	+	0.814120i
$254$	−10.8831	−	14.6135i	−0.682863	−	0.916932i
$255$	−10.3477			−0.647998
$256$	6.35647	+	14.6832i	0.397279	+	0.917698i
$257$	−6.49705			−0.405275			−0.202638	−	0.979254i	$-0.564951\pi$
$257$	−6.49705			−0.405275			−0.202638	+	0.979254i	$0.564951\pi$
$258$	3.02668	+	4.06415i	0.188433	+	0.253023i
$259$		0			0
$260$	9.64038	−	32.2394i	0.597871	−	1.99940i
$261$	11.4567	+	11.4567i	0.709152	+	0.709152i
$262$	−13.0025	−	1.90242i	−0.803298	−	0.117532i
$263$		−	24.7362i		−	1.52530i	−0.646811	−	0.762650i	$-0.723898\pi$
$263$		−	24.7362i		−	1.52530i	0.646811	−	0.762650i	$-0.276102\pi$
$264$	−6.86050	+	2.50083i	−0.422235	+	0.153915i
$265$			12.4862i			0.767023i
$266$		0			0
$267$	2.67298	+	2.67298i	0.163584	+	0.163584i
$268$	−5.78552	−	10.7215i	−0.353407	−	0.654922i
$269$	1.05961	−	1.05961i	0.0646055	−	0.0646055i	−0.674066	−	0.738671i	$-0.735454\pi$
$269$	1.05961	−	1.05961i	0.0646055	−	0.0646055i	0.738671	+	0.674066i	$0.235454\pi$
$270$	−16.9260	+	12.6053i	−1.03009	+	0.767132i
$271$	7.36247			0.447238			0.223619	−	0.974677i	$-0.428213\pi$
$271$	7.36247			0.447238			0.223619	+	0.974677i	$0.428213\pi$
$272$	12.1603	+	7.98658i	0.737327	+	0.484257i
$273$		0			0
$274$	13.3866	−	9.96939i	0.808717	−	0.602273i
$275$	12.0281	−	12.0281i	0.725324	−	0.725324i
$276$	−9.42333	+	5.08499i	−0.567218	+	0.306080i
$277$	−3.20233	−	3.20233i	−0.192410	−	0.192410i	0.604327	−	0.796737i	$-0.293442\pi$
$277$	−3.20233	−	3.20233i	−0.192410	−	0.192410i	−0.796737	+	0.604327i	$0.793442\pi$
$278$	2.36180	−	16.1423i	0.141652	−	0.968151i
$279$		−	4.52464i		−	0.270883i
$280$		0			0
$281$			9.72875i			0.580369i	0.956971	+	0.290184i	$0.0937166\pi$
$281$			9.72875i			0.580369i	−0.956971	+	0.290184i	$0.906283\pi$
$282$	12.3164	+	1.80203i	0.733432	+	0.107310i
$283$	−2.84445	−	2.84445i	−0.169085	−	0.169085i	0.617492	−	0.786577i	$-0.288149\pi$
$283$	−2.84445	−	2.84445i	−0.169085	−	0.169085i	−0.786577	+	0.617492i	$0.788149\pi$
$284$	−18.3026	−	5.47292i	−1.08606	−	0.324758i
$285$	3.33837	−	3.33837i	0.197748	−	0.197748i
$286$	−12.8965	−	17.3170i	−0.762583	−	1.02398i
$287$		0			0
$288$	12.6789	−	0.748855i	0.747112	−	0.0441267i
$289$	−3.77136			−0.221844
$290$	−19.9615	−	26.8038i	−1.17218	−	1.57398i
$291$	4.17840	−	4.17840i	0.244942	−	0.244942i
$292$	2.19047	+	0.655004i	0.128188	+	0.0383312i
$293$	−1.88131	−	1.88131i	−0.109908	−	0.109908i	0.650014	−	0.759922i	$-0.274763\pi$
$293$	−1.88131	−	1.88131i	−0.109908	−	0.109908i	−0.759922	+	0.650014i	$0.774763\pi$
$294$		0			0
$295$			12.3740i			0.720440i
$296$	−14.7896	−	6.88770i	−0.859630	−	0.400339i
$297$			13.5415i			0.785760i
$298$	2.40546	−	16.4407i	0.139345	−	0.952384i
$299$	−22.3883	−	22.3883i	−1.29475	−	1.29475i
$300$	8.75295	−	4.72324i	0.505352	−	0.272696i
$301$		0			0
$302$	22.2394	−	16.5623i	1.27974	−	0.953053i
$303$	−2.76726			−0.158975
$304$	−6.49977	+	1.34652i	−0.372787	+	0.0772284i
$305$	22.1971			1.27100
$306$	9.26241	−	6.89796i	0.529497	−	0.394330i
$307$	−3.98977	+	3.98977i	−0.227708	+	0.227708i	−0.811735	−	0.584026i	$-0.801476\pi$
$307$	−3.98977	+	3.98977i	−0.227708	+	0.227708i	0.584026	+	0.811735i	$0.301476\pi$
$308$		0			0
$309$	−2.30933	−	2.30933i	−0.131373	−	0.131373i
$310$	−1.35113	+	9.23462i	−0.0767391	+	0.524491i
$311$			0.808093i			0.0458228i	0.999737	+	0.0229114i	$0.00729356\pi$
$311$			0.808093i			0.0458228i	−0.999737	+	0.0229114i	$0.992706\pi$
$312$	−4.32371	−	11.8612i	−0.244782	−	0.671509i
$313$			23.2955i			1.31674i	0.752694	+	0.658371i	$0.228754\pi$
$313$			23.2955i			1.31674i	−0.752694	+	0.658371i	$0.771246\pi$
$314$	7.56712	+	1.10716i	0.427037	+	0.0624805i
$315$		0			0
$316$	0.138313	−	0.462549i	0.00778073	−	0.0260204i
$317$	−2.20803	+	2.20803i	−0.124015	+	0.124015i	−0.766390	−	0.642375i	$-0.777949\pi$
$317$	−2.20803	+	2.20803i	−0.124015	+	0.124015i	0.642375	+	0.766390i	$0.277949\pi$
$318$	2.79803	+	3.75713i	0.156906	+	0.210689i
$319$	−21.4442			−1.20064
$320$	−26.1008	−	2.25775i	−1.45908	−	0.126212i
$321$	−0.329497			−0.0183907
$322$		0			0
$323$	−4.26781	+	4.26781i	−0.237467	+	0.237467i
$324$	1.59107	−	5.32088i	0.0883930	−	0.295605i
$325$	20.7956	+	20.7956i	1.15353	+	1.15353i
$326$	15.7839	+	2.30937i	0.874191	+	0.127904i
$327$			8.68524i			0.480295i
$328$	3.59618	+	9.86537i	0.198566	+	0.544724i
$329$		0			0
$330$	1.73093	−	11.8304i	0.0952845	−	0.651244i
$331$	−11.1391	−	11.1391i	−0.612258	−	0.612258i	0.331276	−	0.943534i	$-0.392521\pi$
$331$	−11.1391	−	11.1391i	−0.612258	−	0.612258i	−0.943534	+	0.331276i	$0.892521\pi$
$332$	0.616767	+	1.14297i	0.0338495	+	0.0627288i
$333$	−9.15769	+	9.15769i	−0.501838	+	0.501838i
$334$	−24.7389	+	18.4237i	−1.35365	+	1.00810i
$335$	19.9482			1.08989
$336$		0			0
$337$	−5.36065			−0.292013			−0.146007	−	0.989284i	$-0.546642\pi$
$337$	−5.36065			−0.292013			−0.146007	+	0.989284i	$0.546642\pi$
$338$	15.1946	−	11.3158i	0.826476	−	0.615499i
$339$	−1.60959	+	1.60959i	−0.0874210	+	0.0874210i
$340$	−20.9641	+	11.3126i	−1.13694	+	0.613510i
$341$	4.23452	+	4.23452i	0.229312	+	0.229312i
$342$	−0.762816	+	5.21364i	−0.0412484	+	0.281922i
$343$		0			0
$344$	10.5750	+	4.92491i	0.570168	+	0.265534i
$345$		−	17.5328i		−	0.943934i
$346$	31.7818	+	4.65005i	1.70860	+	0.249988i
$347$	−11.7410	−	11.7410i	−0.630292	−	0.630292i	0.317849	−	0.948141i	$-0.397039\pi$
$347$	−11.7410	−	11.7410i	−0.630292	−	0.630292i	−0.948141	+	0.317849i	$0.897039\pi$
$348$	−12.0129	−	3.59215i	−0.643960	−	0.192560i
$349$	22.2799	−	22.2799i	1.19262	−	1.19262i	0.216286	−	0.976330i	$-0.430606\pi$
$349$	22.2799	−	22.2799i	1.19262	−	1.19262i	0.976330	−	0.216286i	$-0.0693943\pi$
$350$		0			0
$351$	−23.4121			−1.24965
$352$	−11.1651	+	12.5668i	−0.595102	+	0.669812i
$353$	−13.6875			−0.728510			−0.364255	−	0.931299i	$-0.618676\pi$
$353$	−13.6875			−0.728510			−0.364255	+	0.931299i	$0.618676\pi$
$354$	2.77287	+	3.72334i	0.147377	+	0.197894i
$355$	22.1181	−	22.1181i	1.17390	−	1.17390i
$356$	8.33758	+	2.49314i	0.441891	+	0.132136i
$357$		0			0
$358$	−30.1232	−	4.40737i	−1.59206	−	0.232937i
$359$			6.32231i			0.333679i	0.985984	+	0.166840i	$0.0533562\pi$
$359$			6.32231i			0.333679i	−0.985984	+	0.166840i	$0.946644\pi$
$360$	−8.77975	+	18.8524i	−0.462733	+	0.993606i
$361$			16.2462i			0.855066i
$362$	−3.43059	+	23.4471i	−0.180308	+	1.23235i
$363$	1.33260	+	1.33260i	0.0699434	+	0.0699434i
$364$		0			0
$365$	−2.64711	+	2.64711i	−0.138556	+	0.138556i
$366$	6.67916	−	4.97414i	0.349125	−	0.260003i
$367$	37.2328			1.94354			0.971768	−	0.235939i	$-0.0758165\pi$
$367$	37.2328			1.94354			0.971768	+	0.235939i	$0.0758165\pi$
$368$	−13.5322	+	20.6040i	−0.705414	+	1.07406i
$369$	8.33534			0.433920
$370$	21.4251	−	15.9559i	1.11384	−	0.829505i
$371$		0			0
$372$	1.66282	+	3.08149i	0.0862134	+	0.159768i
$373$	3.05659	+	3.05659i	0.158264	+	0.158264i	0.781797	−	0.623533i	$-0.214303\pi$
$373$	3.05659	+	3.05659i	0.158264	+	0.158264i	−0.623533	+	0.781797i	$0.714303\pi$
$374$	−2.21284	+	15.1242i	−0.114423	+	0.782053i
$375$			2.06037i			0.106397i
$376$	26.9227	−	9.81400i	1.38843	−	0.506118i
$377$		−	37.0752i		−	1.90947i
$378$		0			0
$379$	−11.5118	−	11.5118i	−0.591323	−	0.591323i	0.346666	−	0.937989i	$-0.387314\pi$
$379$	−11.5118	−	11.5118i	−0.591323	−	0.591323i	−0.937989	+	0.346666i	$0.887314\pi$
$380$	3.11376	−	10.4131i	0.159732	−	0.534179i
$381$	7.91479	−	7.91479i	0.405487	−	0.405487i
$382$	6.66295	+	8.94684i	0.340906	+	0.457760i
$383$	19.7267			1.00799			0.503993	−	0.863708i	$-0.331864\pi$
$383$	19.7267			1.00799			0.503993	+	0.863708i	$0.331864\pi$
$384$	−8.35971	+	5.16955i	−0.426605	+	0.263808i
$385$		0			0
$386$	21.0167	+	28.2206i	1.06972	+	1.43639i
$387$	6.54802	−	6.54802i	0.332855	−	0.332855i
$388$	3.89728	−	13.0333i	0.197854	−	0.661666i
$389$	−4.19887	−	4.19887i	−0.212891	−	0.212891i	0.592603	−	0.805494i	$-0.298100\pi$
$389$	−4.19887	−	4.19887i	−0.212891	−	0.212891i	−0.805494	+	0.592603i	$0.798100\pi$
$390$	20.4538	+	2.99262i	1.03572	+	0.151537i
$391$			22.4142i			1.13353i
$392$		0			0
$393$		−	8.07264i		−	0.407211i
$394$	2.24512	−	15.3448i	0.113107	−	0.773059i
$395$	0.558974	+	0.558974i	0.0281250	+	0.0281250i
$396$	6.33699	+	11.7435i	0.318446	+	0.590133i
$397$	18.0822	−	18.0822i	0.907520	−	0.907520i	−0.0885515	−	0.996072i	$-0.528224\pi$
$397$	18.0822	−	18.0822i	0.907520	−	0.907520i	0.996072	+	0.0885515i	$0.0282238\pi$
$398$	−12.9838	+	9.66937i	−0.650819	+	0.484682i
$399$		0			0
$400$	12.5695	−	19.1382i	0.628475	−	0.956911i
$401$	3.60293			0.179922			0.0899610	−	0.995945i	$-0.471326\pi$
$401$	3.60293			0.179922			0.0899610	+	0.995945i	$0.471326\pi$
$402$	6.00245	−	4.47018i	0.299375	−	0.222952i
$403$	−7.32112	+	7.32112i	−0.364691	+	0.364691i
$404$	−5.60636	+	3.02529i	−0.278927	+	0.150514i
$405$	6.43010	+	6.43010i	0.319514	+	0.319514i
$406$		0			0
$407$		−	17.1410i		−	0.849648i
$408$	−3.77310	+	8.10180i	−0.186796	+	0.401099i
$409$			15.3319i			0.758114i	0.925373	+	0.379057i	$0.123751\pi$
$409$			15.3319i			0.758114i	−0.925373	+	0.379057i	$0.876249\pi$
$410$	−17.0121	−	2.48907i	−0.840168	−	0.122926i
$411$	7.25032	+	7.25032i	0.357632	+	0.357632i
$412$	−7.20327	−	2.15395i	−0.354880	−	0.106118i
$413$		0			0
$414$	11.6877	+	15.6939i	0.574418	+	0.771314i
$415$	−2.12659			−0.104390
$416$	−21.7269	−	19.3035i	−1.06525	−	0.946432i
$417$	10.0220			0.490778
$418$	−4.16544	−	5.59325i	−0.203738	−	0.273575i
$419$	17.2949	−	17.2949i	0.844910	−	0.844910i	−0.144583	−	0.989493i	$-0.546184\pi$
$419$	17.2949	−	17.2949i	0.844910	−	0.844910i	0.989493	+	0.144583i	$0.0461841\pi$
$420$		0			0
$421$	18.2430	+	18.2430i	0.889111	+	0.889111i	0.994438	−	0.105327i	$-0.0335888\pi$
$421$	18.2430	+	18.2430i	0.889111	+	0.889111i	−0.105327	+	0.994438i	$0.533589\pi$
$422$	−17.2073	−	2.51762i	−0.837637	−	0.122556i
$423$		−	22.7472i		−	1.10601i
$424$	9.77617	+	4.55287i	0.474773	+	0.221107i
$425$		−	20.8196i		−	1.00990i
$426$	1.69894	−	11.6118i	0.0823138	−	0.562593i
$427$		0			0
$428$	−0.667549	+	0.360221i	−0.0322672	+	0.0174119i
$429$	9.37906	−	9.37906i	0.452825	−	0.452825i
$430$	−15.3196	+	11.4089i	−0.738777	+	0.550187i
$431$	33.6195			1.61940			0.809698	−	0.586846i	$-0.199631\pi$
$431$	33.6195			1.61940			0.809698	+	0.586846i	$0.199631\pi$
$432$	3.69760	+	17.8486i	0.177901	+	0.858742i
$433$	−26.5511			−1.27596			−0.637982	−	0.770051i	$-0.720231\pi$
$433$	−26.5511			−1.27596			−0.637982	+	0.770051i	$0.720231\pi$
$434$		0			0
$435$	14.5172	−	14.5172i	0.696046	−	0.696046i
$436$	9.49509	+	17.5960i	0.454732	+	0.842695i
$437$	−7.23124	−	7.23124i	−0.345917	−	0.345917i
$438$	−0.203330	+	1.38971i	−0.00971550	+	0.0664028i
$439$			19.6106i			0.935962i	0.883739	+	0.467981i	$0.155018\pi$
$439$			19.6106i			0.935962i	−0.883739	+	0.467981i	$0.844982\pi$
$440$	−9.42675	−	25.8603i	−0.449403	−	1.23284i
$441$		0			0
$442$	−26.1484	−	3.82581i	−1.24375	−	0.181975i
$443$	4.82383	+	4.82383i	0.229187	+	0.229187i	0.812353	−	0.583166i	$-0.198186\pi$
$443$	4.82383	+	4.82383i	0.229187	+	0.229187i	−0.583166	+	0.812353i	$0.698186\pi$
$444$	2.87132	−	9.60229i	0.136267	−	0.455704i
$445$	−10.0757	+	10.0757i	−0.477633	+	0.477633i
$446$	−18.5396	−	24.8945i	−0.877875	−	1.17879i
$447$	10.2072			0.482786
$448$		0			0
$449$	6.32412			0.298454			0.149227	−	0.988803i	$-0.452322\pi$
$449$	6.32412			0.298454			0.149227	+	0.988803i	$0.452322\pi$
$450$	−10.8562	−	14.5774i	−0.511766	−	0.687187i
$451$	−7.80088	+	7.80088i	−0.367329	+	0.367329i
$452$	−1.50130	+	5.02065i	−0.0706151	+	0.236152i
$453$	12.0451	+	12.0451i	0.565927	+	0.565927i
$454$	34.5197	+	5.05063i	1.62009	+	0.237038i
$455$		0			0
$456$	−1.39652	−	3.83107i	−0.0653981	−	0.179406i
$457$		−	39.4984i		−	1.84766i	−0.382805	−	0.923829i	$-0.625042\pi$
$457$		−	39.4984i		−	1.84766i	0.382805	−	0.923829i	$-0.374958\pi$
$458$	−1.94794	+	13.3136i	−0.0910211	+	0.622104i
$459$	11.7196	+	11.7196i	0.547023	+	0.547023i
$460$	−19.1676	−	35.5208i	−0.893696	−	1.65617i
$461$	1.26773	−	1.26773i	0.0590440	−	0.0590440i	−0.676968	−	0.736012i	$-0.736707\pi$
$461$	1.26773	−	1.26773i	0.0590440	−	0.0590440i	0.736012	+	0.676968i	$0.236707\pi$
$462$		0			0
$463$	−14.4427			−0.671208			−0.335604	−	0.942003i	$-0.608940\pi$
$463$	−14.4427			−0.671208			−0.335604	+	0.942003i	$0.608940\pi$
$464$	−28.2648	+	5.85548i	−1.31216	+	0.271834i
$465$	−5.73334			−0.265877
$466$	−25.2227	+	18.7840i	−1.16842	+	0.870153i
$467$	12.2835	−	12.2835i	0.568412	−	0.568412i	−0.363271	−	0.931683i	$-0.618340\pi$
$467$	12.2835	−	12.2835i	0.568412	−	0.568412i	0.931683	+	0.363271i	$0.118340\pi$
$468$	−20.3035	+	10.9561i	−0.938528	+	0.506446i
$469$		0			0
$470$	−6.79269	+	46.4262i	−0.313323	+	2.14148i
$471$			4.69806i			0.216475i
$472$	9.68827	+	4.51193i	0.445939	+	0.207679i
$473$			12.2563i			0.563547i
$474$	0.293456	+	0.0429361i	0.0134789	+	0.00197212i
$475$	6.71680	+	6.71680i	0.308188	+	0.308188i
$476$		0			0
$477$	6.05337	−	6.05337i	0.277165	−	0.277165i
$478$	12.6349	+	16.9658i	0.577907	+	0.775999i
$479$	4.78688			0.218718			0.109359	−	0.994002i	$-0.465120\pi$
$479$	4.78688			0.218718			0.109359	+	0.994002i	$0.465120\pi$
$480$	−0.948901	−	16.0659i	−0.0433112	−	0.733305i
$481$	29.6353			1.35125
$482$	20.5684	+	27.6187i	0.936863	+	1.25800i
$483$		0			0
$484$	4.15666	+	1.24294i	0.188939	+	0.0564974i
$485$	15.7503	+	15.7503i	0.715184	+	0.715184i
$486$	22.5054	+	3.29279i	1.02086	+	0.149364i
$487$			26.8699i			1.21759i	0.793328	+	0.608795i	$0.208347\pi$
$487$			26.8699i			1.21759i	−0.793328	+	0.608795i	$0.791653\pi$
$488$	8.09377	−	17.3794i	0.366388	−	0.786728i
$489$			9.79948i			0.443148i
$490$		0			0
$491$	−11.7576	−	11.7576i	−0.530611	−	0.530611i	0.390143	−	0.920754i	$-0.372426\pi$
$491$	−11.7576	−	11.7576i	−0.530611	−	0.530611i	−0.920754	+	0.390143i	$0.872426\pi$
$492$	−5.67674	+	3.06327i	−0.255927	+	0.138103i
$493$	−18.5590	+	18.5590i	−0.835854	+	0.835854i
$494$	9.67025	−	7.20169i	0.435085	−	0.324019i
$495$	−21.8496			−0.982068
$496$	6.73764	+	4.42511i	0.302529	+	0.198693i
$497$		0			0
$498$	−0.639893	+	0.476545i	−0.0286743	+	0.0213545i
$499$	−13.9362	+	13.9362i	−0.623868	+	0.623868i	−0.946518	−	0.322650i	$-0.895426\pi$
$499$	−13.9362	+	13.9362i	−0.623868	+	0.623868i	0.322650	+	0.946518i	$0.395426\pi$
$500$	2.25249	+	4.17424i	0.100734	+	0.186677i
$501$	−13.3988	−	13.3988i	−0.598614	−	0.598614i
$502$	−1.01487	+	6.93633i	−0.0452957	+	0.309584i
$503$		−	23.6387i		−	1.05400i	−0.849866	−	0.526999i	$-0.823317\pi$
$503$		−	23.6387i		−	1.05400i	0.849866	−	0.526999i	$-0.176683\pi$
$504$		0			0
$505$		−	10.4311i		−	0.464176i
$506$	−25.6259	−	3.74937i	−1.13921	−	0.166680i
$507$	8.22952	+	8.22952i	0.365486	+	0.365486i
$508$	7.38228	−	24.6879i	0.327536	−	1.09535i
$509$	−24.0695	+	24.0695i	−1.06686	+	1.06686i	−0.0692630	+	0.997598i	$0.522065\pi$
$509$	−24.0695	+	24.0695i	−1.06686	+	1.06686i	−0.997598	+	0.0692630i	$0.977935\pi$
$510$	−8.74065	−	11.7367i	−0.387043	−	0.519711i
$511$		0			0
$512$	−11.2849	+	19.6125i	−0.498726	+	0.866760i
$513$	−7.56192			−0.333867
$514$	−5.48803	−	7.36919i	−0.242067	−	0.325041i
$515$	8.70490	−	8.70490i	0.383584	−	0.383584i
$516$	−2.05308	+	6.86593i	−0.0903818	+	0.302256i
$517$	21.2887	+	21.2887i	0.936274	+	0.936274i
$518$		0			0
$519$			19.7318i			0.866131i
$520$	44.7103	−	16.2980i	1.96068	−	0.714716i
$521$		−	17.6401i		−	0.772828i	−0.922325	−	0.386414i	$-0.873714\pi$
$521$		−	17.6401i		−	0.772828i	0.922325	−	0.386414i	$-0.126286\pi$
$522$	−3.31718	+	22.6720i	−0.145189	+	0.992327i
$523$	−10.1679	−	10.1679i	−0.444612	−	0.444612i	0.448946	−	0.893559i	$-0.351799\pi$
$523$	−10.1679	−	10.1679i	−0.444612	−	0.444612i	−0.893559	+	0.448946i	$0.851799\pi$
$524$	−8.82537	−	16.3549i	−0.385538	−	0.714466i
$525$		0			0
$526$	28.0567	−	20.8946i	1.22333	−	0.911046i
$527$	7.32957			0.319281
$528$	−8.63155	−	5.66899i	−0.375640	−	0.246711i
$529$	−14.9778			−0.651209
$530$	−14.1623	+	10.5471i	−0.615172	+	0.458135i
$531$	5.99894	−	5.99894i	0.260332	−	0.260332i
$532$		0			0
$533$	−13.4870	−	13.4870i	−0.584189	−	0.584189i
$534$	−0.773936	+	5.28964i	−0.0334915	+	0.228905i
$535$		−	1.24202i		−	0.0536974i
$536$	7.27374	−	15.6186i	0.314178	−	0.674620i
$537$		−	18.7020i		−	0.807053i
$538$	2.09689	+	0.306800i	0.0904035	+	0.0132271i
$539$		0			0
$540$	−28.5947	−	8.55050i	−1.23052	−	0.367955i
$541$	21.0200	−	21.0200i	0.903721	−	0.903721i	−0.0920350	−	0.995756i	$-0.529337\pi$
$541$	21.0200	−	21.0200i	0.903721	−	0.903721i	0.995756	+	0.0920350i	$0.0293372\pi$
$542$	6.21904	+	8.35077i	0.267131	+	0.358696i
$543$	−14.5572			−0.624710
$544$	1.21309	+	20.5389i	0.0520107	+	0.880597i
$545$	−32.7386			−1.40237
$546$		0			0
$547$	27.6503	−	27.6503i	1.18224	−	1.18224i	0.203076	−	0.979163i	$-0.434906\pi$
$547$	27.6503	−	27.6503i	1.18224	−	1.18224i	0.979163	−	0.203076i	$-0.0650940\pi$
$548$	22.6153	+	6.76252i	0.966077	+	0.288880i
$549$	−10.7613	−	10.7613i	−0.459279	−	0.459279i
$550$	23.8029	+	3.48263i	1.01496	+	0.148500i
$551$		−	11.9750i		−	0.510150i
$552$	−13.7274	−	6.39301i	−0.584277	−	0.272105i
$553$		0			0
$554$	0.927205	−	6.33720i	0.0393932	−	0.269242i
$555$	11.6040	+	11.6040i	0.492564	+	0.492564i
$556$	20.3042	−	10.9565i	0.861089	−	0.464658i
$557$	4.65226	−	4.65226i	0.197123	−	0.197123i	−0.601643	−	0.798765i	$-0.705487\pi$
$557$	4.65226	−	4.65226i	0.197123	−	0.197123i	0.798765	+	0.601643i	$0.205487\pi$
$558$	5.13201	−	3.82194i	0.217255	−	0.161796i
$559$	−21.1901			−0.896247
$560$		0			0
$561$	−9.38988			−0.396441
$562$	−11.0347	+	8.21783i	−0.465471	+	0.346648i
$563$	18.8252	−	18.8252i	0.793386	−	0.793386i	−0.188657	−	0.982043i	$-0.560413\pi$
$563$	18.8252	−	18.8252i	0.793386	−	0.793386i	0.982043	+	0.188657i	$0.0604134\pi$
$564$	8.35968	+	15.4919i	0.352006	+	0.652326i
$565$	−6.06728	−	6.06728i	−0.255253	−	0.255253i
$566$	0.823582	−	5.62896i	0.0346178	−	0.236603i
$567$		0			0
$568$	−9.25253	−	25.3824i	−0.388228	−	1.06502i
$569$			2.54263i			0.106593i	0.998579	+	0.0532963i	$0.0169728\pi$
$569$			2.54263i			0.106593i	−0.998579	+	0.0532963i	$0.983027\pi$
$570$	6.60639	+	0.966592i	0.276711	+	0.0404861i
$571$	−28.3705	−	28.3705i	−1.18727	−	1.18727i	−0.977819	−	0.209450i	$-0.932833\pi$
$571$	−28.3705	−	28.3705i	−1.18727	−	1.18727i	−0.209450	−	0.977819i	$-0.567167\pi$
$572$	8.74803	−	29.2552i	0.365773	−	1.22322i
$573$	−4.84569	+	4.84569i	−0.202431	+	0.202431i
$574$		0			0
$575$	35.2760			1.47111
$576$	11.5592	+	13.7483i	0.481633	+	0.572847i
$577$	−34.7511			−1.44671			−0.723354	−	0.690478i	$-0.757400\pi$
$577$	−34.7511			−1.44671			−0.723354	+	0.690478i	$0.757400\pi$
$578$	−3.18565	−	4.27760i	−0.132505	−	0.177925i
$579$	−15.2845	+	15.2845i	−0.635204	+	0.635204i
$580$	13.5405	−	45.2821i	0.562237	−	1.88024i
$581$		0			0
$582$	8.26877	+	1.20982i	0.342751	+	0.0501485i
$583$			11.3305i			0.469260i
$584$	1.10735	+	3.03779i	0.0458225	+	0.125705i
$585$		−	37.7761i		−	1.56185i
$586$	0.544717	−	3.72299i	0.0225020	−	0.153795i
$587$	−20.1643	−	20.1643i	−0.832268	−	0.832268i	0.155559	−	0.987827i	$-0.450282\pi$
$587$	−20.1643	−	20.1643i	−0.832268	−	0.832268i	−0.987827	+	0.155559i	$0.950282\pi$
$588$		0			0
$589$	−2.36466	+	2.36466i	−0.0974341	+	0.0974341i
$590$	−14.0350	+	10.4522i	−0.577811	+	0.430311i
$591$	9.52684			0.391882
$592$	−4.68046	−	22.5929i	−0.192366	−	0.928564i
$593$	−8.40923			−0.345326			−0.172663	−	0.984981i	$-0.555237\pi$
$593$	−8.40923			−0.345326			−0.172663	+	0.984981i	$0.555237\pi$
$594$	−15.3593	+	11.4385i	−0.630199	+	0.469326i
$595$		0			0
$596$	20.6795	−	11.1590i	0.847065	−	0.457091i
$597$	−7.03213	−	7.03213i	−0.287806	−	0.287806i
$598$	6.48233	−	44.3049i	0.265082	−	1.81176i
$599$		−	3.56073i		−	0.145488i	−0.997351	−	0.0727438i	$-0.976824\pi$
$599$		−	3.56073i		−	0.145488i	0.997351	−	0.0727438i	$-0.0231755\pi$
$600$	12.7508	+	5.93821i	0.520551	+	0.242426i
$601$			45.3712i			1.85073i	0.379076	+	0.925365i	$0.376242\pi$
$601$			45.3712i			1.85073i	−0.379076	+	0.925365i	$0.623758\pi$
$602$		0			0
$603$	−9.67096	−	9.67096i	−0.393832	−	0.393832i
$604$	37.5711	+	11.2347i	1.52875	+	0.457132i
$605$	−5.02318	+	5.02318i	−0.204221	+	0.204221i
$606$	−2.33749	−	3.13872i	−0.0949540	−	0.127502i
$607$	4.90180			0.198958			0.0994789	−	0.995040i	$-0.468282\pi$
$607$	4.90180			0.198958			0.0994789	+	0.995040i	$0.468282\pi$
$608$	−7.01759	−	6.23486i	−0.284601	−	0.252857i
$609$		0			0
$610$	18.7498	+	25.1768i	0.759158	+	1.01938i
$611$	−36.8062	+	36.8062i	−1.48902	+	1.48902i
$612$	15.6478	+	4.67908i	0.632526	+	0.189141i
$613$	−5.64844	−	5.64844i	−0.228138	−	0.228138i	0.583776	−	0.811915i	$-0.301575\pi$
$613$	−5.64844	−	5.64844i	−0.228138	−	0.228138i	−0.811915	+	0.583776i	$0.801575\pi$
$614$	−7.89548	−	1.15520i	−0.318635	−	0.0466201i
$615$		−	10.5620i		−	0.425901i
$616$		0			0
$617$			40.2966i			1.62228i	0.584852	+	0.811140i	$0.301153\pi$
$617$			40.2966i			1.62228i	−0.584852	+	0.811140i	$0.698847\pi$
$618$	0.668643	−	4.57000i	0.0268968	−	0.183832i
$619$	−14.2321	−	14.2321i	−0.572038	−	0.572038i	0.360660	−	0.932698i	$-0.382552\pi$
$619$	−14.2321	−	14.2321i	−0.572038	−	0.572038i	−0.932698	+	0.360660i	$0.882552\pi$
$620$	−11.6155	+	6.26794i	−0.466491	+	0.251726i
$621$	−19.8573	+	19.8573i	−0.796844	+	0.796844i
$622$	−0.916568	+	0.682592i	−0.0367510	+	0.0273695i
$623$		0			0
$624$	9.80118	−	14.9232i	0.392361	−	0.597406i
$625$	20.8545			0.834181
$626$	−26.4226	+	19.6776i	−1.05606	+	0.786476i
$627$	3.02935	−	3.02935i	0.120981	−	0.120981i
$628$	5.13613	+	9.51810i	0.204954	+	0.379814i
$629$	−14.8348	−	14.8348i	−0.591500	−	0.591500i
$630$		0			0
$631$			15.2886i			0.608631i	0.952571	+	0.304315i	$0.0984277\pi$
$631$			15.2886i			0.608631i	−0.952571	+	0.304315i	$0.901572\pi$
$632$	0.641472	−	0.233833i	0.0255164	−	0.00930137i
$633$		−	10.6832i		−	0.424618i
$634$	−4.36953	−	0.639313i	−0.173536	−	0.0253904i
$635$	29.8345	+	29.8345i	1.18394	+	1.18394i
$636$	−1.89798	+	6.34725i	−0.0752599	+	0.251685i
$637$		0			0
$638$	−18.1138	−	24.3228i	−0.717133	−	0.962948i
$639$	−21.4458			−0.848384
$640$	−19.4864	−	31.5116i	−0.770267	−	1.24560i
$641$	−12.3673			−0.488480			−0.244240	−	0.969715i	$-0.578538\pi$
$641$	−12.3673			−0.488480			−0.244240	+	0.969715i	$0.578538\pi$
$642$	−0.278324	−	0.373727i	−0.0109846	−	0.0147498i
$643$	29.2082	−	29.2082i	1.15186	−	1.15186i	0.165677	−	0.986180i	$-0.447019\pi$
$643$	29.2082	−	29.2082i	1.15186	−	1.15186i	0.986180	−	0.165677i	$-0.0529809\pi$
$644$		0			0
$645$	−8.29724	−	8.29724i	−0.326703	−	0.326703i
$646$	−8.44570	−	1.23570i	−0.332292	−	0.0486181i
$647$			14.3708i			0.564975i	0.959271	+	0.282487i	$0.0911595\pi$
$647$			14.3708i			0.564975i	−0.959271	+	0.282487i	$0.908841\pi$
$648$	7.37911	−	2.68987i	0.289879	−	0.105668i
$649$			11.2286i			0.440760i
$650$	−6.02117	+	41.1531i	−0.236170	+	1.61416i
$651$		0			0
$652$	10.7132	+	19.8534i	0.419563	+	0.777519i
$653$	10.3709	−	10.3709i	0.405844	−	0.405844i	−0.474442	−	0.880287i	$-0.657350\pi$
$653$	10.3709	−	10.3709i	0.405844	−	0.405844i	0.880287	+	0.474442i	$0.157350\pi$
$654$	−9.85111	+	7.33638i	−0.385209	+	0.286875i
$655$	30.4295			1.18898
$656$	−8.15198	+	12.4121i	−0.318281	+	0.484613i
$657$	2.56666			0.100135
$658$		0			0
$659$	−30.0445	+	30.0445i	−1.17037	+	1.17037i	−0.188248	+	0.982122i	$0.560281\pi$
$659$	−30.0445	+	30.0445i	−1.17037	+	1.17037i	−0.982122	+	0.188248i	$0.939719\pi$
$660$	14.8806	−	8.02982i	0.579226	−	0.312560i
$661$	1.95989	+	1.95989i	0.0762309	+	0.0762309i	0.744194	−	0.667963i	$-0.232834\pi$
$661$	1.95989	+	1.95989i	0.0762309	+	0.0762309i	−0.667963	+	0.744194i	$0.732834\pi$
$662$	3.22521	−	22.0434i	0.125351	−	0.856742i
$663$		−	16.2343i		−	0.630487i
$664$	−0.775420	+	1.66502i	−0.0300921	+	0.0646154i
$665$		0			0
$666$	−18.1224	−	2.65152i	−0.702230	−	0.102744i
$667$	−31.4457	−	31.4457i	−1.21758	−	1.21758i
$668$	−41.7936	−	12.4973i	−1.61704	−	0.483535i
$669$	13.4831	−	13.4831i	0.521286	−	0.521286i
$670$	16.8502	+	22.6260i	0.650978	+	0.874118i
$671$	20.1425			0.777592
$672$		0			0
$673$	−4.79538			−0.184848			−0.0924242	−	0.995720i	$-0.529462\pi$
$673$	−4.79538			−0.184848			−0.0924242	+	0.995720i	$0.529462\pi$
$674$	−4.52811	−	6.08024i	−0.174416	−	0.234202i
$675$	18.4446	−	18.4446i	0.709933	−	0.709933i
$676$	25.6696	+	7.67583i	0.987292	+	0.295224i
$677$	−35.1646	−	35.1646i	−1.35149	−	1.35149i	−0.884000	−	0.467486i	$-0.845160\pi$
$677$	−35.1646	−	35.1646i	−1.35149	−	1.35149i	−0.467486	−	0.884000i	$-0.654840\pi$
$678$	−3.18527	−	0.466042i	−0.122330	−	0.0178982i
$679$		0			0
$680$	−30.5394	−	14.2225i	−1.17113	−	0.545409i
$681$			21.4316i			0.821262i
$682$	−1.22607	+	8.37983i	−0.0469485	+	0.320880i
$683$	−2.91144	−	2.91144i	−0.111403	−	0.111403i	0.649208	−	0.760611i	$-0.275101\pi$
$683$	−2.91144	−	2.91144i	−0.111403	−	0.111403i	−0.760611	+	0.649208i	$0.775101\pi$
$684$	−6.55785	+	3.53873i	−0.250746	+	0.135307i
$685$	−27.3298	+	27.3298i	−1.04422	+	1.04422i
$686$		0			0
$687$	−8.26579			−0.315360
$688$	3.34667	+	16.1546i	0.127591	+	0.615890i
$689$	−19.5894			−0.746296
$690$	19.8863	−	14.8099i	0.757059	−	0.563802i
$691$	−25.1130	+	25.1130i	−0.955342	+	0.955342i	−0.999045	−	0.0437029i	$-0.986085\pi$
$691$	−25.1130	+	25.1130i	−0.955342	+	0.955342i	0.0437029	+	0.999045i	$0.486085\pi$
$692$	21.5717	+	39.9759i	0.820033	+	1.51966i
$693$		0			0
$694$	3.39951	−	23.2347i	0.129043	−	0.881977i
$695$			37.7774i			1.43298i
$696$	−6.07290	−	16.6597i	−0.230193	−	0.631486i
$697$			13.5026i			0.511448i
$698$	44.0904	+	6.45093i	1.66885	+	0.244171i
$699$	−13.6608	−	13.6608i	−0.516701	−	0.516701i
$700$		0			0
$701$	15.7687	−	15.7687i	0.595575	−	0.595575i	−0.343557	−	0.939132i	$-0.611632\pi$
$701$	15.7687	−	15.7687i	0.595575	−	0.595575i	0.939132	+	0.343557i	$0.111632\pi$
$702$	−19.7761	−	26.5549i	−0.746401	−	1.00225i
$703$	9.57195			0.361013
$704$	−23.6848	−	2.04876i	−0.892655	−	0.0772156i
$705$	−28.8238			−1.08557
$706$	−11.5617	−	15.5248i	−0.435131	−	0.584283i
$707$		0			0
$708$	−1.88092	+	6.29018i	−0.0706892	+	0.236400i
$709$	−8.16940	−	8.16940i	−0.306808	−	0.306808i	0.536862	−	0.843670i	$-0.319610\pi$
$709$	−8.16940	−	8.16940i	−0.306808	−	0.306808i	−0.843670	+	0.536862i	$0.819610\pi$
$710$	43.7701	+	6.40407i	1.64266	+	0.240341i
$711$		−	0.541985i		−	0.0203260i
$712$	4.21491	+	11.5627i	0.157960	+	0.433331i
$713$			12.4190i			0.465095i
$714$		0			0
$715$	35.3539	+	35.3539i	1.32216	+	1.32216i
$716$	−20.4459	−	37.8897i	−0.764100	−	1.41600i
$717$	−9.18884	+	9.18884i	−0.343163	+	0.343163i
$718$	−7.17099	+	5.34043i	−0.267619	+	0.199303i
$719$	−28.8526			−1.07602			−0.538011	−	0.842938i	$-0.680824\pi$
$719$	−28.8526			−1.07602			−0.538011	+	0.842938i	$0.680824\pi$
$720$	−28.7992	+	5.96618i	−1.07328	+	0.222347i
$721$		0			0
$722$	−18.4271	+	13.7231i	−0.685784	+	0.510722i
$723$	−14.9585	+	14.9585i	−0.556313	+	0.556313i
$724$	−29.4924	+	15.9146i	−1.09608	+	0.591461i
$725$	29.2086	+	29.2086i	1.08478	+	1.08478i
$726$	−0.385842	+	2.63713i	−0.0143199	+	0.0978729i
$727$		−	19.1342i		−	0.709648i	−0.934933	−	0.354824i	$-0.884541\pi$
$727$		−	19.1342i		−	0.709648i	0.934933	−	0.354824i	$-0.115459\pi$
$728$		0			0
$729$			5.64199i			0.208963i
$730$	−5.23845	−	0.766445i	−0.193884	−	0.0283674i
$731$	10.6073	+	10.6073i	0.392325	+	0.392325i
$732$	11.2837	+	3.37410i	0.417058	+	0.124710i
$733$	8.17266	−	8.17266i	0.301864	−	0.301864i	−0.539879	−	0.841743i	$-0.681530\pi$
$733$	8.17266	−	8.17266i	0.301864	−	0.301864i	0.841743	+	0.539879i	$0.181530\pi$
$734$	31.4504	+	42.2308i	1.16085	+	1.55877i
$735$		0			0
$736$	−34.8004	+	2.05541i	−1.28276	+	0.0757636i
$737$	18.1017			0.666786
$738$	7.04082	+	9.45423i	0.259176	+	0.348015i
$739$	−5.86541	+	5.86541i	−0.215763	+	0.215763i	−0.806710	−	0.590947i	$-0.798754\pi$
$739$	−5.86541	+	5.86541i	−0.215763	+	0.215763i	0.590947	+	0.806710i	$0.298754\pi$
$740$	36.1954	+	10.8233i	1.33057	+	0.397873i
$741$	5.23749	+	5.23749i	0.192404	+	0.192404i
$742$		0			0
$743$		−	9.24326i		−	0.339102i	−0.985521	−	0.169551i	$-0.945768\pi$
$743$		−	9.24326i		−	0.339102i	0.985521	−	0.169551i	$-0.0542318\pi$
$744$	−2.09055	+	4.48895i	−0.0766434	+	0.164573i
$745$			38.4757i			1.40964i
$746$	−0.885006	+	6.04878i	−0.0324024	+	0.221462i
$747$	1.03098	+	1.03098i	0.0377214	+	0.0377214i
$748$	−19.0236	+	10.2654i	−0.695570	+	0.375341i
$749$		0			0
$750$	−2.33695	+	1.74038i	−0.0853332	+	0.0635499i
$751$	−20.6757			−0.754467			−0.377234	−	0.926118i	$-0.623125\pi$
$751$	−20.6757			−0.754467			−0.377234	+	0.926118i	$0.623125\pi$
$752$	33.8728	+	22.2468i	1.23522	+	0.811258i
$753$	−4.30644			−0.156935
$754$	42.0520	−	31.3172i	1.53144	−	1.14051i
$755$	−45.4034	+	45.4034i	−1.65240	+	1.65240i
$756$		0			0
$757$	19.3612	+	19.3612i	0.703694	+	0.703694i	0.965201	−	0.261508i	$-0.0842197\pi$
$757$	19.3612	+	19.3612i	0.703694	+	0.703694i	−0.261508	+	0.965201i	$0.584220\pi$
$758$	3.33314	−	22.7811i	0.121065	−	0.827447i
$759$		−	15.9099i		−	0.577493i
$760$	14.4410	−	5.26412i	0.523831	−	0.190950i
$761$			17.6413i			0.639497i	0.947502	+	0.319748i	$0.103598\pi$
$761$			17.6413i			0.639497i	−0.947502	+	0.319748i	$0.896402\pi$
$762$	15.6628	+	2.29165i	0.567404	+	0.0830178i
$763$		0			0
$764$	−4.51966	+	15.1147i	−0.163516	+	0.546831i
$765$	−18.9099	+	18.9099i	−0.683687	+	0.683687i
$766$	16.6630	+	22.3747i	0.602060	+	0.808431i
$767$	−19.4132			−0.700971
$768$	−12.9249	−	5.11518i	−0.466387	−	0.184578i
$769$	33.4127			1.20489			0.602447	−	0.798159i	$-0.294193\pi$
$769$	33.4127			1.20489			0.602447	+	0.798159i	$0.294193\pi$
$770$		0			0
$771$	3.99122	−	3.99122i	0.143740	−	0.143740i
$772$	−14.2562	+	47.6757i	−0.513091	+	1.71589i
$773$	9.47365	+	9.47365i	0.340744	+	0.340744i	0.856647	−	0.515903i	$-0.172544\pi$
$773$	9.47365	+	9.47365i	0.340744	+	0.340744i	−0.515903	+	0.856647i	$0.672544\pi$
$774$	12.9581	+	1.89592i	0.465769	+	0.0681474i
$775$		−	11.5355i		−	0.414367i
$776$	18.0748	−	6.58874i	0.648849	−	0.236522i
$777$		0			0
$778$	1.21574	−	8.30927i	0.0435865	−	0.297902i
$779$	−4.35620	−	4.35620i	−0.156077	−	0.156077i
$780$	13.8829	+	25.7273i	0.497086	+	0.921184i
$781$	20.0707	−	20.0707i	0.718187	−	0.718187i
$782$	−25.4229	+	18.9331i	−0.909123	+	0.677048i
$783$	−32.8837			−1.17517
$784$		0			0
$785$	−17.7091			−0.632066
$786$	9.15628	−	6.81892i	0.326594	−	0.243223i
$787$	6.81141	−	6.81141i	0.242801	−	0.242801i	−0.575207	−	0.818008i	$-0.695079\pi$
$787$	6.81141	−	6.81141i	0.242801	−	0.242801i	0.818008	+	0.575207i	$0.195079\pi$
$788$	19.3010	−	10.4152i	0.687571	−	0.371025i
$789$	15.1958	+	15.1958i	0.540983	+	0.540983i
$790$	−0.161846	+	1.10617i	−0.00575821	+	0.0393558i
$791$		0			0
$792$	−7.96706	+	17.1073i	−0.283097	+	0.607882i
$793$			34.8246i			1.23666i
$794$	35.7834	+	5.23553i	1.26991	+	0.185802i
$795$	−7.67044	−	7.67044i	−0.272042	−	0.272042i
$796$	−21.9347	−	6.55901i	−0.777455	−	0.232478i
$797$	−3.47475	+	3.47475i	−0.123082	+	0.123082i	−0.765965	−	0.642883i	$-0.777738\pi$
$797$	−3.47475	+	3.47475i	−0.123082	+	0.123082i	0.642883	+	0.765965i	$0.277738\pi$
$798$		0			0
$799$	36.8487			1.30361
$800$	32.3246	−	1.90919i	1.14285	−	0.0675001i
$801$	9.76945			0.345186
$802$	3.04338	+	4.08658i	0.107466	+	0.144302i
$803$	−2.40208	+	2.40208i	−0.0847677	+	0.0847677i
$804$	10.1405	+	3.03225i	0.357627	+	0.106939i
$805$		0			0
$806$	−14.4880	−	2.11976i	−0.510318	−	0.0746654i
$807$			1.30186i			0.0458277i
$808$	−8.16706	−	3.80349i	−0.287316	−	0.133806i
$809$			44.9480i			1.58029i	0.612921	+	0.790144i	$0.289994\pi$
$809$			44.9480i			1.58029i	−0.612921	+	0.790144i	$0.710006\pi$
$810$	−1.86178	+	12.7247i	−0.0654161	+	0.447101i
$811$	23.3543	+	23.3543i	0.820080	+	0.820080i	0.986119	−	0.166039i	$-0.0530978\pi$
$811$	23.3543	+	23.3543i	0.820080	+	0.820080i	−0.166039	+	0.986119i	$0.553098\pi$
$812$		0			0
$813$	−4.52285	+	4.52285i	−0.158623	+	0.158623i
$814$	19.4419	−	14.4789i	0.681439	−	0.507486i
$815$	−36.9387			−1.29391
$816$	−12.3765	+	2.56397i	−0.433263	+	0.0897568i
$817$	−6.84423			−0.239449
$818$	−17.3900	+	12.9508i	−0.608026	+	0.452813i
$819$		0			0
$820$	−11.5468	−	21.3982i	−0.403233	−	0.747259i
$821$	−22.7441	−	22.7441i	−0.793774	−	0.793774i	0.188332	−	0.982105i	$-0.439692\pi$
$821$	−22.7441	−	22.7441i	−0.793774	−	0.793774i	−0.982105	+	0.188332i	$0.939692\pi$
$822$	−2.09926	+	14.3479i	−0.0732202	+	0.500440i
$823$			6.46922i			0.225503i	0.993623	+	0.112751i	$0.0359664\pi$
$823$			6.46922i			0.225503i	−0.993623	+	0.112751i	$0.964034\pi$
$824$	−3.64148	−	9.98964i	−0.126857	−	0.348006i
$825$			14.7781i			0.514506i
$826$		0			0
$827$	0.313180	+	0.313180i	0.0108903	+	0.0108903i	0.712531	−	0.701641i	$-0.247549\pi$
$827$	0.313180	+	0.313180i	0.0108903	+	0.0108903i	−0.701641	+	0.712531i	$0.747549\pi$
$828$	−7.92808	+	26.5132i	−0.275520	+	0.921396i
$829$	−20.1834	+	20.1834i	−0.700998	+	0.700998i	−0.964625	−	0.263627i	$-0.915081\pi$
$829$	−20.1834	+	20.1834i	−0.700998	+	0.700998i	0.263627	+	0.964625i	$0.415081\pi$
$830$	−1.79632	−	2.41205i	−0.0623510	−	0.0837234i
$831$	3.93446			0.136485
$832$	3.54213	−	40.9490i	0.122801	−	1.41965i
$833$		0			0
$834$	8.46552	+	11.3673i	0.293137	+	0.393617i
$835$	50.5061	−	50.5061i	1.74784	−	1.74784i
$836$	2.82554	−	9.44919i	0.0977232	−	0.326807i
$837$	6.49345	+	6.49345i	0.224446	+	0.224446i
$838$	34.2253	+	5.00756i	1.18229	+	0.172983i
$839$			49.1079i			1.69539i	0.530482	+	0.847696i	$0.322011\pi$
$839$			49.1079i			1.69539i	−0.530482	+	0.847696i	$0.677989\pi$
$840$		0			0
$841$		−	23.0742i		−	0.795662i
$842$	−5.28210	+	36.1017i	−0.182033	+	1.24415i
$843$	−5.97649	−	5.97649i	−0.205841	−	0.205841i
$844$	−11.6793	−	21.6437i	−0.402019	−	0.745008i
$845$	−31.0208	+	31.0208i	−1.06715	+	1.06715i
$846$	25.8007	−	19.2145i	0.887046	−	0.660606i
$847$		0			0
$848$	3.09385	+	14.9343i	0.106243	+	0.512845i
$849$	3.49475			0.119940
$850$	23.6143	−	17.5862i	0.809965	−	0.603202i
$851$	25.1355	−	25.1355i	0.861634	−	0.861634i
$852$	14.6056	−	7.88142i	0.500379	−	0.270013i
$853$	−4.33966	−	4.33966i	−0.148587	−	0.148587i	0.628899	−	0.777487i	$-0.283506\pi$
$853$	−4.33966	−	4.33966i	−0.148587	−	0.148587i	−0.777487	+	0.628899i	$0.783506\pi$
$854$		0			0
$855$		−	12.2014i		−	0.417278i
$856$	−0.972450	−	0.452881i	−0.0332377	−	0.0154791i
$857$			16.1733i			0.552471i	0.961090	+	0.276235i	$0.0890870\pi$
$857$			16.1733i			0.552471i	−0.961090	+	0.276235i	$0.910913\pi$
$858$	18.5605	+	2.71562i	0.633645	+	0.0927096i
$859$	−31.4890	−	31.4890i	−1.07439	−	1.07439i	−0.997001	−	0.0773900i	$-0.975341\pi$
$859$	−31.4890	−	31.4890i	−1.07439	−	1.07439i	−0.0773900	−	0.997001i	$-0.524659\pi$
$860$	−25.8808	−	7.73899i	−0.882528	−	0.263897i
$861$		0			0
$862$	28.3983	+	38.1325i	0.967249	+	1.29880i
$863$	5.70353			0.194150			0.0970752	−	0.995277i	$-0.469051\pi$
$863$	5.70353			0.194150			0.0970752	+	0.995277i	$0.469051\pi$
$864$	−17.1212	+	19.2706i	−0.582474	+	0.655599i
$865$	−74.3782			−2.52893
$866$	−22.4276	−	30.1152i	−0.762121	−	1.02336i
$867$	2.31679	−	2.31679i	0.0786822	−	0.0786822i
$868$		0			0
$869$	0.507233	+	0.507233i	0.0172067	+	0.0172067i
$870$	28.7285	+	4.20331i	0.973988	+	0.142506i
$871$			31.2963i			1.06044i
$872$	−11.9375	+	25.6329i	−0.404256	+	0.868040i
$873$		−	15.2716i		−	0.516865i
$874$	2.09374	−	14.3101i	0.0708217	−	0.484047i
$875$		0			0
$876$	−1.74801	+	0.943255i	−0.0590598	+	0.0318696i
$877$	11.1824	−	11.1824i	0.377602	−	0.377602i	−0.492634	−	0.870236i	$-0.663966\pi$
$877$	11.1824	−	11.1824i	0.377602	−	0.377602i	0.870236	+	0.492634i	$0.163966\pi$
$878$	−22.2430	+	16.5650i	−0.750665	+	0.559040i
$879$	2.31143			0.0779625
$880$	21.3690	−	32.5363i	0.720349	−	1.09680i
$881$	−20.6047			−0.694190			−0.347095	−	0.937830i	$-0.612832\pi$
$881$	−20.6047			−0.694190			−0.347095	+	0.937830i	$0.612832\pi$
$882$		0			0
$883$	3.92964	−	3.92964i	0.132243	−	0.132243i	−0.637887	−	0.770130i	$-0.720191\pi$
$883$	3.92964	−	3.92964i	0.132243	−	0.132243i	0.770130	+	0.637887i	$0.220191\pi$
$884$	−17.7480	−	32.8901i	−0.596931	−	1.10621i
$885$	−7.60147	−	7.60147i	−0.255521	−	0.255521i
$886$	−1.39669	+	9.54603i	−0.0469229	+	0.320705i
$887$		−	18.5762i		−	0.623726i	−0.950127	−	0.311863i	$-0.899047\pi$
$887$		−	18.5762i		−	0.623726i	0.950127	−	0.311863i	$-0.100953\pi$
$888$	13.3166	−	4.85425i	0.446877	−	0.162898i
$889$		0			0
$890$	−19.9391	−	2.91732i	−0.668359	−	0.0977887i
$891$	5.83491	+	5.83491i	0.195477	+	0.195477i
$892$	12.5759	−	42.0565i	0.421073	−	1.40816i
$893$	−11.8881	+	11.8881i	−0.397820	+	0.397820i
$894$	8.62201	+	11.5774i	0.288363	+	0.387207i
$895$	70.4965			2.35644
$896$		0			0
$897$	27.5068			0.918426
$898$	5.34195	+	7.17304i	0.178263	+	0.239367i
$899$	−10.2829	+	10.2829i	−0.342955	+	0.342955i
$900$	7.36407	−	24.6270i	0.245469	−	0.820899i
$901$	9.80599	+	9.80599i	0.326685	+	0.326685i
$902$	−15.4374	−	2.25867i	−0.514009	−	0.0752055i
$903$		0			0
$904$	−6.96274	+	2.53810i	−0.231577	+	0.0844158i
$905$		−	54.8727i		−	1.82403i
$906$	−3.48753	+	23.8364i	−0.115866	+	0.791910i
$907$	20.1706	+	20.1706i	0.669753	+	0.669753i	0.957659	−	0.287905i	$-0.0929589\pi$
$907$	20.1706	+	20.1706i	0.669753	+	0.669753i	−0.287905	+	0.957659i	$0.592959\pi$
$908$	23.4300	+	43.4197i	0.777552	+	1.44093i
$909$	−5.05701	+	5.05701i	−0.167730	+	0.167730i
$910$		0			0
$911$	40.6520			1.34686			0.673431	−	0.739250i	$-0.264820\pi$
$911$	40.6520			1.34686			0.673431	+	0.739250i	$0.264820\pi$
$912$	3.16570	−	4.82007i	0.104827	−	0.159608i
$913$	−1.92974			−0.0638651
$914$	44.8005	−	33.3641i	1.48187	−	1.10359i
$915$	−13.6360	+	13.6360i	−0.450791	+	0.450791i
$916$	−16.7462	+	9.03653i	−0.553310	+	0.298575i
$917$		0			0
$918$	−3.39329	+	23.1922i	−0.111995	+	0.765458i
$919$		−	26.9677i		−	0.889581i	−0.895635	−	0.444790i	$-0.853278\pi$
$919$		−	26.9677i		−	0.889581i	0.895635	−	0.444790i	$-0.146722\pi$
$920$	24.0982	−	51.7449i	0.794493	−	1.70598i
$921$		−	4.90192i		−	0.161524i
$922$	2.50875	+	0.367058i	0.0826211	+	0.0120884i
$923$	34.7005	+	34.7005i	1.14218	+	1.14218i
$924$		0			0
$925$	−23.3473	+	23.3473i	−0.767656	+	0.767656i
$926$	−12.1997	−	16.3814i	−0.400905	−	0.538326i
$927$	−8.44033			−0.277217
$928$	−30.5167	−	27.1129i	−1.00176	−	0.890024i
$929$	−15.6320			−0.512870			−0.256435	−	0.966561i	$-0.582548\pi$
$929$	−15.6320			−0.512870			−0.256435	+	0.966561i	$0.582548\pi$
$930$	−4.84292	−	6.50295i	−0.158806	−	0.213240i
$931$		0			0
$932$	−42.6110	−	12.7417i	−1.39577	−	0.417369i
$933$	−0.496421	−	0.496421i	−0.0162521	−	0.0162521i
$934$	24.3082	+	3.55657i	0.795388	+	0.116374i
$935$		−	35.3947i		−	1.15753i
$936$	−29.5770	−	13.7744i	−0.966756	−	0.450229i
$937$		−	47.9244i		−	1.56562i	−0.622260	−	0.782811i	$-0.713785\pi$
$937$		−	47.9244i		−	1.56562i	0.622260	−	0.782811i	$-0.286215\pi$
$938$		0			0
$939$	−14.3107	−	14.3107i	−0.467013	−	0.467013i
$940$	−58.3960	+	31.5115i	−1.90467	+	1.02779i
$941$	−7.62070	+	7.62070i	−0.248428	+	0.248428i	−0.820325	−	0.571897i	$-0.806208\pi$
$941$	−7.62070	+	7.62070i	−0.248428	+	0.248428i	0.571897	+	0.820325i	$0.306208\pi$
$942$	−5.32871	+	3.96843i	−0.173619	+	0.129298i
$943$	−22.8784			−0.745022
$944$	3.06604	+	14.8000i	0.0997910	+	0.481698i
$945$		0			0
$946$	−13.9016	+	10.3529i	−0.451979	+	0.336601i
$947$	−19.6254	+	19.6254i	−0.637739	+	0.637739i	−0.949997	−	0.312258i	$-0.898915\pi$
$947$	−19.6254	+	19.6254i	−0.637739	+	0.637739i	0.312258	+	0.949997i	$0.398915\pi$
$948$	0.199182	+	0.369117i	0.00646912	+	0.0119884i
$949$	−4.15299	−	4.15299i	−0.134812	−	0.134812i
$950$	−1.94479	+	13.2921i	−0.0630972	+	0.431252i
$951$		−	2.71283i		−	0.0879696i
$952$		0			0
$953$		−	3.58597i		−	0.116161i	−0.998312	−	0.0580805i	$-0.981502\pi$
$953$		−	3.58597i		−	0.116161i	0.998312	−	0.0580805i	$-0.0184980\pi$
$954$	11.9792	+	1.75269i	0.387841	+	0.0567456i
$955$	−18.2656	−	18.2656i	−0.591061	−	0.591061i
$956$	−8.57060	+	28.6619i	−0.277193	+	0.926992i
$957$	13.1734	−	13.1734i	0.425836	−	0.425836i
$958$	4.04346	+	5.42945i	0.130638	+	0.175418i
$959$		0			0
$960$	17.4210	−	14.6471i	0.562260	−	0.472732i
$961$	−26.9389			−0.868997
$962$	25.0328	+	33.6134i	0.807090	+	1.08374i
$963$	−0.602137	+	0.602137i	−0.0194036	+	0.0194036i
$964$	−13.9521	+	46.6587i	−0.449367	+	1.50278i
$965$	−57.6144	−	57.6144i	−1.85467	−	1.85467i
$966$		0			0
$967$		−	51.9947i		−	1.67204i	−0.548703	−	0.836018i	$-0.684878\pi$
$967$		−	51.9947i		−	1.67204i	0.548703	−	0.836018i	$-0.315122\pi$
$968$	2.10132	+	5.76454i	0.0675390	+	0.185279i
$969$		−	5.24354i		−	0.168447i
$970$	−4.56035	+	31.1688i	−0.146424	+	1.00077i
$971$	35.0803	+	35.0803i	1.12578	+	1.12578i	0.990856	+	0.134925i	$0.0430795\pi$
$971$	35.0803	+	35.0803i	1.12578	+	1.12578i	0.134925	+	0.990856i	$0.456921\pi$
$972$	15.2754	+	28.3078i	0.489958	+	0.907973i
$973$		0			0
$974$	−30.4768	+	22.6968i	−0.976538	+	0.727254i
$975$	−25.5500			−0.818254
$976$	26.5491	−	5.50004i	0.849816	−	0.176052i
$977$	5.67083			0.181426			0.0907129	−	0.995877i	$-0.471085\pi$
$977$	5.67083			0.181426			0.0907129	+	0.995877i	$0.471085\pi$
$978$	−11.1149	+	8.27758i	−0.355416	+	0.264688i
$979$	−9.14303	+	9.14303i	−0.292213	+	0.292213i
$980$		0			0
$981$	15.8718	+	15.8718i	0.506748	+	0.506748i
$982$	3.40429	−	23.2674i	0.108635	−	0.742492i
$983$		−	46.7462i		−	1.49097i	−0.666522	−	0.745486i	$-0.732218\pi$
$983$		−	46.7462i		−	1.49097i	0.666522	−	0.745486i	$-0.267782\pi$
$984$	−8.26958	−	3.85124i	−0.263625	−	0.122773i
$985$			35.9110i			1.14422i
$986$	−36.7269	−	5.37357i	−1.16962	−	0.171129i
$987$		0			0
$988$	16.3368	+	4.88511i	0.519744	+	0.155416i
$989$	−17.9726	+	17.9726i	−0.571497	+	0.571497i
$990$	−18.4563	−	24.7826i	−0.586579	−	0.787644i
$991$	14.4138			0.457870			0.228935	−	0.973442i	$-0.426476\pi$
$991$	14.4138			0.457870			0.228935	+	0.973442i	$0.426476\pi$
$992$	0.672133	+	11.3799i	0.0213403	+	0.361313i
$993$	13.6857			0.434303
$994$		0			0
$995$	26.5073	−	26.5073i	0.840339	−	0.840339i
$996$	−1.08103	−	0.323254i	−0.0342537	−	0.0102427i
$997$	−40.2131	−	40.2131i	−1.27356	−	1.27356i	−0.944205	−	0.329357i	$-0.893168\pi$
$997$	−40.2131	−	40.2131i	−1.27356	−	1.27356i	−0.329357	−	0.944205i	$-0.606832\pi$
$998$	−27.5787	−	4.03508i	−0.872988	−	0.127728i
$999$		−	26.2849i		−	0.831619i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.m.k.197.8		24
7.2	even	3		784.2.x.o.165.9		48
7.3	odd	6		112.2.w.c.37.1	✓	48
7.4	even	3		784.2.x.o.373.1		48
7.5	odd	6		112.2.w.c.53.9	yes	48
7.6	odd	2		784.2.m.j.197.8		24
16.13	even	4	inner	784.2.m.k.589.8		24
28.3	even	6		448.2.ba.c.177.8		48
28.19	even	6		448.2.ba.c.305.5		48
56.3	even	6		896.2.ba.e.737.5		48
56.5	odd	6		896.2.ba.f.865.5		48
56.19	even	6		896.2.ba.e.865.8		48
56.45	odd	6		896.2.ba.f.737.8		48
112.3	even	12		448.2.ba.c.401.5		48
112.5	odd	12		896.2.ba.f.417.8		48
112.13	odd	4		784.2.m.j.589.8		24
112.19	even	12		448.2.ba.c.81.8		48
112.45	odd	12		112.2.w.c.93.9	yes	48
112.59	even	12		896.2.ba.e.289.8		48
112.61	odd	12		112.2.w.c.109.1	yes	48
112.75	even	12		896.2.ba.e.417.5		48
112.93	even	12		784.2.x.o.557.1		48
112.101	odd	12		896.2.ba.f.289.5		48
112.109	even	12		784.2.x.o.765.9		48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.1	✓	48	7.3	odd	6
112.2.w.c.53.9	yes	48	7.5	odd	6
112.2.w.c.93.9	yes	48	112.45	odd	12
112.2.w.c.109.1	yes	48	112.61	odd	12
448.2.ba.c.81.8		48	112.19	even	12
448.2.ba.c.177.8		48	28.3	even	6
448.2.ba.c.305.5		48	28.19	even	6
448.2.ba.c.401.5		48	112.3	even	12
784.2.m.j.197.8		24	7.6	odd	2
784.2.m.j.589.8		24	112.13	odd	4
784.2.m.k.197.8		24	1.1	even	1	trivial
784.2.m.k.589.8		24	16.13	even	4	inner
784.2.x.o.165.9		48	7.2	even	3
784.2.x.o.373.1		48	7.4	even	3
784.2.x.o.557.1		48	112.93	even	12
784.2.x.o.765.9		48	112.109	even	12
896.2.ba.e.289.8		48	112.59	even	12
896.2.ba.e.417.5		48	112.75	even	12
896.2.ba.e.737.5		48	56.3	even	6
896.2.ba.e.865.8		48	56.19	even	6
896.2.ba.f.289.5		48	112.101	odd	12
896.2.ba.f.417.8		48	112.5	odd	12
896.2.ba.f.737.8		48	56.45	odd	6
896.2.ba.f.865.5		48	56.5	odd	6

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.m (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.844695 + 1.13424i) q^{2} +(-0.614312 + 0.614312i) q^{3} +(-0.572980 + 1.91617i) q^{4} +(-2.31562 - 2.31562i) q^{5} +(-1.21568 - 0.177868i) q^{6} +(-2.65738 + 0.968682i) q^{8} +2.24524i q^{9} +(0.670466 - 4.58245i) q^{10} +(-2.10128 - 2.10128i) q^{11} +(-0.825135 - 1.52911i) q^{12} +(3.63293 - 3.63293i) q^{13} +2.84503 q^{15} +(-3.34339 - 2.19585i) q^{16} -3.63712 q^{17} +(-2.54663 + 1.89654i) q^{18} +(1.17340 - 1.17340i) q^{19} +(5.76392 - 3.11031i) q^{20} +(0.608405 - 4.15828i) q^{22} -6.16261i q^{23} +(1.03739 - 2.22753i) q^{24} +5.72420i q^{25} +(7.18931 + 1.05188i) q^{26} +(-3.22221 - 3.22221i) q^{27} +(5.10266 - 5.10266i) q^{29} +(2.40318 + 3.22693i) q^{30} -2.01521 q^{31} +(-0.333530 - 5.64701i) q^{32} +2.58168 q^{33} +(-3.07226 - 4.12535i) q^{34} +(-4.30226 - 1.28648i) q^{36} +(4.07871 + 4.07871i) q^{37} +(2.32209 + 0.339748i) q^{38} +4.46350i q^{39} +(8.39658 + 3.91038i) q^{40} -3.71244i q^{41} +(-2.91640 - 2.91640i) q^{43} +(5.23039 - 2.82241i) q^{44} +(5.19913 - 5.19913i) q^{45} +(6.98986 - 5.20553i) q^{46} -10.1313 q^{47} +(3.40282 - 0.704944i) q^{48} +(-6.49259 + 4.83520i) q^{50} +(2.23433 - 2.23433i) q^{51} +(4.87970 + 9.04289i) q^{52} +(-2.69609 - 2.69609i) q^{53} +(0.932961 - 6.37654i) q^{54} +9.73153i q^{55} +1.44167i q^{57} +(10.0978 + 1.47743i) q^{58} +(-2.67184 - 2.67184i) q^{59} +(-1.63014 + 5.45154i) q^{60} +(-4.79291 + 4.79291i) q^{61} +(-1.70224 - 2.28573i) q^{62} +(6.12331 - 5.14831i) q^{64} -16.8250 q^{65} +(2.18073 + 2.92823i) q^{66} +(-4.30731 + 4.30731i) q^{67} +(2.08400 - 6.96933i) q^{68} +(3.78577 + 3.78577i) q^{69} +9.55168i q^{71} +(-2.17492 - 5.96646i) q^{72} -1.14315i q^{73} +(-1.18095 + 8.07148i) q^{74} +(-3.51644 - 3.51644i) q^{75} +(1.57610 + 2.92078i) q^{76} +(-5.06266 + 3.77030i) q^{78} -0.241393 q^{79} +(2.65726 + 12.8268i) q^{80} -2.77684 q^{81} +(4.21079 - 3.13588i) q^{82} +(0.459183 - 0.459183i) q^{83} +(8.42219 + 8.42219i) q^{85} +(0.844416 - 5.77135i) q^{86} +6.26924i q^{87} +(7.61936 + 3.54842i) q^{88} -4.35118i q^{89} +(10.2887 + 1.50536i) q^{90} +(11.8086 + 3.53106i) q^{92} +(1.23797 - 1.23797i) q^{93} +(-8.55785 - 11.4913i) q^{94} -5.43432 q^{95} +(3.67392 + 3.26414i) q^{96} -6.80176 q^{97} +(4.71788 - 4.71788i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 4 q^{2} + 4 q^{4} + 4 q^{5} + 2 q^{6} - 2 q^{8} - 2 q^{10} + 4 q^{11} + 2 q^{12} + 12 q^{13} - 20 q^{15} - 16 q^{16} + 8 q^{17} - 18 q^{18} - 4 q^{19} + 8 q^{20} + 18 q^{24} - 10 q^{26} + 12 q^{27}+ \cdots - 12 q^{99}+O(q^{100}) \) 24 * q + 4 * q^2 + 4 * q^4 + 4 * q^5 + 2 * q^6 - 2 * q^8 - 2 * q^10 + 4 * q^11 + 2 * q^12 + 12 * q^13 - 20 * q^15 - 16 * q^16 + 8 * q^17 - 18 * q^18 - 4 * q^19 + 8 * q^20 + 18 * q^24 - 10 * q^26 + 12 * q^27 + 12 * q^29 + 4 * q^30 + 28 * q^31 - 16 * q^32 + 16 * q^33 + 22 * q^34 - 36 * q^36 + 24 * q^37 + 20 * q^38 + 26 * q^40 - 20 * q^43 - 6 * q^44 - 28 * q^45 + 14 * q^46 - 20 * q^47 - 28 * q^48 + 28 * q^50 - 24 * q^51 - 16 * q^52 + 16 * q^53 + 64 * q^54 + 6 * q^58 - 20 * q^59 - 46 * q^60 + 8 * q^61 - 12 * q^62 + 40 * q^64 - 8 * q^65 - 20 * q^66 - 48 * q^67 + 20 * q^69 + 32 * q^72 + 8 * q^74 - 4 * q^75 + 18 * q^76 + 58 * q^78 + 36 * q^79 - 28 * q^80 + 2 * q^82 + 4 * q^83 + 20 * q^86 + 42 * q^88 + 10 * q^90 + 38 * q^92 - 8 * q^93 - 72 * q^94 + 4 * q^95 - 120 * q^96 + 24 * q^97 - 12 * q^99

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