LMFDB - Embedded newform 273.2.e.a.209.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(209,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 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("273.209");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.e (of order $2$, degree $1$, 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:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$32$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			209.1
Character	$\chi$	$=$	273.209
Dual form			273.2.e.a.209.31

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.62996i q^{2} +(-0.518189 + 1.65272i) q^{3} -4.91669 q^{4} +2.48925 q^{5} +(4.34658 + 1.36282i) q^{6} +(1.33971 - 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} +O(q^{10})$	\(q-2.62996i q^{2} +(-0.518189 + 1.65272i) q^{3} -4.91669 q^{4} +2.48925 q^{5} +(4.34658 + 1.36282i) q^{6} +(1.33971 - 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} -6.54663i q^{10} -5.20518i q^{11} +(2.54777 - 8.12590i) q^{12} -1.00000i q^{13} +(-6.00022 - 3.52338i) q^{14} +(-1.28990 + 4.11403i) q^{15} +10.3404 q^{16} +2.44427 q^{17} +(-4.50471 + 6.47748i) q^{18} +2.29598i q^{19} -12.2389 q^{20} +(3.07643 + 3.39640i) q^{21} -13.6894 q^{22} -5.95242i q^{23} +(-12.6776 - 3.97491i) q^{24} +1.19637 q^{25} -2.62996 q^{26} +(4.10713 - 3.18300i) q^{27} +(-6.58692 + 11.2174i) q^{28} +2.80952i q^{29} +(10.8197 + 3.39239i) q^{30} +6.81176i q^{31} -11.8534i q^{32} +(8.60270 + 2.69727i) q^{33} -6.42832i q^{34} +(3.33487 - 5.67919i) q^{35} +(12.1096 + 8.42151i) q^{36} +3.17079 q^{37} +6.03833 q^{38} +(1.65272 + 0.518189i) q^{39} +19.0945i q^{40} +0.133822 q^{41} +(8.93240 - 8.09090i) q^{42} +6.61311 q^{43} +25.5922i q^{44} +(-6.13092 - 4.26369i) q^{45} -15.6546 q^{46} -4.15911 q^{47} +(-5.35830 + 17.0898i) q^{48} +(-3.41036 - 6.11305i) q^{49} -3.14640i q^{50} +(-1.26659 + 4.03969i) q^{51} +4.91669i q^{52} +7.32479i q^{53} +(-8.37117 - 10.8016i) q^{54} -12.9570i q^{55} +(17.5007 + 10.2766i) q^{56} +(-3.79461 - 1.18975i) q^{57} +7.38893 q^{58} -0.723671 q^{59} +(6.34205 - 20.2274i) q^{60} +8.23191i q^{61} +17.9147 q^{62} +(-7.20747 + 3.32450i) q^{63} -10.4930 q^{64} -2.48925i q^{65} +(7.09370 - 22.6247i) q^{66} -1.52087 q^{67} -12.0177 q^{68} +(9.83767 + 3.08448i) q^{69} +(-14.9360 - 8.77057i) q^{70} -7.17852i q^{71} +(13.1388 - 18.8928i) q^{72} +16.4534i q^{73} -8.33904i q^{74} +(-0.619945 + 1.97726i) q^{75} -11.2886i q^{76} +(-11.8755 - 6.97342i) q^{77} +(1.36282 - 4.34658i) q^{78} -0.0675159 q^{79} +25.7399 q^{80} +(3.13234 + 8.43732i) q^{81} -0.351945i q^{82} -6.38210 q^{83} +(-15.1259 - 16.6990i) q^{84} +6.08439 q^{85} -17.3922i q^{86} +(-4.64335 - 1.45586i) q^{87} +39.9277 q^{88} +14.3874 q^{89} +(-11.2133 + 16.1241i) q^{90} +(-2.28149 - 1.33971i) q^{91} +29.2662i q^{92} +(-11.2579 - 3.52978i) q^{93} +10.9383i q^{94} +5.71527i q^{95} +(19.5903 + 6.14229i) q^{96} +16.7297i q^{97} +(-16.0771 + 8.96912i) q^{98} +(-8.91565 + 12.8201i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	$ 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) $ 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/273\mathbb{Z}\right)^\times$.

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$		−	2.62996i		−	1.85966i	−0.367987	−	0.929831i	$-0.619953\pi$
$2$		−	2.62996i		−	1.85966i	0.367987	−	0.929831i	$-0.380047\pi$
$3$	−0.518189	+	1.65272i	−0.299177	+	0.954198i
$3$	−0.518189	+	1.65272i	−0.299177	+	0.954198i
$4$	−4.91669			−2.45834
$5$	2.48925			1.11323			0.556613	−	0.830772i	$-0.312101\pi$
$5$	2.48925			1.11323			0.556613	+	0.830772i	$0.312101\pi$
$6$	4.34658	+	1.36282i	1.77449	+	0.556367i
$7$	1.33971	−	2.28149i	0.506362	−	0.862321i
$7$	1.33971	−	2.28149i	0.506362	−	0.862321i
$8$			7.67077i			2.71203i
$9$	−2.46296	−	1.71284i	−0.820987	−	0.570947i
$10$		−	6.54663i		−	2.07023i
$11$		−	5.20518i		−	1.56942i	−0.619863	−	0.784710i	$-0.712812\pi$
$11$		−	5.20518i		−	1.56942i	0.619863	−	0.784710i	$-0.287188\pi$
$12$	2.54777	−	8.12590i	0.735479	−	2.34575i
$13$		−	1.00000i		−	0.277350i
$13$		−	1.00000i		−	0.277350i
$14$	−6.00022	−	3.52338i	−1.60363	−	0.941662i
$15$	−1.28990	+	4.11403i	−0.333051	+	1.06224i
$16$	10.3404			2.58511
$17$	2.44427			0.592822			0.296411	−	0.955061i	$-0.404210\pi$
$17$	2.44427			0.592822			0.296411	+	0.955061i	$0.404210\pi$
$18$	−4.50471	+	6.47748i	−1.06177	+	1.52676i
$19$			2.29598i			0.526734i	0.964696	+	0.263367i	$0.0848330\pi$
$19$			2.29598i			0.526734i	−0.964696	+	0.263367i	$0.915167\pi$
$20$	−12.2389			−2.73669
$21$	3.07643	+	3.39640i	0.671333	+	0.741156i
$22$	−13.6894			−2.91859
$23$		−	5.95242i		−	1.24116i	−0.784141	−	0.620582i	$-0.786896\pi$
$23$		−	5.95242i		−	1.24116i	0.784141	−	0.620582i	$-0.213104\pi$
$24$	−12.6776	−	3.97491i	−2.58781	−	0.811375i
$25$	1.19637			0.239273
$26$	−2.62996			−0.515777
$27$	4.10713	−	3.18300i	0.790417	−	0.612569i
$28$	−6.58692	+	11.2174i	−1.24481	+	2.11988i
$29$			2.80952i			0.521715i	0.965377	+	0.260858i	$0.0840053\pi$
$29$			2.80952i			0.521715i	−0.965377	+	0.260858i	$0.915995\pi$
$30$	10.8197	+	3.39239i	1.97540	+	0.619363i
$31$			6.81176i			1.22343i	0.791079	+	0.611714i	$0.209520\pi$
$31$			6.81176i			1.22343i	−0.791079	+	0.611714i	$0.790480\pi$
$32$		−	11.8534i		−	2.09540i
$33$	8.60270	+	2.69727i	1.49754	+	0.469534i
$34$		−	6.42832i		−	1.10245i
$35$	3.33487	−	5.67919i	0.563696	−	0.959959i
$36$	12.1096	+	8.42151i	2.01827	+	1.40358i
$37$	3.17079			0.521274			0.260637	−	0.965437i	$-0.416067\pi$
$37$	3.17079			0.521274			0.260637	+	0.965437i	$0.416067\pi$
$38$	6.03833			0.979547
$39$	1.65272	+	0.518189i	0.264647	+	0.0829767i
$40$			19.0945i			3.01910i
$41$	0.133822			0.0208994			0.0104497	−	0.999945i	$-0.496674\pi$
$41$	0.133822			0.0208994			0.0104497	+	0.999945i	$0.496674\pi$
$42$	8.93240	−	8.09090i	1.37830	−	1.24845i
$43$	6.61311			1.00849			0.504245	−	0.863561i	$-0.331771\pi$
$43$	6.61311			1.00849			0.504245	+	0.863561i	$0.331771\pi$
$44$			25.5922i			3.85817i
$45$	−6.13092	−	4.26369i	−0.913944	−	0.635594i
$46$	−15.6546			−2.30815
$47$	−4.15911			−0.606669			−0.303334	−	0.952884i	$-0.598100\pi$
$47$	−4.15911			−0.606669			−0.303334	+	0.952884i	$0.598100\pi$
$48$	−5.35830	+	17.0898i	−0.773404	+	2.46670i
$49$	−3.41036	−	6.11305i	−0.487195	−	0.873293i
$50$		−	3.14640i		−	0.444968i
$51$	−1.26659	+	4.03969i	−0.177358	+	0.565669i
$52$			4.91669i			0.681822i
$53$			7.32479i			1.00614i	0.864247	+	0.503069i	$0.167796\pi$
$53$			7.32479i			1.00614i	−0.864247	+	0.503069i	$0.832204\pi$
$54$	−8.37117	−	10.8016i	−1.13917	−	1.46991i
$55$		−	12.9570i		−	1.74712i
$56$	17.5007	+	10.2766i	2.33864	+	1.37327i
$57$	−3.79461	−	1.18975i	−0.502608	−	0.157586i
$58$	7.38893			0.970214
$59$	−0.723671			−0.0942140			−0.0471070	−	0.998890i	$-0.515000\pi$
$59$	−0.723671			−0.0942140			−0.0471070	+	0.998890i	$0.515000\pi$
$60$	6.34205	−	20.2274i	0.818755	−	2.61135i
$61$			8.23191i			1.05399i	0.849869	+	0.526994i	$0.176681\pi$
$61$			8.23191i			1.05399i	−0.849869	+	0.526994i	$0.823319\pi$
$62$	17.9147			2.27516
$63$	−7.20747	+	3.32450i	−0.908056	+	0.418848i
$64$	−10.4930			−1.31163
$65$		−	2.48925i		−	0.308754i
$66$	7.09370	−	22.6247i	0.873174	−	2.78491i
$67$	−1.52087			−0.185804			−0.0929020	−	0.995675i	$-0.529614\pi$
$67$	−1.52087			−0.185804			−0.0929020	+	0.995675i	$0.529614\pi$
$68$	−12.0177			−1.45736
$69$	9.83767	+	3.08448i	1.18432	+	0.371328i
$70$	−14.9360	−	8.77057i	−1.78520	−	1.04828i
$71$		−	7.17852i		−	0.851933i	−0.904739	−	0.425967i	$-0.859934\pi$
$71$		−	7.17852i		−	0.851933i	0.904739	−	0.425967i	$-0.140066\pi$
$72$	13.1388	−	18.8928i	1.54842	−	2.22654i
$73$			16.4534i			1.92573i	0.269989	+	0.962864i	$0.412980\pi$
$73$			16.4534i			1.92573i	−0.269989	+	0.962864i	$0.587020\pi$
$74$		−	8.33904i		−	0.969394i
$75$	−0.619945	+	1.97726i	−0.0715850	+	0.228314i
$76$		−	11.2886i		−	1.29489i
$77$	−11.8755	−	6.97342i	−1.35334	−	0.794695i
$78$	1.36282	−	4.34658i	0.154309	−	0.492154i
$79$	−0.0675159			−0.00759613			−0.00379806	−	0.999993i	$-0.501209\pi$
$79$	−0.0675159			−0.00759613			−0.00379806	+	0.999993i	$0.501209\pi$
$80$	25.7399			2.87781
$81$	3.13234	+	8.43732i	0.348038	+	0.937480i
$82$		−	0.351945i		−	0.0388659i
$83$	−6.38210			−0.700526			−0.350263	−	0.936651i	$-0.613908\pi$
$83$	−6.38210			−0.700526			−0.350263	+	0.936651i	$0.613908\pi$
$84$	−15.1259	−	16.6990i	−1.65037	−	1.82202i
$85$	6.08439			0.659945
$86$		−	17.3922i		−	1.87545i
$87$	−4.64335	−	1.45586i	−0.497819	−	0.156085i
$88$	39.9277			4.25631
$89$	14.3874			1.52506			0.762531	−	0.646952i	$-0.223957\pi$
$89$	14.3874			1.52506			0.762531	+	0.646952i	$0.223957\pi$
$90$	−11.2133	+	16.1241i	−1.18199	+	1.69963i
$91$	−2.28149	−	1.33971i	−0.239165	−	0.140440i
$92$			29.2662i			3.05121i
$93$	−11.2579	−	3.52978i	−1.16739	−	0.366021i
$94$			10.9383i			1.12820i
$95$			5.71527i			0.586374i
$96$	19.5903	+	6.14229i	1.99943	+	0.626895i
$97$			16.7297i			1.69864i	0.527875	+	0.849322i	$0.322989\pi$
$97$			16.7297i			1.69864i	−0.527875	+	0.849322i	$0.677011\pi$
$98$	−16.0771	+	8.96912i	−1.62403	+	0.906018i
$99$	−8.91565	+	12.8201i	−0.896056	+	1.28847i
$100$	−5.88216			−0.588216
$101$	−7.10159			−0.706634			−0.353317	−	0.935504i	$-0.614946\pi$
$101$	−7.10159			−0.706634			−0.353317	+	0.935504i	$0.614946\pi$
$102$	10.6242	+	3.33109i	1.05195	+	0.329827i
$103$		−	6.92654i		−	0.682492i	−0.939974	−	0.341246i	$-0.889151\pi$
$103$		−	6.92654i		−	0.682492i	0.939974	−	0.341246i	$-0.110849\pi$
$104$	7.67077			0.752180
$105$	7.65801	+	8.45450i	0.747346	+	0.825074i
$106$	19.2639			1.87108
$107$			5.50532i			0.532219i	0.963943	+	0.266110i	$0.0857383\pi$
$107$			5.50532i			0.532219i	−0.963943	+	0.266110i	$0.914262\pi$
$108$	−20.1934	+	15.6498i	−1.94312	+	1.50591i
$109$	19.7025			1.88716			0.943579	−	0.331146i	$-0.107435\pi$
$109$	19.7025			1.88716			0.943579	+	0.331146i	$0.107435\pi$
$110$	−34.0764			−3.24905
$111$	−1.64307	+	5.24042i	−0.155953	+	0.497399i
$112$	13.8532	−	23.5916i	1.30900	−	2.22919i
$113$		−	1.15948i		−	0.109075i	−0.998512	−	0.0545375i	$-0.982632\pi$
$113$		−	1.15948i		−	0.109075i	0.998512	−	0.0545375i	$-0.0173684\pi$
$114$	−3.12900	+	9.97966i	−0.293057	+	0.934681i
$115$		−	14.8171i		−	1.38170i
$116$		−	13.8135i		−	1.28255i
$117$	−1.71284	+	2.46296i	−0.158352	+	0.227701i
$118$			1.90323i			0.175206i
$119$	3.27460	−	5.57656i	0.300183	−	0.511203i
$120$	−31.5578	−	9.89454i	−2.88082	−	0.903244i
$121$	−16.0939			−1.46308
$122$	21.6496			1.96006
$123$	−0.0693449	+	0.221169i	−0.00625262	+	0.0199422i
$124$		−	33.4913i		−	3.00761i
$125$	−9.46819			−0.846861
$126$	8.74330	+	18.9554i	0.778915	+	1.68868i
$127$	−9.96125			−0.883918			−0.441959	−	0.897035i	$-0.645716\pi$
$127$	−9.96125			−0.883918			−0.441959	+	0.897035i	$0.645716\pi$
$128$			3.88951i			0.343788i
$129$	−3.42684	+	10.9296i	−0.301717	+	0.962299i
$130$	−6.54663			−0.574177
$131$	−0.482982			−0.0421983			−0.0210991	−	0.999777i	$-0.506717\pi$
$131$	−0.482982			−0.0421983			−0.0210991	+	0.999777i	$0.506717\pi$
$132$	−42.2968	−	13.2616i	−3.68146	−	1.15428i
$133$	5.23825	+	3.07594i	0.454213	+	0.266718i
$134$			3.99983i			0.345533i
$135$	10.2237	−	7.92329i	0.879913	−	0.681929i
$136$			18.7494i			1.60775i
$137$			14.2883i			1.22073i	0.792119	+	0.610366i	$0.208978\pi$
$137$			14.2883i			1.22073i	−0.792119	+	0.610366i	$0.791022\pi$
$138$	8.11205	−	25.8727i	0.690544	−	2.20243i
$139$		−	15.6954i		−	1.33127i	−0.746280	−	0.665633i	$-0.768162\pi$
$139$		−	15.6954i		−	1.33127i	0.746280	−	0.665633i	$-0.231838\pi$
$140$	−16.3965	+	27.9228i	−1.38576	+	2.35991i
$141$	2.15521	−	6.87384i	0.181501	−	0.578882i
$142$	−18.8792			−1.58431
$143$	−5.20518			−0.435279
$144$	−25.4681	−	17.7115i	−2.12234	−	1.47596i
$145$			6.99360i			0.580787i
$146$	43.2718			3.58120
$147$	11.8704	−	2.46865i	0.979052	−	0.203611i
$148$	−15.5898			−1.28147
$149$			2.86126i			0.234403i	0.993108	+	0.117202i	$0.0373924\pi$
$149$			2.86126i			0.234403i	−0.993108	+	0.117202i	$0.962608\pi$
$150$	5.20011	+	1.63043i	0.424587	+	0.133124i
$151$	7.22458			0.587928			0.293964	−	0.955816i	$-0.405025\pi$
$151$	7.22458			0.587928			0.293964	+	0.955816i	$0.405025\pi$
$152$	−17.6119			−1.42851
$153$	−6.02013	−	4.18664i	−0.486699	−	0.338470i
$154$	−18.3398	+	31.2322i	−1.47786	+	2.51676i
$155$			16.9562i			1.36195i
$156$	−8.12590	−	2.54777i	−0.650593	−	0.203985i
$157$		−	5.09913i		−	0.406955i	−0.979080	−	0.203477i	$-0.934776\pi$
$157$		−	5.09913i		−	0.406955i	0.979080	−	0.203477i	$-0.0652243\pi$
$158$			0.177564i			0.0141262i
$159$	−12.1058	−	3.79563i	−0.960054	−	0.301013i
$160$		−	29.5060i		−	2.33266i
$161$	−13.5804	−	7.97450i	−1.07028	−	0.628479i
$162$	22.1898	−	8.23794i	1.74340	−	0.647233i
$163$	13.2180			1.03531			0.517657	−	0.855588i	$-0.326804\pi$
$163$	13.2180			1.03531			0.517657	+	0.855588i	$0.326804\pi$
$164$	−0.657959			−0.0513779
$165$	21.4143	+	6.71417i	1.66710	+	0.522698i
$166$			16.7847i			1.30274i
$167$	−14.8090			−1.14596			−0.572979	−	0.819570i	$-0.694212\pi$
$167$	−14.8090			−1.14596			−0.572979	+	0.819570i	$0.694212\pi$
$168$	−26.0530	+	23.5986i	−2.01003	+	1.82067i
$169$	−1.00000			−0.0769231
$170$		−	16.0017i		−	1.22727i
$171$	3.93265	−	5.65490i	0.300737	−	0.432441i
$172$	−32.5146			−2.47921
$173$	−5.26717			−0.400455			−0.200228	−	0.979749i	$-0.564168\pi$
$173$	−5.26717			−0.400455			−0.200228	+	0.979749i	$0.564168\pi$
$174$	−3.82886	+	12.2118i	−0.290265	+	0.925776i
$175$	1.60278	−	2.72950i	0.121159	−	0.206331i
$176$		−	53.8238i		−	4.05712i
$177$	0.374999	−	1.19603i	0.0281866	−	0.0898988i
$178$		−	37.8383i		−	2.83610i
$179$			1.62411i			0.121391i	0.998156	+	0.0606957i	$0.0193319\pi$
$179$			1.62411i			0.121391i	−0.998156	+	0.0606957i	$0.980668\pi$
$180$	30.1438	+	20.9632i	2.24679	+	1.56251i
$181$		−	2.03409i		−	0.151193i	−0.997139	−	0.0755963i	$-0.975914\pi$
$181$		−	2.03409i		−	0.151193i	0.997139	−	0.0755963i	$-0.0240860\pi$
$182$	−3.52338	+	6.00022i	−0.261170	+	0.444766i
$183$	−13.6050	−	4.26568i	−1.00571	−	0.315328i
$184$	45.6596			3.36607
$185$	7.89288			0.580296
$186$	−9.28318	+	29.6079i	−0.680676	+	2.17096i
$187$		−	12.7228i		−	0.930386i
$188$	20.4491			1.49140
$189$	−1.75963	−	13.6347i	−0.127994	−	0.991775i
$190$	15.0309			1.09046
$191$		−	3.53954i		−	0.256112i	−0.991767	−	0.128056i	$-0.959126\pi$
$191$		−	3.53954i		−	0.256112i	0.991767	−	0.128056i	$-0.0408738\pi$
$192$	5.43738	−	17.3420i	0.392409	−	1.25155i
$193$	−12.8190			−0.922732			−0.461366	−	0.887210i	$-0.652640\pi$
$193$	−12.8190			−0.922732			−0.461366	+	0.887210i	$0.652640\pi$
$194$	43.9985			3.15891
$195$	4.11403	+	1.28990i	0.294612	+	0.0923718i
$196$	16.7677	+	30.0560i	1.19769	+	2.14685i
$197$		−	15.2887i		−	1.08927i	−0.838673	−	0.544636i	$-0.816668\pi$
$197$		−	15.2887i		−	1.08927i	0.838673	−	0.544636i	$-0.183332\pi$
$198$	33.7165	+	23.4478i	2.39612	+	1.66636i
$199$		−	9.65388i		−	0.684345i	−0.939637	−	0.342173i	$-0.888837\pi$
$199$		−	9.65388i		−	0.684345i	0.939637	−	0.342173i	$-0.111163\pi$
$200$			9.17705i			0.648916i
$201$	0.788099	−	2.51357i	0.0555882	−	0.177294i
$202$			18.6769i			1.31410i
$203$	6.40989	+	3.76394i	0.449886	+	0.264177i
$204$	6.22744	−	19.8619i	0.436008	−	1.39061i
$205$	0.333115			0.0232658
$206$	−18.2165			−1.26921
$207$	−10.1956	+	14.6606i	−0.708640	+	1.01898i
$208$		−	10.3404i		−	0.716980i
$209$	11.9510			0.826666
$210$	22.2350	−	20.1403i	1.53436	−	1.38981i
$211$	−1.99971			−0.137666			−0.0688328	−	0.997628i	$-0.521928\pi$
$211$	−1.99971			−0.137666			−0.0688328	+	0.997628i	$0.521928\pi$
$212$		−	36.0137i		−	2.47343i
$213$	11.8641	+	3.71983i	0.812913	+	0.254879i
$214$	14.4788			0.989748
$215$	16.4617			1.12268
$216$	24.4161	+	31.5048i	1.66130	+	2.14363i
$217$	15.5409	+	9.12577i	1.05499	+	0.619498i
$218$		−	51.8168i		−	3.50948i
$219$	−27.1929	−	8.52598i	−1.83752	−	0.576133i
$220$			63.7055i			4.29502i
$221$		−	2.44427i		−	0.164419i
$222$	13.7821	+	4.32120i	0.924993	+	0.290020i
$223$			13.5978i			0.910579i	0.890343	+	0.455290i	$0.150464\pi$
$223$			13.5978i			0.910579i	−0.890343	+	0.455290i	$0.849536\pi$
$224$	−27.0433	−	15.8801i	−1.80691	−	1.06103i
$225$	−2.94660	−	2.04919i	−0.196440	−	0.136613i
$226$	−3.04939			−0.202843
$227$	3.90471			0.259165			0.129582	−	0.991569i	$-0.458636\pi$
$227$	3.90471			0.259165			0.129582	+	0.991569i	$0.458636\pi$
$228$	18.6569	+	5.84963i	1.23558	+	0.387401i
$229$		−	17.1919i		−	1.13608i	−0.823002	−	0.568038i	$-0.807703\pi$
$229$		−	17.1919i		−	1.13608i	0.823002	−	0.568038i	$-0.192297\pi$
$230$	−38.9683			−2.56949
$231$	17.6789	−	16.0134i	1.16318	−	1.05360i
$232$	−21.5512			−1.41490
$233$		−	7.00005i		−	0.458589i	−0.973357	−	0.229294i	$-0.926358\pi$
$233$		−	7.00005i		−	0.458589i	0.973357	−	0.229294i	$-0.0736418\pi$
$234$	6.47748	+	4.50471i	0.423446	+	0.294482i
$235$	−10.3531			−0.675360
$236$	3.55806			0.231610
$237$	0.0349860	−	0.111585i	0.00227258	−	0.00724821i
$238$	−14.6661	−	8.61208i	−0.950664	−	0.558238i
$239$			11.5946i			0.749991i	0.927027	+	0.374995i	$0.122356\pi$
$239$			11.5946i			0.749991i	−0.927027	+	0.374995i	$0.877644\pi$
$240$	−13.3381	+	42.5408i	−0.860974	+	2.74600i
$241$		−	21.0706i		−	1.35727i	−0.734473	−	0.678637i	$-0.762571\pi$
$241$		−	21.0706i		−	1.35727i	0.734473	−	0.678637i	$-0.237429\pi$
$242$			42.3262i			2.72083i
$243$	−15.5677	+	0.804754i	−0.998667	+	0.0516250i
$244$		−	40.4737i		−	2.59106i
$245$	−8.48925	−	15.2169i	−0.542358	−	0.972173i
$246$	0.581667	+	0.182374i	0.0370857	+	0.0116278i
$247$	2.29598			0.146090
$248$	−52.2514			−3.31797
$249$	3.30713	−	10.5478i	0.209581	−	0.668441i
$250$			24.9010i			1.57488i
$251$	−2.45633			−0.155042			−0.0775212	−	0.996991i	$-0.524701\pi$
$251$	−2.45633			−0.155042			−0.0775212	+	0.996991i	$0.524701\pi$
$252$	35.4369	−	16.3455i	2.23231	−	1.02967i
$253$	−30.9834			−1.94791
$254$			26.1977i			1.64379i
$255$	−3.15287	+	10.0558i	−0.197440	+	0.629718i
$256$	−10.7568			−0.672301
$257$	−9.21648			−0.574908			−0.287454	−	0.957794i	$-0.592809\pi$
$257$	−9.21648			−0.574908			−0.287454	+	0.957794i	$0.592809\pi$
$258$	28.7444	+	9.01245i	1.78955	+	0.561091i
$259$	4.24793	−	7.23411i	0.263953	−	0.449506i
$260$			12.2389i			0.759022i
$261$	4.81227	−	6.91974i	0.297872	−	0.428321i
$262$			1.27022i			0.0784746i
$263$			20.7018i			1.27653i	0.769817	+	0.638265i	$0.220348\pi$
$263$			20.7018i			1.27653i	−0.769817	+	0.638265i	$0.779652\pi$
$264$	−20.6901	+	65.9893i	−1.27339	+	4.06136i
$265$			18.2332i			1.12006i
$266$	8.08960	−	13.7764i	0.496005	−	0.844684i
$267$	−7.45539	+	23.7783i	−0.456263	+	1.45521i
$268$	7.47764			0.456770
$269$	29.7555			1.81422			0.907111	−	0.420891i	$-0.138282\pi$
$269$	29.7555			1.81422			0.907111	+	0.420891i	$0.138282\pi$
$270$	−20.8379	−	26.8878i	−1.26816	−	1.63634i
$271$			2.24336i			0.136274i	0.997676	+	0.0681372i	$0.0217056\pi$
$271$			2.24336i			0.136274i	−0.997676	+	0.0681372i	$0.978294\pi$
$272$	25.2748			1.53251
$273$	3.39640	−	3.07643i	0.205560	−	0.186194i
$274$	37.5777			2.27015
$275$		−	6.22730i		−	0.375521i
$276$	−48.3687	−	15.1654i	−2.91146	−	0.912850i
$277$	11.1835			0.671949			0.335974	−	0.941871i	$-0.390934\pi$
$277$	11.1835			0.671949			0.335974	+	0.941871i	$0.390934\pi$
$278$	−41.2782			−2.47570
$279$	11.6675	−	16.7771i	0.698513	−	1.00442i
$280$	43.5637	+	25.5810i	2.60343	+	1.52876i
$281$		−	20.1280i		−	1.20074i	−0.799724	−	0.600368i	$-0.795021\pi$
$281$		−	20.1280i		−	1.20074i	0.799724	−	0.600368i	$-0.204979\pi$
$282$	−18.0779	−	5.66811i	−1.07653	−	0.337531i
$283$			1.71130i			0.101726i	0.998706	+	0.0508632i	$0.0161972\pi$
$283$			1.71130i			0.101726i	−0.998706	+	0.0508632i	$0.983803\pi$
$284$			35.2945i			2.09434i
$285$	−9.44573	−	2.96159i	−0.559517	−	0.175429i
$286$			13.6894i			0.809472i
$287$	0.179282	−	0.305312i	0.0105827	−	0.0180220i
$288$	−20.3030	+	29.1944i	−1.19636	+	1.72030i
$289$	−11.0256			−0.648562
$290$	18.3929			1.08007
$291$	−27.6495	−	8.66915i	−1.62084	−	0.508195i
$292$		−	80.8963i		−	4.73410i
$293$	−10.3117			−0.602414			−0.301207	−	0.953559i	$-0.597390\pi$
$293$	−10.3117			−0.602414			−0.301207	+	0.953559i	$0.597390\pi$
$294$	−6.49246	−	31.2186i	−0.378648	−	1.82071i
$295$	−1.80140			−0.104881
$296$			24.3224i			1.41371i
$297$	−16.5681	−	21.3783i	−0.961379	−	1.24050i
$298$	7.52499			0.435911
$299$	−5.95242			−0.344237
$300$	3.04807	−	9.72156i	0.175981	−	0.561275i
$301$	8.85964	−	15.0877i	0.510661	−	0.869642i
$302$		−	19.0004i		−	1.09335i
$303$	3.67997	−	11.7369i	0.211409	−	0.674269i
$304$			23.7414i			1.36166i
$305$			20.4913i			1.17333i
$306$	−11.0107	+	15.8327i	−0.629440	+	0.905095i
$307$		−	5.34432i		−	0.305017i	−0.988302	−	0.152508i	$-0.951265\pi$
$307$		−	5.34432i		−	0.305017i	0.988302	−	0.152508i	$-0.0487351\pi$
$308$	58.3883	+	34.2861i	3.32698	+	1.95363i
$309$	11.4476	+	3.58926i	0.651233	+	0.204186i
$310$	44.5941			2.53277
$311$	27.6338			1.56697			0.783483	−	0.621413i	$-0.213441\pi$
$311$	27.6338			1.56697			0.783483	+	0.621413i	$0.213441\pi$
$312$	−3.97491	+	12.6776i	−0.225035	+	0.717729i
$313$			16.7987i			0.949516i	0.880116	+	0.474758i	$0.157464\pi$
$313$			16.7987i			0.949516i	−0.880116	+	0.474758i	$0.842536\pi$
$314$	−13.4105			−0.756798
$315$	−17.9412	+	8.27552i	−1.01087	+	0.466273i
$316$	0.331954			0.0186739
$317$		−	13.4327i		−	0.754457i	−0.926120	−	0.377228i	$-0.876877\pi$
$317$		−	13.4327i		−	0.754457i	0.926120	−	0.377228i	$-0.123123\pi$
$318$	−9.98234	+	31.8378i	−0.559782	+	1.78538i
$319$	14.6241			0.818790
$320$	−26.1198			−1.46014
$321$	−9.09874	−	2.85280i	−0.507842	−	0.159228i
$322$	−20.9726	+	35.7158i	−1.16876	+	1.99036i
$323$			5.61198i			0.312259i
$324$	−15.4008	−	41.4837i	−0.855597	−	2.30465i
$325$		−	1.19637i		−	0.0663625i
$326$		−	34.7628i		−	1.92534i
$327$	−10.2096	+	32.5627i	−0.564594	+	1.80072i
$328$			1.02651i			0.0566798i
$329$	−5.57200	+	9.48896i	−0.307194	+	0.523143i
$330$	17.6580	−	56.3186i	0.972041	−	3.10024i
$331$	−5.47069			−0.300696			−0.150348	−	0.988633i	$-0.548039\pi$
$331$	−5.47069			−0.300696			−0.150348	+	0.988633i	$0.548039\pi$
$332$	31.3788			1.72213
$333$	−7.80952	−	5.43106i	−0.427959	−	0.297620i
$334$			38.9472i			2.13110i
$335$	−3.78583			−0.206842
$336$	31.8116	+	35.1203i	1.73547	+	1.91597i
$337$	26.4845			1.44270			0.721351	−	0.692570i	$-0.243521\pi$
$337$	26.4845			1.44270			0.721351	+	0.692570i	$0.243521\pi$
$338$			2.62996i			0.143051i
$339$	1.91630	+	0.600832i	0.104079	+	0.0326327i
$340$	−29.9150			−1.62237
$341$	35.4564			1.92007
$342$	−14.8722	−	10.3427i	−0.804195	−	0.559270i
$343$	−18.5157	−	0.409009i	−0.999756	−	0.0220844i
$344$			50.7276i			2.73505i
$345$	24.4884	+	7.67804i	1.31841	+	0.413372i
$346$			13.8524i			0.744712i
$347$		−	2.33454i		−	0.125325i	−0.998035	−	0.0626625i	$-0.980041\pi$
$347$		−	2.33454i		−	0.125325i	0.998035	−	0.0626625i	$-0.0199592\pi$
$348$	22.8299	+	7.15802i	1.22381	+	0.383710i
$349$			6.44496i			0.344991i	0.985010	+	0.172495i	$0.0551830\pi$
$349$			6.44496i			0.344991i	−0.985010	+	0.172495i	$0.944817\pi$
$350$	−7.17846	−	4.21525i	−0.383705	−	0.225315i
$351$	−3.18300	−	4.10713i	−0.169896	−	0.219222i
$352$	−61.6989			−3.28856
$353$	−4.66374			−0.248226			−0.124113	−	0.992268i	$-0.539608\pi$
$353$	−4.66374			−0.248226			−0.124113	+	0.992268i	$0.539608\pi$
$354$	−3.14550	−	0.986231i	−0.167181	−	0.0524176i
$355$		−	17.8691i		−	0.948395i
$356$	−70.7383			−3.74912
$357$	7.51963	+	8.30172i	0.397981	+	0.439373i
$358$	4.27133			0.225747
$359$		−	9.24058i		−	0.487699i	−0.969813	−	0.243850i	$-0.921590\pi$
$359$		−	9.24058i		−	0.487699i	0.969813	−	0.243850i	$-0.0784103\pi$
$360$	32.7058	−	47.0289i	1.72375	−	2.47864i
$361$	13.7285			0.722552
$362$	−5.34957			−0.281167
$363$	8.33967	−	26.5987i	0.437719	−	1.39607i
$364$	11.2174	+	6.58692i	0.587949	+	0.345249i
$365$			40.9567i			2.14377i
$366$	−11.2186	+	35.7807i	−0.586404	+	1.87029i
$367$			22.3513i			1.16673i	0.812211	+	0.583363i	$0.198264\pi$
$367$			22.3513i			1.16673i	−0.812211	+	0.583363i	$0.801736\pi$
$368$		−	61.5505i		−	3.20854i
$369$	−0.329597	−	0.229215i	−0.0171581	−	0.0119325i
$370$		−	20.7580i		−	1.07915i
$371$	16.7114	+	9.81308i	0.867613	+	0.509470i
$372$	55.3517	+	17.3548i	2.86985	+	0.899806i
$373$	9.69869			0.502179			0.251090	−	0.967964i	$-0.419211\pi$
$373$	9.69869			0.502179			0.251090	+	0.967964i	$0.419211\pi$
$374$	−33.4606			−1.73020
$375$	4.90632	−	15.6483i	0.253361	−	0.808073i
$376$		−	31.9036i		−	1.64530i
$377$	2.80952			0.144698
$378$	−35.8586	+	4.62776i	−1.84437	+	0.238026i
$379$	−4.26162			−0.218905			−0.109452	−	0.993992i	$-0.534910\pi$
$379$	−4.26162			−0.218905			−0.109452	+	0.993992i	$0.534910\pi$
$380$		−	28.1002i		−	1.44151i
$381$	5.16181	−	16.4631i	0.264448	−	0.843432i
$382$	−9.30885			−0.476282
$383$	26.7904			1.36893			0.684463	−	0.729047i	$-0.260037\pi$
$383$	26.7904			1.36893			0.684463	+	0.729047i	$0.260037\pi$
$384$	−6.42827	−	2.01550i	−0.328041	−	0.102853i
$385$	−29.5612	−	17.3586i	−1.50658	−	0.884676i
$386$			33.7135i			1.71597i
$387$	−16.2878	−	11.3272i	−0.827957	−	0.575795i
$388$		−	82.2547i		−	4.17585i
$389$		−	32.2579i		−	1.63554i	−0.575543	−	0.817771i	$-0.695209\pi$
$389$		−	32.2579i		−	1.63554i	0.575543	−	0.817771i	$-0.304791\pi$
$390$	3.39239	−	10.8197i	0.171780	−	0.547879i
$391$		−	14.5493i		−	0.735790i
$392$	46.8918	−	26.1601i	2.36839	−	1.32128i
$393$	0.250276	−	0.798233i	0.0126247	−	0.0402655i
$394$	−40.2086			−2.02568
$395$	−0.168064			−0.00845621
$396$	43.8354	−	63.0326i	2.20281	−	3.16751i
$397$		−	4.07733i		−	0.204635i	−0.994752	−	0.102318i	$-0.967374\pi$
$397$		−	4.07733i		−	0.204635i	0.994752	−	0.102318i	$-0.0326258\pi$
$398$	−25.3893			−1.27265
$399$	−7.79807	+	7.06343i	−0.390392	+	0.353614i
$400$	12.3710			0.618548
$401$			35.7637i			1.78595i	0.450103	+	0.892977i	$0.351387\pi$
$401$			35.7637i			1.78595i	−0.450103	+	0.892977i	$0.648613\pi$
$402$	−6.61059	−	2.07267i	−0.329706	−	0.103375i
$403$	6.81176			0.339318
$404$	34.9163			1.73715
$405$	7.79719	+	21.0026i	0.387445	+	1.04363i
$406$	9.89901	−	16.8577i	0.491280	−	0.836636i
$407$		−	16.5045i		−	0.818098i
$408$	−30.9875	−	9.71573i	−1.53411	−	0.481001i
$409$			20.5606i			1.01665i	0.861164	+	0.508327i	$0.169736\pi$
$409$			20.5606i			1.01665i	−0.861164	+	0.508327i	$0.830264\pi$
$410$		−	0.876080i		−	0.0432665i
$411$	−23.6146	−	7.40405i	−1.16482	−	0.365215i
$412$			34.0556i			1.67780i
$413$	−0.969508	+	1.65105i	−0.0477064	+	0.0812427i
$414$	38.5567	+	26.8139i	1.89496	+	1.31783i
$415$	−15.8866			−0.779845
$416$	−11.8534			−0.581160
$417$	25.9401	+	8.13318i	1.27029	+	0.398283i
$418$		−	31.4306i		−	1.53732i
$419$	10.2990			0.503139			0.251570	−	0.967839i	$-0.419053\pi$
$419$	10.2990			0.503139			0.251570	+	0.967839i	$0.419053\pi$
$420$	−37.6521	−	41.5681i	−1.83723	−	2.02832i
$421$	−25.8012			−1.25747			−0.628737	−	0.777618i	$-0.716428\pi$
$421$	−25.8012			−1.25747			−0.628737	+	0.777618i	$0.716428\pi$
$422$			5.25915i			0.256012i
$423$	10.2437	+	7.12390i	0.498067	+	0.346376i
$424$	−56.1867			−2.72867
$425$	2.92424			0.141847
$426$	9.78300	−	31.2020i	0.473988	−	1.51174i
$427$	18.7810	+	11.0284i	0.908876	+	0.533699i
$428$		−	27.0679i		−	1.30838i
$429$	2.69727	−	8.60270i	0.130225	−	0.415342i
$430$		−	43.2936i		−	2.08780i
$431$			27.5266i			1.32591i	0.748660	+	0.662954i	$0.230697\pi$
$431$			27.5266i			1.32591i	−0.748660	+	0.662954i	$0.769303\pi$
$432$	42.4694	−	32.9136i	2.04331	−	1.58356i
$433$			10.7663i			0.517397i	0.965958	+	0.258698i	$0.0832936\pi$
$433$			10.7663i			0.517397i	−0.965958	+	0.258698i	$0.916706\pi$
$434$	24.0004	−	40.8720i	1.15206	−	1.96192i
$435$	−11.5585	−	3.62401i	−0.554186	−	0.173758i
$436$	−96.8711			−4.63928
$437$	13.6666			0.653763
$438$	−22.4230	+	71.5162i	−1.07141	+	3.41717i
$439$			9.68084i			0.462041i	0.972949	+	0.231021i	$0.0742065\pi$
$439$			9.68084i			0.462041i	−0.972949	+	0.231021i	$0.925794\pi$
$440$	99.3900			4.73823
$441$	−2.07111	+	20.8976i	−0.0986241	+	0.995125i
$442$	−6.42832			−0.305764
$443$			11.8594i			0.563459i	0.959494	+	0.281729i	$0.0909080\pi$
$443$			11.8594i			0.563459i	−0.959494	+	0.281729i	$0.909092\pi$
$444$	8.07845	−	25.7655i	0.383386	−	1.22278i
$445$	35.8138			1.69774
$446$	35.7618			1.69337
$447$	−4.72885	−	1.48267i	−0.223667	−	0.0701280i
$448$	−14.0576	+	23.9397i	−0.664160	+	1.13105i
$449$			34.4245i			1.62459i	0.583245	+	0.812296i	$0.301783\pi$
$449$			34.4245i			1.62459i	−0.583245	+	0.812296i	$0.698217\pi$
$450$	−5.38928	+	7.74945i	−0.254053	+	0.365313i
$451$		−	0.696565i		−	0.0328000i
$452$			5.70082i			0.268144i
$453$	−3.74370	+	11.9402i	−0.175894	+	0.561000i
$454$		−	10.2692i		−	0.481959i
$455$	−5.67919	−	3.33487i	−0.266245	−	0.156341i
$456$	9.12630	−	29.1075i	0.427378	−	1.36309i
$457$	−39.3323			−1.83989			−0.919943	−	0.392053i	$-0.871765\pi$
$457$	−39.3323			−1.83989			−0.919943	+	0.392053i	$0.871765\pi$
$458$	−45.2141			−2.11272
$459$	10.0389	−	7.78011i	0.468576	−	0.363145i
$460$			72.8508i			3.39669i
$461$	−34.8799			−1.62452			−0.812260	−	0.583295i	$-0.801763\pi$
$461$	−34.8799			−1.62452			−0.812260	+	0.583295i	$0.801763\pi$
$462$	−42.1146	−	46.4947i	−1.95935	−	2.16313i
$463$	−16.5025			−0.766936			−0.383468	−	0.923554i	$-0.625270\pi$
$463$	−16.5025			−0.766936			−0.383468	+	0.923554i	$0.625270\pi$
$464$			29.0517i			1.34869i
$465$	−28.0238	−	8.78651i	−1.29957	−	0.407465i
$466$	−18.4099			−0.852820
$467$	−31.5382			−1.45941			−0.729706	−	0.683761i	$-0.760343\pi$
$467$	−31.5382			−1.45941			−0.729706	+	0.683761i	$0.760343\pi$
$468$	8.42151	−	12.1096i	0.389284	−	0.559766i
$469$	−2.03752	+	3.46985i	−0.0940841	+	0.160223i
$470$			27.2282i			1.25594i
$471$	8.42742	+	2.64231i	0.388315	+	0.121751i
$472$		−	5.55111i		−	0.255511i
$473$		−	34.4224i		−	1.58274i
$474$	−0.293463	−	0.0920117i	−0.0134792	−	0.00422624i
$475$			2.74683i			0.126033i
$476$	−16.1002	+	27.4182i	−0.737952	+	1.25671i
$477$	12.5462	−	18.0407i	0.574451	−	0.826025i
$478$	30.4933			1.39473
$479$	−23.0063			−1.05118			−0.525592	−	0.850737i	$-0.676156\pi$
$479$	−23.0063			−1.05118			−0.525592	+	0.850737i	$0.676156\pi$
$480$	48.7652	+	15.2897i	2.22581	+	0.697876i
$481$		−	3.17079i		−	0.144575i
$482$	−55.4148			−2.52407
$483$	20.2168	−	18.3122i	0.919897	−	0.833235i
$484$	79.1285			3.59675
$485$			41.6444i			1.89098i
$486$	2.11647	+	40.9423i	0.0960051	+	1.85718i
$487$	10.7586			0.487519			0.243759	−	0.969836i	$-0.421619\pi$
$487$	10.7586			0.487519			0.243759	+	0.969836i	$0.421619\pi$
$488$	−63.1450			−2.85844
$489$	−6.84943	+	21.8457i	−0.309742	+	0.987895i
$490$	−40.0199	+	22.3264i	−1.80791	+	1.00860i
$491$		−	19.7765i		−	0.892502i	−0.894908	−	0.446251i	$-0.852759\pi$
$491$		−	19.7765i		−	0.892502i	0.894908	−	0.446251i	$-0.147241\pi$
$492$	0.340947	−	1.08742i	0.0153711	−	0.0490247i
$493$			6.86722i			0.309284i
$494$		−	6.03833i		−	0.271677i
$495$	−22.1933	+	31.9125i	−0.997514	+	1.43436i
$496$			70.4365i			3.16269i
$497$	−16.3777	−	9.61712i	−0.734640	−	0.431387i
$498$	−27.7403	−	8.69763i	−1.24307	−	0.389750i
$499$	25.7171			1.15126			0.575629	−	0.817711i	$-0.304757\pi$
$499$	25.7171			1.15126			0.575629	+	0.817711i	$0.304757\pi$
$500$	46.5521			2.08187
$501$	7.67389	−	24.4752i	0.342844	−	1.09347i
$502$			6.46005i			0.288326i
$503$	−0.0498348			−0.00222202			−0.00111101	−	0.999999i	$-0.500354\pi$
$503$	−0.0498348			−0.00222202			−0.00111101	+	0.999999i	$0.500354\pi$
$504$	−25.5015	−	55.2868i	−1.13593	−	2.46267i
$505$	−17.6776			−0.786644
$506$			81.4851i			3.62245i
$507$	0.518189	−	1.65272i	0.0230136	−	0.0733998i
$508$	48.9763			2.17297
$509$	5.38039			0.238482			0.119241	−	0.992865i	$-0.461954\pi$
$509$	5.38039			0.238482			0.119241	+	0.992865i	$0.461954\pi$
$510$	26.4463	+	8.29191i	1.17106	+	0.367172i
$511$	37.5383	+	22.0428i	1.66059	+	0.975115i
$512$			36.0690i			1.59404i
$513$	7.30811	+	9.42987i	0.322661	+	0.416339i
$514$			24.2390i			1.06914i
$515$		−	17.2419i		−	0.759769i
$516$	16.8487	−	53.7375i	0.741723	−	2.36566i
$517$			21.6489i			0.952118i
$518$	−19.0254	−	11.1719i	−0.835929	−	0.490864i
$519$	2.72939	−	8.70515i	0.119807	−	0.382114i
$520$	19.0945			0.837347
$521$	−0.957985			−0.0419701			−0.0209850	−	0.999780i	$-0.506680\pi$
$521$	−0.957985			−0.0419701			−0.0209850	+	0.999780i	$0.506680\pi$
$522$	−18.1986	−	12.6561i	−0.796533	−	0.553941i
$523$		−	21.4942i		−	0.939877i	−0.882699	−	0.469939i	$-0.844276\pi$
$523$		−	21.4942i		−	0.939877i	0.882699	−	0.469939i	$-0.155724\pi$
$524$	2.37467			0.103738
$525$	3.68055	+	4.06335i	0.160632	+	0.177339i
$526$	54.4450			2.37391
$527$			16.6498i			0.725275i
$528$	88.9556	+	27.8909i	3.87129	+	1.21380i
$529$	−12.4313			−0.540490
$530$	47.9527			2.08293
$531$	1.78237	+	1.23953i	0.0773484	+	0.0537912i
$532$	−25.7548	−	15.1234i	−1.11661	−	0.655684i
$533$		−	0.133822i		−	0.00579646i
$534$	62.5360	+	19.6074i	2.70620	+	0.848494i
$535$			13.7041i			0.592481i
$536$		−	11.6662i		−	0.503905i
$537$	−2.68419	−	0.841594i	−0.115831	−	0.0363175i
$538$		−	78.2557i		−	3.37384i
$539$	−31.8195	+	17.7515i	−1.37056	+	0.764613i
$540$	−50.2665	+	38.9564i	−2.16313	+	1.67641i
$541$	9.68496			0.416389			0.208195	−	0.978087i	$-0.433241\pi$
$541$	9.68496			0.416389			0.208195	+	0.978087i	$0.433241\pi$
$542$	5.89995			0.253424
$543$	3.36178	+	1.05404i	0.144268	+	0.0452333i
$544$		−	28.9728i		−	1.24220i
$545$	49.0445			2.10084
$546$	−8.09090	−	8.93240i	−0.346258	−	0.382271i
$547$	−27.7026			−1.18448			−0.592238	−	0.805763i	$-0.701756\pi$
$547$	−27.7026			−1.18448			−0.592238	+	0.805763i	$0.701756\pi$
$548$		−	70.2511i		−	3.00098i
$549$	14.1000	−	20.2749i	0.601771	−	0.865310i
$550$	−16.3776			−0.698341
$551$	−6.45060			−0.274805
$552$	−23.6603	+	75.4625i	−1.00705	+	3.21190i
$553$	−0.0904516	+	0.154037i	−0.00384639	+	0.00655030i
$554$		−	29.4120i		−	1.24960i
$555$	−4.09001	+	13.0447i	−0.173611	+	0.553717i
$556$			77.1693i			3.27271i
$557$		−	34.1530i		−	1.44711i	−0.690266	−	0.723556i	$-0.742507\pi$
$557$		−	34.1530i		−	1.44711i	0.690266	−	0.723556i	$-0.257493\pi$
$558$	−44.1231	−	30.6850i	−1.86788	−	1.29900i
$559$		−	6.61311i		−	0.279705i
$560$	34.4840	−	58.7253i	1.45721	−	2.48160i
$561$	21.0273	+	6.59284i	0.887773	+	0.278350i
$562$	−52.9358			−2.23296
$563$	−30.0552			−1.26668			−0.633338	−	0.773875i	$-0.718316\pi$
$563$	−30.0552			−1.26668			−0.633338	+	0.773875i	$0.718316\pi$
$564$	−10.5965	+	33.7965i	−0.446192	+	1.42309i
$565$		−	2.88624i		−	0.121425i
$566$	4.50065			0.189177
$567$	23.4461	+	4.15715i	0.984642	+	0.174584i
$568$	55.0647			2.31046
$569$		−	38.1685i		−	1.60011i	−0.599928	−	0.800054i	$-0.704804\pi$
$569$		−	38.1685i		−	1.60011i	0.599928	−	0.800054i	$-0.295196\pi$
$570$	−7.78886	+	24.8419i	−0.326239	+	1.04051i
$571$	−18.7251			−0.783620			−0.391810	−	0.920046i	$-0.628151\pi$
$571$	−18.7251			−0.783620			−0.391810	+	0.920046i	$0.628151\pi$
$572$	25.5922			1.07006
$573$	5.84987	+	1.83415i	0.244382	+	0.0766228i
$574$	−0.802959	−	0.471504i	−0.0335148	−	0.0196802i
$575$		−	7.12128i		−	0.296978i
$576$	25.8439	+	17.9729i	1.07683	+	0.748872i
$577$		−	12.3887i		−	0.515750i	−0.966178	−	0.257875i	$-0.916978\pi$
$577$		−	12.3887i		−	0.515750i	0.966178	−	0.257875i	$-0.0830223\pi$
$578$			28.9968i			1.20611i
$579$	6.64267	−	21.1862i	0.276060	−	0.880469i
$580$		−	34.3854i		−	1.42777i
$581$	−8.55015	+	14.5607i	−0.354720	+	0.604079i
$582$	−22.7995	+	72.7171i	−0.945071	+	3.01422i
$583$	38.1268			1.57905
$584$	−126.210			−5.22262
$585$	−4.26369	+	6.13092i	−0.176282	+	0.253483i
$586$			27.1193i			1.12029i
$587$	−45.0894			−1.86104			−0.930520	−	0.366240i	$-0.880645\pi$
$587$	−45.0894			−1.86104			−0.930520	+	0.366240i	$0.880645\pi$
$588$	−58.3629	+	12.1376i	−2.40685	+	0.500546i
$589$	−15.6397			−0.644421
$590$			4.73761i			0.195044i
$591$	25.2679	+	7.92242i	1.03938	+	0.325885i
$592$	32.7873			1.34755
$593$	47.2250			1.93930			0.969649	−	0.244501i	$-0.0786242\pi$
$593$	47.2250			1.93930			0.969649	+	0.244501i	$0.0786242\pi$
$594$	−56.2241	+	43.5734i	−2.30690	+	1.78784i
$595$	8.15131	−	13.8815i	0.334171	−	0.569084i
$596$		−	14.0679i		−	0.576244i
$597$	15.9552	+	5.00254i	0.653001	+	0.204740i
$598$			15.6546i			0.640165i
$599$			39.4389i			1.61143i	0.592303	+	0.805715i	$0.298219\pi$
$599$			39.4389i			1.61143i	−0.592303	+	0.805715i	$0.701781\pi$
$600$	−15.1671	−	4.75545i	−0.619194	−	0.194140i
$601$		−	14.6955i		−	0.599440i	−0.954027	−	0.299720i	$-0.903107\pi$
$601$		−	14.6955i		−	0.599440i	0.954027	−	0.299720i	$-0.0968933\pi$
$602$	−39.6801	−	23.3005i	−1.61724	−	0.949657i
$603$	3.74584	+	2.60501i	0.152543	+	0.106084i
$604$	−35.5210			−1.44533
$605$	−40.0617			−1.62874
$606$	−30.8676	−	9.67816i	−1.25391	−	0.393148i
$607$		−	14.1329i		−	0.573637i	−0.957985	−	0.286818i	$-0.907402\pi$
$607$		−	14.1329i		−	0.573637i	0.957985	−	0.286818i	$-0.0925976\pi$
$608$	27.2151			1.10372
$609$	−9.54227	+	8.64331i	−0.386672	+	0.350245i
$610$	53.8912			2.18199
$611$			4.15911i			0.168260i
$612$	29.5991	+	20.5844i	1.19647	+	0.832075i
$613$	0.855412			0.0345498			0.0172749	−	0.999851i	$-0.494501\pi$
$613$	0.855412			0.0345498			0.0172749	+	0.999851i	$0.494501\pi$
$614$	−14.0554			−0.567228
$615$	−0.172617	+	0.550546i	−0.00696058	+	0.0222002i
$616$	53.4915	−	91.0945i	2.15523	−	3.67030i
$617$			0.301821i			0.0121509i	0.999982	+	0.00607543i	$0.00193388\pi$
$617$			0.301821i			0.0121509i	−0.999982	+	0.00607543i	$0.998066\pi$
$618$	9.43960	−	30.1068i	0.379717	−	1.21107i
$619$			17.1645i			0.689899i	0.938621	+	0.344949i	$0.112104\pi$
$619$			17.1645i			0.689899i	−0.938621	+	0.344949i	$0.887896\pi$
$620$		−	83.3682i		−	3.34815i
$621$	−18.9466	−	24.4473i	−0.760300	−	0.981037i
$622$		−	72.6757i		−	2.91403i
$623$	19.2749	−	32.8247i	0.772233	−	1.31509i
$624$	17.0898	+	5.35830i	0.684140	+	0.214504i
$625$	−29.5505			−1.18202
$626$	44.1798			1.76578
$627$	−6.19287	+	19.7516i	−0.247319	+	0.788803i
$628$			25.0708i			1.00043i
$629$	7.75025			0.309023
$630$	21.7643	+	47.1846i	0.867109	+	1.87988i
$631$	36.1119			1.43759			0.718797	−	0.695220i	$-0.244693\pi$
$631$	36.1119			1.43759			0.718797	+	0.695220i	$0.244693\pi$
$632$		−	0.517898i		−	0.0206009i
$633$	1.03623	−	3.30496i	0.0411864	−	0.131360i
$634$	−35.3275			−1.40303
$635$	−24.7960			−0.984001
$636$	59.5205	+	18.6619i	2.36014	+	0.739993i
$637$	−6.11305	+	3.41036i	−0.242208	+	0.135124i
$638$		−	38.4607i		−	1.52267i
$639$	−12.2957	+	17.6804i	−0.486409	+	0.699426i
$640$			9.68197i			0.382714i
$641$		−	17.5910i		−	0.694802i	−0.937717	−	0.347401i	$-0.887064\pi$
$641$		−	17.5910i		−	0.694802i	0.937717	−	0.347401i	$-0.112936\pi$
$642$	−7.50274	+	23.9293i	−0.296109	+	0.944415i
$643$			16.4792i			0.649878i	0.945735	+	0.324939i	$0.105344\pi$
$643$			16.4792i			0.649878i	−0.945735	+	0.324939i	$0.894656\pi$
$644$	66.7704	+	39.2081i	2.63112	+	1.54502i
$645$	−8.53027	+	27.2065i	−0.335879	+	1.07126i
$646$	14.7593			0.580697
$647$	−38.1387			−1.49939			−0.749694	−	0.661785i	$-0.769799\pi$
$647$	−38.1387			−1.49939			−0.749694	+	0.661785i	$0.769799\pi$
$648$	−64.7207	+	24.0275i	−2.54247	+	0.943888i
$649$			3.76684i			0.147861i
$650$	−3.14640			−0.123412
$651$	−23.1355	+	20.9559i	−0.906751	+	0.821328i
$652$	−64.9888			−2.54516
$653$			9.85577i			0.385686i	0.981230	+	0.192843i	$0.0617708\pi$
$653$			9.85577i			0.385686i	−0.981230	+	0.192843i	$0.938229\pi$
$654$	85.6386	+	26.8509i	3.34874	+	1.04995i
$655$	−1.20226			−0.0469763
$656$	1.38377			0.0540272
$657$	28.1821	−	40.5241i	1.09949	−	1.58100i
$658$	24.9556	+	14.6541i	0.972870	+	0.571277i
$659$		−	40.0519i		−	1.56020i	−0.625655	−	0.780100i	$-0.715168\pi$
$659$		−	40.0519i		−	1.56020i	0.625655	−	0.780100i	$-0.284832\pi$
$660$	−105.287	−	33.0115i	−4.09830	−	1.28497i
$661$			47.9693i			1.86579i	0.360147	+	0.932896i	$0.382727\pi$
$661$			47.9693i			1.86579i	−0.360147	+	0.932896i	$0.617273\pi$
$662$			14.3877i			0.559193i
$663$	4.03969	+	1.26659i	0.156888	+	0.0491904i
$664$		−	48.9556i		−	1.89985i
$665$	13.0393	+	7.65679i	0.505642	+	0.296918i
$666$	−14.2835	+	20.5387i	−0.553473	+	0.795859i
$667$	16.7234			0.647534
$668$	72.8114			2.81716
$669$	−22.4734	−	7.04626i	−0.868873	−	0.272424i
$670$			9.95657i			0.384656i
$671$	42.8485			1.65415
$672$	40.2588	−	36.4661i	1.55302	−	1.40671i
$673$	−8.51964			−0.328408			−0.164204	−	0.986426i	$-0.552506\pi$
$673$	−8.51964			−0.328408			−0.164204	+	0.986426i	$0.552506\pi$
$674$		−	69.6531i		−	2.68294i
$675$	4.91363	−	3.80804i	0.189126	−	0.146572i
$676$	4.91669			0.189103
$677$	−4.89321			−0.188061			−0.0940307	−	0.995569i	$-0.529975\pi$
$677$	−4.89321			−0.188061			−0.0940307	+	0.995569i	$0.529975\pi$
$678$	1.58016	−	5.03979i	0.0606858	−	0.193552i
$679$	38.1686	+	22.4129i	1.46478	+	0.860129i
$680$			46.6719i			1.78979i
$681$	−2.02338	+	6.45339i	−0.0775360	+	0.247294i
$682$		−	93.2490i		−	3.57069i
$683$		−	24.7729i		−	0.947910i	−0.880549	−	0.473955i	$-0.842826\pi$
$683$		−	24.7729i		−	0.947910i	0.880549	−	0.473955i	$-0.157174\pi$
$684$	−19.3356	+	27.8034i	−0.739315	+	1.06309i
$685$			35.5672i			1.35895i
$686$	−1.07568	+	48.6956i	−0.0410695	+	1.85921i
$687$	28.4135	+	8.90868i	1.08404	+	0.339887i
$688$	68.3824			2.60705
$689$	7.32479			0.279052
$690$	20.1929	−	64.4036i	0.768732	−	2.45180i
$691$		−	20.7376i		−	0.788895i	−0.918919	−	0.394447i	$-0.870936\pi$
$691$		−	20.7376i		−	0.788895i	0.918919	−	0.394447i	$-0.129064\pi$
$692$	25.8970			0.984457
$693$	17.3046	+	37.5162i	0.657348	+	1.42512i
$694$	−6.13976			−0.233062
$695$		−	39.0697i		−	1.48200i
$696$	11.1676	−	35.6180i	0.423306	−	1.35010i
$697$	0.327096			0.0123896
$698$	16.9500			0.641566
$699$	11.5691	+	3.62735i	0.437584	+	0.137199i
$700$	−7.88038	+	13.4201i	−0.297850	+	0.507231i
$701$			50.4855i			1.90681i	0.301693	+	0.953405i	$0.402448\pi$
$701$			50.4855i			1.90681i	−0.301693	+	0.953405i	$0.597552\pi$
$702$	−10.8016	+	8.37117i	−0.407679	+	0.315950i
$703$			7.28006i			0.274573i
$704$			54.6181i			2.05850i
$705$	5.36485	−	17.1107i	0.202052	−	0.644427i
$706$			12.2654i			0.461616i
$707$	−9.51406	+	16.2022i	−0.357813	+	0.609346i
$708$	−1.84375	+	5.88048i	−0.0692924	+	0.221002i
$709$	−22.2910			−0.837155			−0.418577	−	0.908181i	$-0.637471\pi$
$709$	−22.2910			−0.837155			−0.418577	+	0.908181i	$0.637471\pi$
$710$	−46.9951			−1.76369
$711$	0.166289	+	0.115644i	0.00623632	+	0.00433699i
$712$			110.362i			4.13600i
$713$	40.5464			1.51848
$714$	21.8332	−	19.7763i	0.817086	−	0.740110i
$715$	−12.9570			−0.484564
$716$		−	7.98522i		−	0.298422i
$717$	−19.1626	−	6.00818i	−0.715639	−	0.224380i
$718$	−24.3023			−0.906956
$719$	31.8409			1.18747			0.593733	−	0.804662i	$-0.297654\pi$
$719$	31.8409			1.18747			0.593733	+	0.804662i	$0.297654\pi$
$720$	−63.3964	−	44.0884i	−2.36264	−	1.64308i
$721$	−15.8028	−	9.27955i	−0.588528	−	0.345588i
$722$		−	36.1053i		−	1.34370i
$723$	34.8237	+	10.9185i	1.29511	+	0.406065i
$724$			10.0010i			0.371683i
$725$			3.36122i			0.124833i
$726$	−69.9534	−	21.9330i	−2.59621	−	0.814010i
$727$			26.1490i			0.969811i	0.874566	+	0.484906i	$0.161146\pi$
$727$			26.1490i			0.969811i	−0.874566	+	0.484906i	$0.838854\pi$
$728$	10.2766	−	17.5007i	0.380876	−	0.648621i
$729$	6.73697	−	26.1460i	0.249517	−	0.968370i
$730$	107.714			3.98669
$731$	16.1642			0.597855
$732$	66.8916	+	20.9730i	2.47239	+	0.775186i
$733$			15.7431i			0.581484i	0.956802	+	0.290742i	$0.0939021\pi$
$733$			15.7431i			0.581484i	−0.956802	+	0.290742i	$0.906098\pi$
$734$	58.7829			2.16972
$735$	29.5483	−	6.14510i	1.08991	−	0.226665i
$736$	−70.5562			−2.60074
$737$			7.91640i			0.291604i
$738$	−0.602827	+	0.866827i	−0.0221904	+	0.0319084i
$739$	−25.5426			−0.939600			−0.469800	−	0.882773i	$-0.655674\pi$
$739$	−25.5426			−0.939600			−0.469800	+	0.882773i	$0.655674\pi$
$740$	−38.8068			−1.42657
$741$	−1.18975	+	3.79461i	−0.0437066	+	0.139398i
$742$	25.8080	−	43.9503i	0.947442	−	1.61347i
$743$			10.3372i			0.379234i	0.981858	+	0.189617i	$0.0607246\pi$
$743$			10.3372i			0.379234i	−0.981858	+	0.189617i	$0.939275\pi$
$744$	27.0761	−	86.3569i	0.992659	−	3.16600i
$745$			7.12239i			0.260944i
$746$		−	25.5072i		−	0.933883i
$747$	15.7189	+	10.9315i	0.575123	+	0.399964i
$748$			62.5542i			2.28721i
$749$	12.5603	+	7.37552i	0.458944	+	0.269496i
$750$	−41.1543	−	12.9034i	−1.50274	−	0.471166i
$751$	38.9962			1.42299			0.711496	−	0.702691i	$-0.248018\pi$
$751$	38.9962			1.42299			0.711496	+	0.702691i	$0.248018\pi$
$752$	−43.0070			−1.56830
$753$	1.27284	−	4.05963i	0.0463850	−	0.147941i
$754$		−	7.38893i		−	0.269089i
$755$	17.9838			0.654497
$756$	8.65156	+	67.0373i	0.314654	+	2.43812i
$757$	3.99142			0.145071			0.0725354	−	0.997366i	$-0.476891\pi$
$757$	3.99142			0.145071			0.0725354	+	0.997366i	$0.476891\pi$
$758$			11.2079i			0.407089i
$759$	16.0553	−	51.2068i	0.582769	−	1.85869i
$760$	−43.8405			−1.59026
$761$	−38.0670			−1.37993			−0.689964	−	0.723844i	$-0.742374\pi$
$761$	−38.0670			−1.37993			−0.689964	+	0.723844i	$0.742374\pi$
$762$	−43.2974	−	13.5754i	−1.56850	−	0.491783i
$763$	26.3956	−	44.9510i	0.955586	−	1.62734i
$764$			17.4028i			0.629612i
$765$	−14.9856	−	10.4216i	−0.541806	−	0.376794i
$766$		−	70.4577i		−	2.54574i
$767$			0.723671i			0.0261303i
$768$	5.57407	−	17.7780i	0.201137	−	0.641508i
$769$		−	49.6363i		−	1.78993i	−0.446135	−	0.894966i	$-0.647200\pi$
$769$		−	49.6363i		−	1.78993i	0.446135	−	0.894966i	$-0.352800\pi$
$770$	−45.6524	+	77.7448i	−1.64520	+	2.80173i
$771$	4.77588	−	15.2323i	0.171999	−	0.548576i
$772$	63.0270			2.26839
$773$	−25.7709			−0.926916			−0.463458	−	0.886119i	$-0.653391\pi$
$773$	−25.7709			−0.926916			−0.463458	+	0.886119i	$0.653391\pi$
$774$	−29.7901	+	42.8363i	−1.07078	+	1.53972i
$775$			8.14937i			0.292734i
$776$	−128.330			−4.60677
$777$	9.75472	+	10.7693i	0.349949	+	0.386345i
$778$	−84.8371			−3.04156
$779$			0.307252i			0.0110084i
$780$	−20.2274	−	6.34205i	−0.724257	−	0.227082i
$781$	−37.3655			−1.33704
$782$	−38.2641			−1.36832
$783$	8.94272	+	11.5391i	0.319587	+	0.412372i
$784$	−35.2646	−	63.2116i	−1.25945	−	2.25756i
$785$		−	12.6930i		−	0.453033i
$786$	−2.09932	−	0.658215i	−0.0748803	−	0.0234778i
$787$			49.8715i			1.77773i	0.458171	+	0.888864i	$0.348505\pi$
$787$			49.8715i			1.77773i	−0.458171	+	0.888864i	$0.651495\pi$
$788$			75.1695i			2.67780i
$789$	−34.2143	−	10.7275i	−1.21806	−	0.381908i
$790$			0.442001i			0.0157257i
$791$	−2.64535	−	1.55337i	−0.0940577	−	0.0552315i
$792$	−98.3403	−	68.3898i	−3.49437	−	2.43013i
$793$	8.23191			0.292324
$794$	−10.7232			−0.380552
$795$	−30.1344	−	9.44826i	−1.06876	−	0.335095i
$796$			47.4651i			1.68236i
$797$	−31.5593			−1.11789			−0.558944	−	0.829205i	$-0.688793\pi$
$797$	−31.5593			−1.11789			−0.558944	+	0.829205i	$0.688793\pi$
$798$	18.5765	+	20.5086i	0.657602	+	0.725997i
$799$	−10.1660			−0.359647
$800$		−	14.1810i		−	0.501374i
$801$	−35.4356	−	24.6433i	−1.25205	−	0.870730i
$802$	94.0570			3.32127
$803$	85.6430			3.02227
$804$	−3.87483	+	12.3584i	−0.136655	+	0.435849i
$805$	−33.8049	−	19.8505i	−1.19147	−	0.699639i
$806$		−	17.9147i		−	0.631017i
$807$	−15.4190	+	49.1774i	−0.542773	+	1.73113i
$808$		−	54.4746i		−	1.91641i
$809$		−	42.3362i		−	1.48846i	−0.667923	−	0.744230i	$-0.732817\pi$
$809$		−	42.3362i		−	1.48846i	0.667923	−	0.744230i	$-0.267183\pi$
$810$	55.2360	−	20.5063i	1.94080	−	0.720517i
$811$			15.2751i			0.536380i	0.963366	+	0.268190i	$0.0864255\pi$
$811$			15.2751i			0.536380i	−0.963366	+	0.268190i	$0.913574\pi$
$812$	−31.5154	−	18.5061i	−1.10597	−	0.649437i
$813$	−3.70764	−	1.16249i	−0.130033	−	0.0407701i
$814$	−43.4062			−1.52139
$815$	32.9029			1.15254
$816$	−13.0971	+	41.7721i	−0.458491	+	1.46232i
$817$			15.1836i			0.531205i
$818$	54.0734			1.89063
$819$	3.32450	+	7.20747i	0.116167	+	0.251850i
$820$	−1.63782			−0.0571953
$821$		−	1.23687i		−	0.0431672i	−0.999767	−	0.0215836i	$-0.993129\pi$
$821$		−	1.23687i		−	0.0431672i	0.999767	−	0.0215836i	$-0.00687081\pi$
$822$	−19.4723	+	62.1053i	−0.679176	+	2.16617i
$823$	−4.50870			−0.157164			−0.0785818	−	0.996908i	$-0.525039\pi$
$823$	−4.50870			−0.157164			−0.0785818	+	0.996908i	$0.525039\pi$
$824$	53.1319			1.85094
$825$	10.2920	+	3.22692i	0.358321	+	0.112347i
$826$	4.34218	+	2.54977i	0.151084	+	0.0887178i
$827$		−	29.0856i		−	1.01140i	−0.862708	−	0.505702i	$-0.831233\pi$
$827$		−	29.0856i		−	1.01140i	0.862708	−	0.505702i	$-0.168767\pi$
$828$	50.1283	−	72.0814i	1.74208	−	2.50500i
$829$		−	45.0204i		−	1.56362i	−0.623514	−	0.781812i	$-0.714296\pi$
$829$		−	45.0204i		−	1.56362i	0.623514	−	0.781812i	$-0.285704\pi$
$830$			41.7812i			1.45025i
$831$	−5.79514	+	18.4831i	−0.201031	+	0.641172i
$832$			10.4930i			0.363781i
$833$	−8.33584	−	14.9419i	−0.288820	−	0.517707i
$834$	21.3899	−	68.2213i	0.740673	−	2.36231i
$835$	−36.8634			−1.27571
$836$	−58.7592			−2.03223
$837$	21.6819	+	27.9768i	0.749435	+	0.967018i
$838$		−	27.0860i		−	0.935669i
$839$	−47.7484			−1.64846			−0.824229	−	0.566256i	$-0.808391\pi$
$839$	−47.7484			−1.64846			−0.824229	+	0.566256i	$0.808391\pi$
$840$	−64.8525	+	58.7428i	−2.23762	+	2.02682i
$841$	21.1066			0.727813
$842$			67.8561i			2.33848i
$843$	33.2659	+	10.4301i	1.14574	+	0.359232i
$844$	9.83194			0.338429
$845$	−2.48925			−0.0856328
$846$	18.7356	−	26.9406i	0.644142	−	0.926237i
$847$	−21.5611	+	36.7180i	−0.740848	+	1.26164i
$848$			75.7415i			2.60097i
$849$	−2.82830	−	0.886778i	−0.0970671	−	0.0304341i
$850$		−	7.69064i		−	0.263787i
$851$		−	18.8738i		−	0.646987i
$852$	−58.3319	−	18.2892i	−1.99842	−	0.626579i
$853$		−	9.77198i		−	0.334586i	−0.985907	−	0.167293i	$-0.946497\pi$
$853$		−	9.77198i		−	0.334586i	0.985907	−	0.167293i	$-0.0535026\pi$
$854$	29.0041	−	49.3932i	0.992500	−	1.69020i
$855$	9.78935	−	14.0765i	0.334789	−	0.481405i
$856$	−42.2300			−1.44339
$857$	−6.35976			−0.217245			−0.108623	−	0.994083i	$-0.534644\pi$
$857$	−6.35976			−0.217245			−0.108623	+	0.994083i	$0.534644\pi$
$858$	−22.6247	−	7.09370i	−0.772396	−	0.242175i
$859$		−	43.5034i		−	1.48432i	−0.670225	−	0.742158i	$-0.733803\pi$
$859$		−	43.5034i		−	1.48432i	0.670225	−	0.742158i	$-0.266197\pi$
$860$	−80.9369			−2.75993
$861$	0.411693	+	0.454512i	0.0140305	+	0.0154897i
$862$	72.3937			2.46574
$863$		−	3.75973i		−	0.127983i	−0.997950	−	0.0639914i	$-0.979617\pi$
$863$		−	3.75973i		−	0.127983i	0.997950	−	0.0639914i	$-0.0203830\pi$
$864$	−37.7293	−	48.6833i	−1.28358	−	1.65624i
$865$	−13.1113			−0.445798
$866$	28.3150			0.962183
$867$	5.71333	−	18.2222i	0.194035	−	0.618857i
$868$	−76.4099	−	44.8686i	−2.59352	−	1.52294i
$869$			0.351432i			0.0119215i
$870$	−9.53100	+	30.3983i	−0.323131	+	1.03060i
$871$			1.52087i			0.0515327i
$872$			151.133i			5.11802i
$873$	28.6554	−	41.2046i	0.969837	−	1.39456i
$874$		−	35.9427i		−	1.21578i
$875$	−12.6846	+	21.6016i	−0.428818	+	0.730266i
$876$	133.699	+	41.9196i	4.51727	+	1.41633i
$877$	−13.4380			−0.453769			−0.226885	−	0.973922i	$-0.572854\pi$
$877$	−13.4380			−0.453769			−0.226885	+	0.973922i	$0.572854\pi$
$878$	25.4602			0.859240
$879$	5.34340	−	17.0423i	0.180228	−	0.574823i
$880$		−	133.981i		−	4.51649i
$881$	−14.3019			−0.481842			−0.240921	−	0.970545i	$-0.577449\pi$
$881$	−14.3019			−0.481842			−0.240921	+	0.970545i	$0.577449\pi$
$882$	54.9599	+	5.44692i	1.85060	+	0.183407i
$883$	−25.8260			−0.869115			−0.434557	−	0.900644i	$-0.643095\pi$
$883$	−25.8260			−0.869115			−0.434557	+	0.900644i	$0.643095\pi$
$884$			12.0177i			0.404199i
$885$	0.933465	−	2.97721i	0.0313781	−	0.100078i
$886$	31.1898			1.04784
$887$	13.9430			0.468160			0.234080	−	0.972217i	$-0.424792\pi$
$887$	13.9430			0.468160			0.234080	+	0.972217i	$0.424792\pi$
$888$	−40.1980	−	12.6036i	−1.34896	−	0.422949i
$889$	−13.3452	+	22.7265i	−0.447582	+	0.762221i
$890$		−	94.1889i		−	3.15722i
$891$	43.9178	−	16.3044i	1.47130	−	0.546218i
$892$		−	66.8564i		−	2.23852i
$893$		−	9.54923i		−	0.319553i
$894$	−3.89937	+	12.4367i	−0.130414	+	0.415945i
$895$			4.04281i			0.135136i
$896$	8.87387	+	5.21081i	0.296455	+	0.174081i
$897$	3.08448	−	9.83767i	0.102988	−	0.328470i
$898$	90.5350			3.02119
$899$	−19.1378			−0.638281
$900$	14.4875	+	10.0752i	0.482918	+	0.335841i
$901$			17.9037i			0.596460i
$902$	−1.83194			−0.0609969
$903$	20.3448	+	22.4608i	0.677032	+	0.747448i
$904$	8.89413			0.295814
$905$		−	5.06335i		−	0.168312i
$906$	31.4023	+	9.84578i	1.04327	+	0.327104i
$907$	−35.4212			−1.17614			−0.588072	−	0.808809i	$-0.700113\pi$
$907$	−35.4212			−1.17614			−0.588072	+	0.808809i	$0.700113\pi$
$908$	−19.1982			−0.637116
$909$	17.4909	+	12.1639i	0.580137	+	0.403451i
$910$	−8.77057	+	14.9360i	−0.290742	+	0.495125i
$911$		−	14.6081i		−	0.483987i	−0.970278	−	0.241994i	$-0.922199\pi$
$911$		−	14.6081i		−	0.483987i	0.970278	−	0.241994i	$-0.0778013\pi$
$912$	−39.2379	−	12.3025i	−1.29930	−	0.407378i
$913$			33.2200i			1.09942i
$914$			103.442i			3.42156i
$915$	−33.8663	−	10.6184i	−1.11959	−	0.351032i
$916$			84.5274i			2.79286i
$917$	−0.647054	+	1.10192i	−0.0213676	+	0.0363885i
$918$	−20.4614	−	26.4019i	−0.675326	−	0.871394i
$919$	1.38147			0.0455704			0.0227852	−	0.999740i	$-0.492747\pi$
$919$	1.38147			0.0455704			0.0227852	+	0.999740i	$0.492747\pi$
$920$	113.658			3.74720
$921$	8.83267	+	2.76937i	0.291046	+	0.0912539i
$922$			91.7328i			3.02106i
$923$	−7.17852			−0.236284
$924$	−86.9215	+	78.7328i	−2.85951	+	2.59012i
$925$	3.79343			0.124727
$926$			43.4009i			1.42624i
$927$	−11.8641	+	17.0598i	−0.389667	+	0.560317i
$928$	33.3023			1.09320
$929$	0.336654			0.0110453			0.00552263	−	0.999985i	$-0.498242\pi$
$929$	0.336654			0.0110453			0.00552263	+	0.999985i	$0.498242\pi$
$930$	−23.1082	+	73.7014i	−0.757746	+	2.41677i
$931$	14.0354	−	7.83012i	0.459993	−	0.256622i
$932$			34.4171i			1.12737i
$933$	−14.3195	+	45.6708i	−0.468800	+	1.49520i
$934$			82.9441i			2.71401i
$935$		−	31.6703i		−	1.03573i
$936$	−18.8928	−	13.1388i	−0.617530	−	0.429455i
$937$			9.34072i			0.305148i	0.988292	+	0.152574i	$0.0487563\pi$
$937$			9.34072i			0.305148i	−0.988292	+	0.152574i	$0.951244\pi$
$938$	9.12555	+	5.35860i	0.297960	+	0.174965i
$939$	−27.7635	−	8.70488i	−0.906026	−	0.284073i
$940$	50.9028			1.66027
$941$	37.7545			1.23076			0.615380	−	0.788230i	$-0.289002\pi$
$941$	37.7545			1.23076			0.615380	+	0.788230i	$0.289002\pi$
$942$	6.94917	−	22.1638i	0.226416	−	0.722135i
$943$		−	0.796562i		−	0.0259396i
$944$	−7.48307			−0.243553
$945$	−4.38016	−	33.9401i	−0.142487	−	1.10407i
$946$	−90.5295			−2.94337
$947$			29.5311i			0.959633i	0.877369	+	0.479816i	$0.159297\pi$
$947$			29.5311i			0.959633i	−0.877369	+	0.479816i	$0.840703\pi$
$948$	−0.172015	+	0.548627i	−0.00558679	+	0.0178186i
$949$	16.4534			0.534101
$950$	7.22406			0.234380
$951$	22.2005	+	6.96069i	0.719901	+	0.225716i
$952$	42.7765	+	25.1187i	1.38639	+	0.814102i
$953$		−	31.3418i		−	1.01526i	−0.861575	−	0.507630i	$-0.830522\pi$
$953$		−	31.3418i		−	1.01526i	0.861575	−	0.507630i	$-0.169478\pi$
$954$	−47.4462	−	32.9960i	−1.53613	−	1.06829i
$955$		−	8.81081i		−	0.285111i
$956$		−	57.0069i		−	1.84373i
$957$	−7.57803	+	24.1695i	−0.244963	+	0.781288i
$958$			60.5056i			1.95485i
$959$	32.5986	+	19.1422i	1.05266	+	0.618133i
$960$	13.5350	−	43.1687i	0.436840	−	1.39326i
$961$	−15.4001			−0.496777
$962$	−8.33904			−0.268861
$963$	9.42974	−	13.5594i	0.303869	−	0.436945i
$964$			103.597i			3.33665i
$965$	−31.9097			−1.02721
$966$	−48.1604	−	53.1694i	−1.54954	−	1.71070i
$967$	20.2236			0.650347			0.325173	−	0.945654i	$-0.394577\pi$
$967$	20.2236			0.650347			0.325173	+	0.945654i	$0.394577\pi$
$968$		−	123.452i		−	3.96791i
$969$	−9.27503	−	2.90807i	−0.297957	−	0.0934207i
$970$	109.523			3.51658
$971$	7.96623			0.255649			0.127824	−	0.991797i	$-0.459201\pi$
$971$	7.96623			0.255649			0.127824	+	0.991797i	$0.459201\pi$
$972$	76.5413	−	3.95673i	2.45506	−	0.126912i
$973$	−35.8088	−	21.0272i	−1.14798	−	0.674102i
$974$		−	28.2947i		−	0.906620i
$975$	1.97726	+	0.619945i	0.0633230	+	0.0198541i
$976$			85.1214i			2.72467i
$977$			25.2368i			0.807397i	0.914892	+	0.403698i	$0.132275\pi$
$977$			25.2368i			0.807397i	−0.914892	+	0.403698i	$0.867725\pi$
$978$	57.4532	+	18.0137i	1.83715	+	0.576015i
$979$		−	74.8890i		−	2.39346i
$980$	41.7390	+	74.8168i	1.33330	+	2.38994i
$981$	−48.5265	−	33.7473i	−1.54933	−	1.07747i
$982$	−52.0115			−1.65975
$983$	−17.8377			−0.568933			−0.284466	−	0.958686i	$-0.591816\pi$
$983$	−17.8377			−0.568933			−0.284466	+	0.958686i	$0.591816\pi$
$984$	−1.69654	−	0.531928i	−0.0540837	−	0.0169573i
$985$		−	38.0573i		−	1.21261i
$986$	18.0605			0.575164
$987$	−12.7952	−	14.1260i	−0.407277	−	0.449636i
$988$	−11.2886			−0.359138
$989$		−	39.3640i		−	1.25170i
$990$	83.9287	+	58.3674i	2.66743	+	1.85504i
$991$	−29.8604			−0.948547			−0.474273	−	0.880378i	$-0.657289\pi$
$991$	−29.8604			−0.948547			−0.474273	+	0.880378i	$0.657289\pi$
$992$	80.7424			2.56357
$993$	2.83485	−	9.04151i	0.0899612	−	0.286924i
$994$	−25.2926	+	43.0727i	−0.802234	+	1.36618i
$995$		−	24.0309i		−	0.761832i
$996$	−16.2601	+	51.8603i	−0.515222	+	1.64326i
$997$		−	37.4471i		−	1.18596i	−0.805216	−	0.592981i	$-0.797951\pi$
$997$		−	37.4471i		−	1.18596i	0.805216	−	0.592981i	$-0.202049\pi$
$998$		−	67.6350i		−	2.14095i
$999$	13.0228	−	10.0926i	0.412024	−	0.319317i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.e.a.209.1	✓	32
3.2	odd	2	inner	273.2.e.a.209.32	yes	32
7.6	odd	2	inner	273.2.e.a.209.2	yes	32
21.20	even	2	inner	273.2.e.a.209.31	yes	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.e.a.209.1	✓	32	1.1	even	1	trivial
273.2.e.a.209.2	yes	32	7.6	odd	2	inner
273.2.e.a.209.31	yes	32	21.20	even	2	inner
273.2.e.a.209.32	yes	32	3.2	odd	2	inner

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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.e (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-2.62996i q^{2} +(-0.518189 + 1.65272i) q^{3} -4.91669 q^{4} +2.48925 q^{5} +(4.34658 + 1.36282i) q^{6} +(1.33971 - 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} +O(q^{10})\)	\(q-2.62996i q^{2} +(-0.518189 + 1.65272i) q^{3} -4.91669 q^{4} +2.48925 q^{5} +(4.34658 + 1.36282i) q^{6} +(1.33971 - 2.28149i) q^{7} +7.67077i q^{8} +(-2.46296 - 1.71284i) q^{9} -6.54663i q^{10} -5.20518i q^{11} +(2.54777 - 8.12590i) q^{12} -1.00000i q^{13} +(-6.00022 - 3.52338i) q^{14} +(-1.28990 + 4.11403i) q^{15} +10.3404 q^{16} +2.44427 q^{17} +(-4.50471 + 6.47748i) q^{18} +2.29598i q^{19} -12.2389 q^{20} +(3.07643 + 3.39640i) q^{21} -13.6894 q^{22} -5.95242i q^{23} +(-12.6776 - 3.97491i) q^{24} +1.19637 q^{25} -2.62996 q^{26} +(4.10713 - 3.18300i) q^{27} +(-6.58692 + 11.2174i) q^{28} +2.80952i q^{29} +(10.8197 + 3.39239i) q^{30} +6.81176i q^{31} -11.8534i q^{32} +(8.60270 + 2.69727i) q^{33} -6.42832i q^{34} +(3.33487 - 5.67919i) q^{35} +(12.1096 + 8.42151i) q^{36} +3.17079 q^{37} +6.03833 q^{38} +(1.65272 + 0.518189i) q^{39} +19.0945i q^{40} +0.133822 q^{41} +(8.93240 - 8.09090i) q^{42} +6.61311 q^{43} +25.5922i q^{44} +(-6.13092 - 4.26369i) q^{45} -15.6546 q^{46} -4.15911 q^{47} +(-5.35830 + 17.0898i) q^{48} +(-3.41036 - 6.11305i) q^{49} -3.14640i q^{50} +(-1.26659 + 4.03969i) q^{51} +4.91669i q^{52} +7.32479i q^{53} +(-8.37117 - 10.8016i) q^{54} -12.9570i q^{55} +(17.5007 + 10.2766i) q^{56} +(-3.79461 - 1.18975i) q^{57} +7.38893 q^{58} -0.723671 q^{59} +(6.34205 - 20.2274i) q^{60} +8.23191i q^{61} +17.9147 q^{62} +(-7.20747 + 3.32450i) q^{63} -10.4930 q^{64} -2.48925i q^{65} +(7.09370 - 22.6247i) q^{66} -1.52087 q^{67} -12.0177 q^{68} +(9.83767 + 3.08448i) q^{69} +(-14.9360 - 8.77057i) q^{70} -7.17852i q^{71} +(13.1388 - 18.8928i) q^{72} +16.4534i q^{73} -8.33904i q^{74} +(-0.619945 + 1.97726i) q^{75} -11.2886i q^{76} +(-11.8755 - 6.97342i) q^{77} +(1.36282 - 4.34658i) q^{78} -0.0675159 q^{79} +25.7399 q^{80} +(3.13234 + 8.43732i) q^{81} -0.351945i q^{82} -6.38210 q^{83} +(-15.1259 - 16.6990i) q^{84} +6.08439 q^{85} -17.3922i q^{86} +(-4.64335 - 1.45586i) q^{87} +39.9277 q^{88} +14.3874 q^{89} +(-11.2133 + 16.1241i) q^{90} +(-2.28149 - 1.33971i) q^{91} +29.2662i q^{92} +(-11.2579 - 3.52978i) q^{93} +10.9383i q^{94} +5.71527i q^{95} +(19.5903 + 6.14229i) q^{96} +16.7297i q^{97} +(-16.0771 + 8.96912i) q^{98} +(-8.91565 + 12.8201i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9	\( 32 q - 32 q^{4} + 4 q^{7} - 8 q^{9} - 12 q^{15} + 16 q^{16} - 20 q^{18} - 4 q^{21} - 16 q^{22} - 28 q^{28} + 16 q^{30} + 24 q^{36} + 24 q^{37} + 32 q^{43} - 24 q^{46} - 24 q^{49} - 8 q^{51} + 32 q^{57} + 24 q^{58} - 28 q^{60} + 8 q^{63} + 48 q^{64} - 32 q^{67} - 8 q^{70} + 64 q^{72} + 20 q^{78} - 32 q^{79} + 32 q^{81} - 48 q^{84} - 16 q^{85} + 64 q^{88} + 4 q^{91} - 52 q^{93} + 20 q^{99}+O(q^{100}) \) 32 * q - 32 * q^4 + 4 * q^7 - 8 * q^9 - 12 * q^15 + 16 * q^16 - 20 * q^18 - 4 * q^21 - 16 * q^22 - 28 * q^28 + 16 * q^30 + 24 * q^36 + 24 * q^37 + 32 * q^43 - 24 * q^46 - 24 * q^49 - 8 * q^51 + 32 * q^57 + 24 * q^58 - 28 * q^60 + 8 * q^63 + 48 * q^64 - 32 * q^67 - 8 * q^70 + 64 * q^72 + 20 * q^78 - 32 * q^79 + 32 * q^81 - 48 * q^84 - 16 * q^85 + 64 * q^88 + 4 * q^91 - 52 * q^93 + 20 * q^99

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