LMFDB - Embedded newform 273.2.r.b.68.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [273,2,Mod(68,273)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(273, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5, 2]))

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

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

chi := DirichletCharacter("273.68");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 273 = 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	273.r (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.17991597518$
Analytic rank:	$0$
Dimension:	$64$
Relative dimension:	$32$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			68.3
Character	$\chi$	$=$	273.68
Dual form			273.2.r.b.269.30

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q-2.39671i q^{2} +(1.60287 + 0.656371i) q^{3} -3.74420 q^{4} +(1.10064 - 1.90637i) q^{5} +(1.57313 - 3.84160i) q^{6} +(-1.62460 - 2.08822i) q^{7} +4.18035i q^{8} +(2.13835 + 2.10415i) q^{9} +(-4.56901 - 2.63792i) q^{10} +(1.30172 + 0.751546i) q^{11} +(-6.00145 - 2.45759i) q^{12} +(3.47069 + 0.976871i) q^{13} +(-5.00485 + 3.89370i) q^{14} +(3.01547 - 2.33322i) q^{15} +2.53065 q^{16} -4.90720 q^{17} +(5.04303 - 5.12501i) q^{18} +(-2.77060 + 1.59960i) q^{19} +(-4.12104 + 7.13784i) q^{20} +(-1.23337 - 4.41348i) q^{21} +(1.80123 - 3.11983i) q^{22} -4.94443i q^{23} +(-2.74386 + 6.70053i) q^{24} +(0.0771661 + 0.133656i) q^{25} +(2.34127 - 8.31824i) q^{26} +(2.04639 + 4.77622i) q^{27} +(6.08284 + 7.81872i) q^{28} +(-0.775914 + 0.447974i) q^{29} +(-5.59206 - 7.22720i) q^{30} +(2.33226 - 1.34653i) q^{31} +2.29545i q^{32} +(1.59318 + 2.05904i) q^{33} +11.7611i q^{34} +(-5.76903 + 0.798709i) q^{35} +(-8.00643 - 7.87837i) q^{36} +10.0463 q^{37} +(3.83378 + 6.64031i) q^{38} +(4.92187 + 3.84386i) q^{39} +(7.96929 + 4.60107i) q^{40} +(4.98596 + 8.63593i) q^{41} +(-10.5778 + 2.95603i) q^{42} +(-0.820714 + 1.42152i) q^{43} +(-4.87389 - 2.81394i) q^{44} +(6.36486 - 1.76057i) q^{45} -11.8504 q^{46} +(-0.165217 + 0.286164i) q^{47} +(4.05630 + 1.66105i) q^{48} +(-1.72133 + 6.78506i) q^{49} +(0.320334 - 0.184945i) q^{50} +(-7.86558 - 3.22095i) q^{51} +(-12.9950 - 3.65760i) q^{52} +(-5.36111 + 3.09524i) q^{53} +(11.4472 - 4.90459i) q^{54} +(2.86545 - 1.65437i) q^{55} +(8.72948 - 6.79140i) q^{56} +(-5.49083 + 0.745410i) q^{57} +(1.07366 + 1.85964i) q^{58} +13.8477 q^{59} +(-11.2905 + 8.73607i) q^{60} +(2.44902 - 1.41394i) q^{61} +(-3.22724 - 5.58975i) q^{62} +(0.919954 - 7.88376i) q^{63} +10.5628 q^{64} +(5.68228 - 5.54125i) q^{65} +(4.93490 - 3.81839i) q^{66} +(3.46728 - 6.00551i) q^{67} +18.3736 q^{68} +(3.24539 - 7.92526i) q^{69} +(1.91427 + 13.8267i) q^{70} +(-13.9370 - 8.04655i) q^{71} +(-8.79607 + 8.93905i) q^{72} +(-2.87045 + 1.65726i) q^{73} -24.0780i q^{74} +(0.0359591 + 0.264882i) q^{75} +(10.3737 - 5.98924i) q^{76} +(-0.545377 - 3.93923i) q^{77} +(9.21260 - 11.7963i) q^{78} +(-3.02508 + 5.23959i) q^{79} +(2.78535 - 4.82437i) q^{80} +(0.145107 + 8.99883i) q^{81} +(20.6978 - 11.9499i) q^{82} +2.74309 q^{83} +(4.61799 + 16.5250i) q^{84} +(-5.40108 + 9.35495i) q^{85} +(3.40696 + 1.96701i) q^{86} +(-1.53772 + 0.208754i) q^{87} +(-3.14172 + 5.44162i) q^{88} -12.6297 q^{89} +(-4.21958 - 15.2547i) q^{90} +(-3.59858 - 8.83460i) q^{91} +18.5130i q^{92} +(4.62213 - 0.627479i) q^{93} +(0.685851 + 0.395976i) q^{94} +7.04238i q^{95} +(-1.50667 + 3.67930i) q^{96} +(-11.5690 - 6.67939i) q^{97} +(16.2618 + 4.12552i) q^{98} +(1.20216 + 4.34607i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) $ 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

Character values

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

$n$	$92$	$106$	$157$
$\chi(n)$	$-1$	$e\left(\frac{1}{3}\right)$	$e\left(\frac{5}{6}\right)$

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 $

$2$		−	2.39671i		−	1.69473i	−0.531013	−	0.847364i	$-0.678188\pi$
$2$		−	2.39671i		−	1.69473i	0.531013	−	0.847364i	$-0.321812\pi$
$3$	1.60287	+	0.656371i	0.925415	+	0.378956i
$3$	1.60287	+	0.656371i	0.925415	+	0.378956i
$4$	−3.74420			−1.87210
$5$	1.10064	−	1.90637i	0.492223	−	0.852555i	−0.507737	−	0.861512i	$-0.669518\pi$
$5$	1.10064	−	1.90637i	0.492223	−	0.852555i	0.999960	+	0.00895706i	$0.00285116\pi$
$6$	1.57313	−	3.84160i	0.642228	−	1.56833i
$7$	−1.62460	−	2.08822i	−0.614042	−	0.789273i
$7$	−1.62460	−	2.08822i	−0.614042	−	0.789273i
$8$			4.18035i			1.47798i
$9$	2.13835	+	2.10415i	0.712784	+	0.701383i
$10$	−4.56901	−	2.63792i	−1.44485	−	0.834184i
$11$	1.30172	+	0.751546i	0.392482	+	0.226600i	0.683235	−	0.730199i	$-0.260572\pi$
$11$	1.30172	+	0.751546i	0.392482	+	0.226600i	−0.290753	+	0.956798i	$0.593906\pi$
$12$	−6.00145	−	2.45759i	−1.73247	−	0.709445i
$13$	3.47069	+	0.976871i	0.962598	+	0.270935i
$13$	3.47069	+	0.976871i	0.962598	+	0.270935i
$14$	−5.00485	+	3.89370i	−1.33760	+	1.04063i
$15$	3.01547	−	2.33322i	0.778591	−	0.602436i
$16$	2.53065			0.632664
$17$	−4.90720			−1.19017			−0.595085	−	0.803662i	$-0.702882\pi$
$17$	−4.90720			−1.19017			−0.595085	+	0.803662i	$0.702882\pi$
$18$	5.04303	−	5.12501i	1.18865	−	1.20798i
$19$	−2.77060	+	1.59960i	−0.635618	+	0.366974i	−0.782925	−	0.622117i	$-0.786273\pi$
$19$	−2.77060	+	1.59960i	−0.635618	+	0.366974i	0.147306	+	0.989091i	$0.452940\pi$
$20$	−4.12104	+	7.13784i	−0.921491	+	1.59607i
$21$	−1.23337	−	4.41348i	−0.269144	−	0.963100i
$22$	1.80123	−	3.11983i	0.384025	−	0.665150i
$23$		−	4.94443i		−	1.03099i	−0.856894	−	0.515493i	$-0.827609\pi$
$23$		−	4.94443i		−	1.03099i	0.856894	−	0.515493i	$-0.172391\pi$
$24$	−2.74386	+	6.70053i	−0.560088	+	1.36774i
$25$	0.0771661	+	0.133656i	0.0154332	+	0.0267311i
$26$	2.34127	−	8.31824i	0.459161	−	1.63134i
$27$	2.04639	+	4.77622i	0.393827	+	0.919184i
$28$	6.08284	+	7.81872i	1.14955	+	1.47760i
$29$	−0.775914	+	0.447974i	−0.144084	+	0.0831867i	−0.570309	−	0.821430i	$-0.693176\pi$
$29$	−0.775914	+	0.447974i	−0.144084	+	0.0831867i	0.426225	+	0.904617i	$0.359843\pi$
$30$	−5.59206	−	7.22720i	−1.02096	−	1.31950i
$31$	2.33226	−	1.34653i	0.418886	−	0.241844i	−0.275714	−	0.961240i	$-0.588914\pi$
$31$	2.33226	−	1.34653i	0.418886	−	0.241844i	0.694601	+	0.719395i	$0.255581\pi$
$32$			2.29545i			0.405783i
$33$	1.59318	+	2.05904i	0.277337	+	0.358432i
$34$			11.7611i			2.01702i
$35$	−5.76903	+	0.798709i	−0.975145	+	0.135006i
$36$	−8.00643	−	7.87837i	−1.33440	−	1.31306i
$37$	10.0463			1.65160			0.825800	−	0.563964i	$-0.190724\pi$
$37$	10.0463			1.65160			0.825800	+	0.563964i	$0.190724\pi$
$38$	3.83378	+	6.64031i	0.621922	+	1.07720i
$39$	4.92187	+	3.84386i	0.788129	+	0.615510i
$40$	7.96929	+	4.60107i	1.26006	+	0.727493i
$41$	4.98596	+	8.63593i	0.778676	+	1.34871i	0.932705	+	0.360639i	$0.117441\pi$
$41$	4.98596	+	8.63593i	0.778676	+	1.34871i	−0.154030	+	0.988066i	$0.549225\pi$
$42$	−10.5778	+	2.95603i	−1.63219	+	0.456125i
$43$	−0.820714	+	1.42152i	−0.125158	+	0.216780i	−0.921795	−	0.387679i	$-0.873277\pi$
$43$	−0.820714	+	1.42152i	−0.125158	+	0.216780i	0.796637	+	0.604458i	$0.206610\pi$
$44$	−4.87389	−	2.81394i	−0.734766	−	0.424217i
$45$	6.36486	−	1.76057i	0.948817	−	0.262451i
$46$	−11.8504			−1.74724
$47$	−0.165217	+	0.286164i	−0.0240993	+	0.0417413i	−0.877824	−	0.478984i	$-0.841005\pi$
$47$	−0.165217	+	0.286164i	−0.0240993	+	0.0417413i	0.853724	+	0.520725i	$0.174338\pi$
$48$	4.05630	+	1.66105i	0.585476	+	0.239752i
$49$	−1.72133	+	6.78506i	−0.245904	+	0.969294i
$50$	0.320334	−	0.184945i	0.0453020	−	0.0261551i
$51$	−7.86558	−	3.22095i	−1.10140	−	0.451023i
$52$	−12.9950	−	3.65760i	−1.80208	−	0.507218i
$53$	−5.36111	+	3.09524i	−0.736404	+	0.425163i	−0.820761	−	0.571272i	$-0.806450\pi$
$53$	−5.36111	+	3.09524i	−0.736404	+	0.425163i	0.0843561	+	0.996436i	$0.473117\pi$
$54$	11.4472	−	4.90459i	1.55777	−	0.667430i
$55$	2.86545	−	1.65437i	0.386377	−	0.223075i
$56$	8.72948	−	6.79140i	1.16653	−	0.907539i
$57$	−5.49083	+	0.745410i	−0.727278	+	0.0987319i
$58$	1.07366	+	1.85964i	0.140979	+	0.244182i
$59$	13.8477			1.80282			0.901410	−	0.432966i	$-0.142533\pi$
$59$	13.8477			1.80282			0.901410	+	0.432966i	$0.142533\pi$
$60$	−11.2905	+	8.73607i	−1.45760	+	1.12782i
$61$	2.44902	−	1.41394i	0.313565	−	0.181037i	−0.334956	−	0.942234i	$-0.608721\pi$
$61$	2.44902	−	1.41394i	0.313565	−	0.181037i	0.648521	+	0.761197i	$0.275388\pi$
$62$	−3.22724	−	5.58975i	−0.409860	−	0.709899i
$63$	0.919954	−	7.88376i	0.115903	−	0.993260i
$64$	10.5628			1.32035
$65$	5.68228	−	5.54125i	0.704800	−	0.687307i
$66$	4.93490	−	3.81839i	0.607445	−	0.470011i
$67$	3.46728	−	6.00551i	0.423596	−	0.733690i	−0.572692	−	0.819771i	$-0.694101\pi$
$67$	3.46728	−	6.00551i	0.423596	−	0.733690i	0.996288	+	0.0860807i	$0.0274343\pi$
$68$	18.3736			2.22812
$69$	3.24539	−	7.92526i	0.390698	−	0.954089i
$70$	1.91427	+	13.8267i	0.228799	+	1.65260i
$71$	−13.9370	−	8.04655i	−1.65402	−	0.954950i	−0.975394	−	0.220469i	$-0.929241\pi$
$71$	−13.9370	−	8.04655i	−1.65402	−	0.954950i	−0.678628	−	0.734482i	$-0.737425\pi$
$72$	−8.79607	+	8.93905i	−1.03663	+	1.05348i
$73$	−2.87045	+	1.65726i	−0.335961	+	0.193967i	−0.658485	−	0.752594i	$-0.728802\pi$
$73$	−2.87045	+	1.65726i	−0.335961	+	0.193967i	0.322524	+	0.946561i	$0.395469\pi$
$74$		−	24.0780i		−	2.79901i
$75$	0.0359591	+	0.264882i	0.00415220	+	0.0305859i
$76$	10.3737	−	5.98924i	1.18994	−	0.687014i
$77$	−0.545377	−	3.93923i	−0.0621515	−	0.448917i
$78$	9.21260	−	11.7963i	1.04312	−	1.33566i
$79$	−3.02508	+	5.23959i	−0.340348	+	0.589500i	−0.984497	−	0.175400i	$-0.943878\pi$
$79$	−3.02508	+	5.23959i	−0.340348	+	0.589500i	0.644149	+	0.764900i	$0.277211\pi$
$80$	2.78535	−	4.82437i	0.311412	−	0.539381i
$81$	0.145107	+	8.99883i	0.0161230	+	0.999870i
$82$	20.6978	−	11.9499i	2.28569	−	1.31964i
$83$	2.74309			0.301094			0.150547	−	0.988603i	$-0.451897\pi$
$83$	2.74309			0.301094			0.150547	+	0.988603i	$0.451897\pi$
$84$	4.61799	+	16.5250i	0.503864	+	1.80302i
$85$	−5.40108	+	9.35495i	−0.585829	+	1.01469i
$86$	3.40696	+	1.96701i	0.367382	+	0.212108i
$87$	−1.53772	+	0.208754i	−0.164861	+	0.0223808i
$88$	−3.14172	+	5.44162i	−0.334909	+	0.580079i
$89$	−12.6297			−1.33874			−0.669372	−	0.742928i	$-0.733437\pi$
$89$	−12.6297			−1.33874			−0.669372	+	0.742928i	$0.733437\pi$
$90$	−4.21958	−	15.2547i	−0.444783	−	1.60799i
$91$	−3.59858	−	8.83460i	−0.377234	−	0.926118i
$92$			18.5130i			1.93011i
$93$	4.62213	−	0.627479i	0.479292	−	0.0650665i
$94$	0.685851	+	0.395976i	0.0707401	+	0.0408418i
$95$			7.04238i			0.722533i
$96$	−1.50667	+	3.67930i	−0.153774	+	0.375517i
$97$	−11.5690	−	6.67939i	−1.17466	−	0.678190i	−0.219886	−	0.975526i	$-0.570568\pi$
$97$	−11.5690	−	6.67939i	−1.17466	−	0.678190i	−0.954773	+	0.297336i	$0.903902\pi$
$98$	16.2618	+	4.12552i	1.64269	+	0.416741i
$99$	1.20216	+	4.34607i	0.120822	+	0.436797i
$100$	−0.288926	−	0.500434i	−0.0288926	−	0.0500434i
$101$	−8.75688	+	15.1674i	−0.871342	+	1.50921i	−0.0107340	+	0.999942i	$0.503417\pi$
$101$	−8.75688	+	15.1674i	−0.871342	+	1.50921i	−0.860609	+	0.509267i	$0.829917\pi$
$102$	−7.71966	+	18.8515i	−0.764361	+	1.86658i
$103$	2.76437	+	1.59601i	0.272381	+	0.157259i	0.629969	−	0.776620i	$-0.283067\pi$
$103$	2.76437	+	1.59601i	0.272381	+	0.157259i	−0.357588	+	0.933879i	$0.616401\pi$
$104$	−4.08366	+	14.5087i	−0.400436	+	1.42270i
$105$	−9.77123	−	2.50641i	−0.953574	−	0.244600i
$106$	7.41837	+	12.8490i	0.720536	+	1.24801i
$107$			2.05885i			0.199036i	0.995036	+	0.0995181i	$0.0317301\pi$
$107$			2.05885i			0.199036i	−0.995036	+	0.0995181i	$0.968270\pi$
$108$	−7.66209	−	17.8831i	−0.737285	−	1.72081i
$109$	2.54162	+	4.40221i	0.243443	+	0.421656i	0.961693	−	0.274130i	$-0.0883898\pi$
$109$	2.54162	+	4.40221i	0.243443	+	0.421656i	−0.718250	+	0.695785i	$0.755056\pi$
$110$	−3.96504	−	6.86764i	−0.378051	−	0.654804i
$111$	16.1028	+	6.59410i	1.52841	+	0.625884i
$112$	−4.11131	−	5.28457i	−0.388482	−	0.499345i
$113$	−3.72227	−	2.14905i	−0.350161	−	0.202166i	0.314595	−	0.949226i	$-0.398131\pi$
$113$	−3.72227	−	2.14905i	−0.350161	−	0.202166i	−0.664756	+	0.747060i	$0.731465\pi$
$114$	1.78653	+	13.1599i	0.167324	+	1.23254i
$115$	−9.42593	−	5.44206i	−0.878972	−	0.507475i
$116$	2.90518	−	1.67731i	0.269739	−	0.155734i
$117$	5.36609	+	9.39176i	0.496095	+	0.868268i
$118$		−	33.1889i		−	3.05529i
$119$	7.97225	+	10.2473i	0.730815	+	0.939370i
$120$	9.75368	+	12.6057i	0.890385	+	1.15074i
$121$	−4.37036	−	7.56968i	−0.397305	−	0.688153i
$122$	−3.38881	−	5.86959i	−0.306808	−	0.531408i
$123$	2.32344	+	17.1149i	0.209497	+	1.54320i
$124$	−8.73246	+	5.04169i	−0.784198	+	0.452757i
$125$	11.3462			1.01483
$126$	−18.8951	−	2.20486i	−1.68331	−	0.196425i
$127$	−8.84285	−	15.3163i	−0.784676	−	1.35910i	−0.929192	−	0.369596i	$-0.879496\pi$
$127$	−8.84285	−	15.3163i	−0.784676	−	1.35910i	0.144516	−	0.989502i	$-0.453837\pi$
$128$		−	20.7251i		−	1.83186i
$129$	−2.24854	+	1.73981i	−0.197973	+	0.153182i
$130$	−13.2807	−	13.6188i	−1.16480	−	1.19444i
$131$	−6.22200	+	10.7768i	−0.543619	+	0.941576i	0.455073	+	0.890454i	$0.349613\pi$
$131$	−6.22200	+	10.7768i	−0.543619	+	0.941576i	−0.998692	+	0.0511218i	$0.983720\pi$
$132$	−5.96519	−	7.70945i	−0.519204	−	0.671021i
$133$	7.84145	+	3.18689i	0.679940	+	0.276339i
$134$	−14.3934	−	8.31006i	−1.24340	−	0.717880i
$135$	11.3576	+	1.35575i	0.977506	+	0.116684i
$136$		−	20.5138i		−	1.75904i
$137$		−	9.44464i		−	0.806910i	−0.914999	−	0.403455i	$-0.867809\pi$
$137$		−	9.44464i		−	0.806910i	0.914999	−	0.403455i	$-0.132191\pi$
$138$	−18.9945	−	7.77824i	−1.61692	−	0.662128i
$139$	−3.90386	−	2.25389i	−0.331121	−	0.191173i	0.325218	−	0.945639i	$-0.394562\pi$
$139$	−3.90386	−	2.25389i	−0.331121	−	0.191173i	−0.656339	+	0.754466i	$0.727896\pi$
$140$	21.6004	−	2.99053i	1.82557	−	0.252746i
$141$	−0.452650	+	0.350238i	−0.0381200	+	0.0294954i
$142$	−19.2852	+	33.4030i	−1.61838	+	2.80312i
$143$	3.78369	+	3.87999i	0.316408	+	0.324461i
$144$	5.41143	+	5.32488i	0.450953	+	0.443740i
$145$			1.97224i			0.163786i
$146$	3.97196	+	6.87963i	0.328722	+	0.569362i
$147$	−7.21258	+	9.74570i	−0.594884	+	0.803812i
$148$	−37.6153			−3.09196
$149$	−16.3166	+	9.42041i	−1.33671	+	0.771750i	−0.986318	−	0.164853i	$-0.947285\pi$
$149$	−16.3166	+	9.42041i	−1.33671	+	0.771750i	−0.350392	+	0.936603i	$0.613952\pi$
$150$	0.634844	−	0.0861835i	0.0518348	−	0.00703686i
$151$	−4.12058	−	7.13706i	−0.335328	−	0.580805i	0.648220	−	0.761453i	$-0.275514\pi$
$151$	−4.12058	−	7.13706i	−0.335328	−	0.580805i	−0.983548	+	0.180648i	$0.942181\pi$
$152$	−6.68690	−	11.5820i	−0.542379	−	0.939428i
$153$	−10.4933	−	10.3255i	−0.848335	−	0.834766i
$154$	−9.44119	+	1.30711i	−0.760792	+	0.105330i
$155$		−	5.92821i		−	0.476165i
$156$	−18.4285	−	14.3922i	−1.47546	−	1.15230i
$157$	12.0751	−	6.97157i	0.963699	−	0.556392i	0.0663895	−	0.997794i	$-0.478852\pi$
$157$	12.0751	−	6.97157i	0.963699	−	0.556392i	0.897310	+	0.441402i	$0.145519\pi$
$158$	12.5578	+	7.25023i	0.999042	+	0.576797i
$159$	−10.6248	+	1.44237i	−0.842598	+	0.114387i
$160$	4.37599	+	2.52648i	0.345952	+	0.199735i
$161$	−10.3251	+	8.03274i	−0.813729	+	0.633069i
$162$	21.5676	−	0.347780i	1.69451	−	0.0273242i
$163$	−5.61643	−	9.72795i	−0.439913	−	0.761952i	0.557769	−	0.829996i	$-0.311657\pi$
$163$	−5.61643	−	9.72795i	−0.439913	−	0.761952i	−0.997682	+	0.0680444i	$0.978324\pi$
$164$	−18.6684	−	32.3347i	−1.45776	−	2.52491i
$165$	5.67881	−	0.770930i	0.442095	−	0.0600168i
$166$		−	6.57439i		−	0.510272i
$167$	−2.80640	−	4.86082i	−0.217165	−	0.376142i	0.736775	−	0.676138i	$-0.236348\pi$
$167$	−2.80640	−	4.86082i	−0.217165	−	0.376142i	−0.953940	+	0.299997i	$0.903014\pi$
$168$	18.4499	−	5.15592i	1.42344	−	0.397788i
$169$	11.0914	+	6.78084i	0.853188	+	0.521603i
$170$	22.4211	+	12.9448i	1.71962	+	0.992821i
$171$	−9.29032	−	2.40923i	−0.710449	−	0.184238i
$172$	3.07292	−	5.32246i	0.234308	−	0.405834i
$173$	11.9534	+	20.7038i	0.908797	+	1.57408i	0.815738	+	0.578422i	$0.196331\pi$
$173$	11.9534	+	20.7038i	0.908797	+	1.57408i	0.0930589	+	0.995661i	$0.470336\pi$
$174$	0.500323	+	3.68547i	0.0379294	+	0.279395i
$175$	0.153738	−	0.378277i	0.0116215	−	0.0285951i
$176$	3.29419	+	1.90190i	0.248309	+	0.143361i
$177$	22.1960	+	9.08925i	1.66836	+	0.683190i
$178$			30.2696i			2.26881i
$179$	−16.9456	−	9.78353i	−1.26657	−	0.731255i	−0.292233	−	0.956347i	$-0.594398\pi$
$179$	−16.9456	−	9.78353i	−1.26657	−	0.731255i	−0.974338	+	0.225092i	$0.927732\pi$
$180$	−23.8313	+	6.59195i	−1.77628	+	0.491335i
$181$		−	1.52824i		−	0.113593i	−0.998386	−	0.0567967i	$-0.981911\pi$
$181$		−	1.52824i		−	0.113593i	0.998386	−	0.0567967i	$-0.0180887\pi$
$182$	−21.1740	+	8.62474i	−1.56952	+	0.639308i
$183$	4.85352	−	0.658893i	0.358783	−	0.0487067i
$184$	20.6694			1.52377
$185$	11.0574	−	19.1519i	0.812955	−	1.40808i
$186$	−1.50388	−	11.0779i	−0.110270	−	0.812270i
$187$	−6.38778	−	3.68799i	−0.467121	−	0.269692i
$188$	0.618605	−	1.07146i	0.0451164	−	0.0781439i
$189$	6.64924	−	12.0328i	0.483661	−	0.875255i
$190$	16.8785			1.22450
$191$	5.34689	−	3.08703i	0.386887	−	0.223370i	−0.293923	−	0.955829i	$-0.594961\pi$
$191$	5.34689	−	3.08703i	0.386887	−	0.223370i	0.680811	+	0.732459i	$0.261628\pi$
$192$	16.9308	+	6.93315i	1.22188	+	0.500357i
$193$	−5.22852	+	9.05607i	−0.376357	+	0.651870i	−0.990529	−	0.137302i	$-0.956157\pi$
$193$	−5.22852	+	9.05607i	−0.376357	+	0.651870i	0.614172	+	0.789172i	$0.289490\pi$
$194$	−16.0085	+	27.7276i	−1.14935	+	1.99073i
$195$	12.7450	−	5.15218i	0.912691	−	0.368956i
$196$	6.44501	−	25.4046i	0.460358	−	1.81462i
$197$	4.00557	−	2.31262i	0.285385	−	0.164767i	−0.350474	−	0.936573i	$-0.613979\pi$
$197$	4.00557	−	2.31262i	0.285385	−	0.164767i	0.635859	+	0.771805i	$0.280646\pi$
$198$	10.4163	−	2.88123i	0.740252	−	0.204760i
$199$			8.76573i			0.621386i	0.950510	+	0.310693i	$0.100561\pi$
$199$			8.76573i			0.621386i	−0.950510	+	0.310693i	$0.899439\pi$
$200$	−0.558727	+	0.322581i	−0.0395080	+	0.0228099i
$201$	9.49943	−	7.35020i	0.670038	−	0.518443i
$202$	36.3517	+	20.9877i	2.55770	+	1.47669i
$203$	2.19602	+	0.892499i	0.154130	+	0.0626412i
$204$	29.4503	+	12.0599i	2.06194	+	0.844360i
$205$	21.9510			1.53313
$206$	3.82517	−	6.62538i	0.266512	−	0.461612i
$207$	10.4038	−	10.5729i	0.723116	−	0.734871i
$208$	8.78313	+	2.47212i	0.609001	+	0.171411i
$209$	−4.80870			−0.332625
$210$	−6.00712	+	23.4188i	−0.414531	+	1.61605i
$211$	0.494306	+	0.856163i	0.0340294	+	0.0589407i	0.882539	−	0.470240i	$-0.155833\pi$
$211$	0.494306	+	0.856163i	0.0340294	+	0.0589407i	−0.848509	+	0.529181i	$0.822499\pi$
$212$	20.0731	−	11.5892i	1.37862	−	0.795949i
$213$	−17.0577	−	22.0454i	−1.16877	−	1.51053i
$214$	4.93445			0.337312
$215$	1.80663	+	3.12917i	0.123211	+	0.213408i
$216$	−19.9663	+	8.55461i	−1.35853	+	0.582067i
$217$	−6.60085	−	2.68270i	−0.448095	−	0.182113i
$218$	10.5508	−	6.09152i	0.714591	−	0.412570i
$219$	−5.68872	+	0.772275i	−0.384408	+	0.0521855i
$220$	−10.7288	+	6.19429i	−0.723338	+	0.417619i
$221$	−17.0314	−	4.79370i	−1.14566	−	0.322459i
$222$	15.8041	−	38.5938i	1.06070	−	2.59025i
$223$	−18.4022	+	10.6245i	−1.23230	+	0.711471i	−0.967510	−	0.252833i	$-0.918638\pi$
$223$	−18.4022	+	10.6245i	−1.23230	+	0.711471i	−0.264795	+	0.964305i	$0.585304\pi$
$224$	4.79341	−	3.72920i	0.320273	−	0.249168i
$225$	−0.116223	+	0.448172i	−0.00774821	+	0.0298781i
$226$	−5.15065	+	8.92118i	−0.342616	+	0.593428i
$227$	3.98583			0.264549			0.132274	−	0.991213i	$-0.457772\pi$
$227$	3.98583			0.264549			0.132274	+	0.991213i	$0.457772\pi$
$228$	20.5588	−	2.79097i	1.36154	−	0.184836i
$229$	1.31206	+	0.757520i	0.0867036	+	0.0500583i	0.542725	−	0.839910i	$-0.317393\pi$
$229$	1.31206	+	0.757520i	0.0867036	+	0.0500583i	−0.456021	+	0.889969i	$0.650726\pi$
$230$	−13.0430	+	22.5912i	−0.860032	+	1.48962i
$231$	1.71143	−	6.67203i	0.112604	−	0.438987i
$232$	−1.87269	−	3.24359i	−0.122948	−	0.212952i
$233$	5.86812	+	3.38796i	0.384433	+	0.221953i	0.679745	−	0.733448i	$-0.262090\pi$
$233$	5.86812	+	3.38796i	0.384433	+	0.221953i	−0.295312	+	0.955401i	$0.595424\pi$
$234$	22.5093	−	12.8609i	1.47148	−	0.840746i
$235$	0.363690	+	0.629929i	0.0237245	+	0.0410920i
$236$	−51.8487			−3.37506
$237$	−8.28791	+	6.41278i	−0.538357	+	0.416555i
$238$	24.5598	−	19.1072i	1.59198	−	1.23853i
$239$		−	15.4434i		−	0.998954i	−0.866327	−	0.499477i	$-0.833526\pi$
$239$		−	15.4434i		−	0.998954i	0.866327	−	0.499477i	$-0.166474\pi$
$240$	7.63112	−	5.90459i	0.492586	−	0.381139i
$241$		−	7.03908i		−	0.453427i	−0.973962	−	0.226713i	$-0.927202\pi$
$241$		−	7.03908i		−	0.453427i	0.973962	−	0.226713i	$-0.0727981\pi$
$242$	−18.1423	+	10.4745i	−1.16623	+	0.673324i
$243$	−5.67399	+	14.5192i	−0.363986	+	0.931404i
$244$	−9.16964	+	5.29409i	−0.587026	+	0.338920i
$245$	11.0403	+	10.7494i	0.705337	+	0.686756i
$246$	41.0193	−	5.56860i	2.61530	−	0.355041i
$247$	−11.1785	+	2.84522i	−0.711271	+	0.181037i
$248$	5.62897	+	9.74966i	0.357440	+	0.619104i
$249$	4.39681	+	1.80049i	0.278637	+	0.114101i
$250$		−	27.1934i		−	1.71986i
$251$	−1.69284	+	2.93209i	−0.106851	+	0.185072i	−0.914493	−	0.404602i	$-0.867410\pi$
$251$	−1.69284	+	2.93209i	−0.106851	+	0.185072i	0.807642	+	0.589673i	$0.200744\pi$
$252$	−3.44450	+	29.5184i	−0.216983	+	1.85948i
$253$	3.71597	−	6.43625i	0.233621	−	0.404643i
$254$	−36.7086	+	21.1937i	−2.30330	+	1.32981i
$255$	−14.7975	+	11.4496i	−0.926657	+	0.717002i
$256$	−28.5464			−1.78415
$257$	20.6197			1.28622			0.643112	−	0.765772i	$-0.277643\pi$
$257$	20.6197			1.28622			0.643112	+	0.765772i	$0.277643\pi$
$258$	4.16981	+	5.38909i	0.259601	+	0.335510i
$259$	−16.3212	−	20.9789i	−1.01415	−	1.30356i
$260$	−21.2756	+	20.7476i	−1.31946	+	1.28671i
$261$	−2.60178	−	0.674712i	−0.161046	−	0.0417636i
$262$	25.8289	+	14.9123i	1.59571	+	0.921286i
$263$	−4.80598	−	2.77473i	−0.296349	−	0.171097i	0.344452	−	0.938804i	$-0.388065\pi$
$263$	−4.80598	−	2.77473i	−0.296349	−	0.171097i	−0.640802	+	0.767706i	$0.721398\pi$
$264$	−8.60748	+	6.66005i	−0.529754	+	0.409898i
$265$			13.6270i			0.837100i
$266$	7.63805	−	18.7936i	0.468319	−	1.15231i
$267$	−20.2437	−	8.28976i	−1.23889	−	0.507325i
$268$	−12.9822	+	22.4859i	−0.793015	+	1.37354i
$269$	9.16772			0.558966			0.279483	−	0.960151i	$-0.409837\pi$
$269$	9.16772			0.558966			0.279483	+	0.960151i	$0.409837\pi$
$270$	3.24932	−	27.2208i	0.197748	−	1.65661i
$271$			6.82441i			0.414553i	0.978282	+	0.207277i	$0.0664600\pi$
$271$			6.82441i			0.414553i	−0.978282	+	0.207277i	$0.933540\pi$
$272$	−12.4184			−0.752978
$273$	0.0307453	−	16.5227i	0.00186079	−	0.999998i
$274$	−22.6360			−1.36749
$275$			0.231976i			0.0139887i
$276$	−12.1514	+	29.6738i	−0.731427	+	1.78615i
$277$	−2.96712			−0.178277			−0.0891385	−	0.996019i	$-0.528411\pi$
$277$	−2.96712			−0.178277			−0.0891385	+	0.996019i	$0.528411\pi$
$278$	−5.40192	+	9.35640i	−0.323986	+	0.561160i
$279$	7.82050	+	2.02807i	0.468201	+	0.121417i
$280$	−3.33888	−	24.1165i	−0.199536	−	1.44124i
$281$		−	25.9693i		−	1.54920i	−0.632454	−	0.774598i	$-0.717952\pi$
$281$		−	25.9693i		−	1.54920i	0.632454	−	0.774598i	$-0.282048\pi$
$282$	0.839419	+	1.08487i	0.0499867	+	0.0646030i
$283$	−9.43593	−	5.44784i	−0.560908	−	0.323840i	0.192602	−	0.981277i	$-0.438307\pi$
$283$	−9.43593	−	5.44784i	−0.560908	−	0.323840i	−0.753510	+	0.657437i	$0.771641\pi$
$284$	52.1831	+	30.1279i	3.09650	+	1.78776i
$285$	−4.62242	+	11.2880i	−0.273808	+	0.668642i
$286$	9.29921	−	9.06840i	0.549874	−	0.536226i
$287$	9.93353	−	24.4417i	0.586358	−	1.44275i
$288$	−4.82998	+	4.90849i	−0.284609	+	0.289235i
$289$	7.08062			0.416507
$290$	4.72688			0.277572
$291$	−14.1595	−	18.2998i	−0.830042	−	1.07275i
$292$	10.7476	−	6.20511i	0.628953	−	0.363126i
$293$	5.70408	−	9.87975i	0.333236	−	0.577181i	−0.649909	−	0.760012i	$-0.725193\pi$
$293$	5.70408	−	9.87975i	0.333236	−	0.577181i	0.983144	+	0.182831i	$0.0585262\pi$
$294$	23.3576	+	17.2864i	1.36224	+	1.00817i
$295$	15.2414	−	26.3989i	0.887390	−	1.53700i
$296$			41.9969i			2.44102i
$297$	−0.925735	+	7.75524i	−0.0537166	+	0.450004i
$298$	22.5780	+	39.1062i	1.30791	+	2.26536i
$299$	4.83007	−	17.1606i	0.279330	−	0.992424i
$300$	−0.134638	−	0.991771i	−0.00777335	−	0.0572599i
$301$	4.30178	−	0.595571i	0.247951	−	0.0343282i
$302$	−17.1054	+	9.87583i	−0.984307	+	0.568290i
$303$	−23.9915	+	18.5635i	−1.37828	+	1.06644i
$304$	−7.01142	+	4.04805i	−0.402133	+	0.232171i
$305$		−	6.22499i		−	0.356442i
$306$	−24.7472	+	25.1494i	−1.41470	+	1.43770i
$307$			1.16158i			0.0662951i	0.999450	+	0.0331476i	$0.0105531\pi$
$307$			1.16158i			0.0662951i	−0.999450	+	0.0331476i	$0.989447\pi$
$308$	2.04200	+	14.7493i	0.116354	+	0.840419i
$309$	3.38334	+	4.37264i	0.192471	+	0.248751i
$310$	−14.2082			−0.806970
$311$	3.49022	+	6.04524i	0.197912	+	0.342794i	0.947851	−	0.318713i	$-0.103251\pi$
$311$	3.49022	+	6.04524i	0.197912	+	0.342794i	−0.749939	+	0.661507i	$0.769917\pi$
$312$	−16.0687	+	20.5751i	−0.909708	+	1.16484i
$313$	17.1288	+	9.88930i	0.968175	+	0.558976i	0.898679	−	0.438606i	$-0.144528\pi$
$313$	17.1288	+	9.88930i	0.968175	+	0.558976i	0.0694956	+	0.997582i	$0.477861\pi$
$314$	−16.7088	−	28.9405i	−0.942933	−	1.63321i
$315$	−14.0168	−	10.4310i	−0.789759	−	0.587720i
$316$	11.3265	−	19.6181i	0.637166	−	1.10360i
$317$	6.37868	+	3.68273i	0.358262	+	0.206843i	0.668318	−	0.743875i	$-0.267014\pi$
$317$	6.37868	+	3.68273i	0.358262	+	0.206843i	−0.310056	+	0.950718i	$0.600348\pi$
$318$	3.45693	+	25.4644i	0.193855	+	1.42797i
$319$	−1.34669			−0.0754003
$320$	11.6259	−	20.1367i	0.649909	−	1.12568i
$321$	−1.35137	+	3.30005i	−0.0754260	+	0.184191i
$322$	19.2521	+	24.7462i	1.07288	+	1.37905i
$323$	13.5959	−	7.84958i	0.756494	−	0.436762i
$324$	−0.543311	−	33.6935i	−0.0301840	−	1.87186i
$325$	0.137256	+	0.539259i	0.00761358	+	0.0299127i
$326$	−23.3150	+	13.4609i	−1.29130	+	0.745533i
$327$	1.18439	+	8.72440i	0.0654967	+	0.482461i
$328$	−36.1012	+	20.8430i	−1.99335	+	1.15086i
$329$	0.865985	−	0.119894i	0.0477433	−	0.00660995i
$330$	−1.84769	−	13.6104i	−0.101712	−	0.749230i
$331$	−1.15274	−	1.99660i	−0.0633601	−	0.109743i	0.832605	−	0.553867i	$-0.186848\pi$
$331$	−1.15274	−	1.99660i	−0.0633601	−	0.109743i	−0.895965	+	0.444124i	$0.853515\pi$
$332$	−10.2707			−0.563678
$333$	21.4825	+	21.1389i	1.17723	+	1.15840i
$334$	−11.6500	+	6.72611i	−0.637458	+	0.368036i
$335$	−7.63249	−	13.2199i	−0.417007	−	0.722278i
$336$	−3.12124	−	11.1690i	−0.170277	−	0.609318i
$337$	−9.99425			−0.544421			−0.272211	−	0.962238i	$-0.587755\pi$
$337$	−9.99425			−0.544421			−0.272211	+	0.962238i	$0.587755\pi$
$338$	16.2517	−	26.5829i	0.883975	−	1.44592i
$339$	−4.55571	−	5.88783i	−0.247432	−	0.319783i
$340$	20.2227	−	35.0268i	1.09673	−	1.89960i
$341$	4.04792			0.219207
$342$	−5.77422	+	22.2662i	−0.312234	+	1.20402i
$343$	16.9652	−	7.42851i	0.916034	−	0.401102i
$344$	−5.94244	−	3.43087i	−0.320395	−	0.184980i
$345$	−11.5365	−	14.9098i	−0.621103	−	0.802717i
$346$	49.6210	−	28.6487i	2.66764	−	1.54016i
$347$			30.3026i			1.62673i	0.581754	+	0.813365i	$0.302367\pi$
$347$			30.3026i			1.62673i	−0.581754	+	0.813365i	$0.697633\pi$
$348$	5.75755	−	0.781619i	0.308637	−	0.0418992i
$349$	18.7898	−	10.8483i	1.00580	−	0.580696i	0.0958377	−	0.995397i	$-0.469447\pi$
$349$	18.7898	−	10.8483i	1.00580	−	0.580696i	0.909958	+	0.414701i	$0.136114\pi$
$350$	−0.906620	−	0.368465i	−0.0484609	−	0.0196953i
$351$	2.43663	+	18.5759i	0.130058	+	0.991506i
$352$	−1.72514	+	2.98803i	−0.0919502	+	0.159262i
$353$	−7.88107	+	13.6504i	−0.419467	+	0.726538i	−0.995886	−	0.0906163i	$-0.971116\pi$
$353$	−7.88107	+	13.6504i	−0.419467	+	0.726538i	0.576419	+	0.817154i	$0.304450\pi$
$354$	21.7843	−	53.1974i	1.15782	−	2.82741i
$355$	−30.6794	+	17.7128i	−1.62830	+	0.940097i
$356$	47.2881			2.50626
$357$	6.05240	+	21.6578i	0.320327	+	1.14625i
$358$	−23.4482	+	40.6136i	−1.23928	+	2.14649i
$359$	5.88803	+	3.39946i	0.310759	+	0.179417i	0.647266	−	0.762264i	$-0.275912\pi$
$359$	5.88803	+	3.39946i	0.310759	+	0.179417i	−0.336507	+	0.941681i	$0.609246\pi$
$360$	7.35981	+	26.6073i	0.387896	+	1.40233i
$361$	−4.38253	+	7.59077i	−0.230660	+	0.399514i
$362$	−3.66275			−0.192510
$363$	−2.03657	−	15.0018i	−0.106892	−	0.787388i
$364$	13.4738	+	33.0786i	0.706220	+	1.73379i
$365$			7.29620i			0.381900i
$366$	−1.57917	−	11.6325i	−0.0825447	−	0.608039i
$367$	−14.0718	−	8.12438i	−0.734544	−	0.424089i	0.0855383	−	0.996335i	$-0.472739\pi$
$367$	−14.0718	−	8.12438i	−0.734544	−	0.424089i	−0.820082	+	0.572246i	$0.806072\pi$
$368$		−	12.5127i		−	0.652267i
$369$	−7.50955	+	28.9579i	−0.390932	+	1.50749i
$370$	−45.9016	−	26.5013i	−2.38631	−	1.37774i
$371$	15.1732	+	6.16664i	0.787753	+	0.320156i
$372$	−17.3062	+	2.34941i	−0.897284	+	0.121811i
$373$	6.67655	+	11.5641i	0.345699	+	0.598767i	0.985480	−	0.169789i	$-0.0543086\pi$
$373$	6.67655	+	11.5641i	0.345699	+	0.598767i	−0.639782	+	0.768557i	$0.720975\pi$
$374$	−8.83902	+	15.3096i	−0.457055	+	0.791642i
$375$	18.1864	+	7.44730i	0.939140	+	0.384577i
$376$	−1.19626	−	0.690663i	−0.0616926	−	0.0356182i
$377$	−3.13057	+	0.796814i	−0.161233	+	0.0410380i
$378$	−28.8390	−	15.9363i	−1.48332	−	0.819674i
$379$	−11.9437	−	20.6870i	−0.613504	−	1.06262i	−0.990645	−	0.136464i	$-0.956426\pi$
$379$	−11.9437	−	20.6870i	−0.613504	−	1.06262i	0.377141	−	0.926156i	$-0.376907\pi$
$380$		−	26.3681i		−	1.35266i
$381$	−4.12074	−	30.3541i	−0.211112	−	1.55509i
$382$	−7.39870	−	12.8149i	−0.378551	−	0.655669i
$383$	0.798871	+	1.38369i	0.0408204	+	0.0707030i	0.885714	−	0.464232i	$-0.153670\pi$
$383$	0.798871	+	1.38369i	0.0408204	+	0.0707030i	−0.844893	+	0.534935i	$0.820336\pi$
$384$	13.6034	−	33.2196i	0.694194	−	1.69523i
$385$	−8.10991	−	3.29600i	−0.413319	−	0.167980i
$386$	21.7047	+	12.5312i	1.10474	+	0.637823i
$387$	−4.74607	+	1.31280i	−0.241256	+	0.0667336i
$388$	43.3169	+	25.0090i	2.19908	+	1.26964i
$389$	19.3984	−	11.1997i	0.983539	−	0.567846i	0.0802022	−	0.996779i	$-0.474443\pi$
$389$	19.3984	−	11.1997i	0.983539	−	0.567846i	0.903337	+	0.428932i	$0.141110\pi$
$390$	−12.3483	−	30.5461i	−0.625279	−	1.54676i
$391$			24.2633i			1.22705i
$392$	−28.3639	−	7.19576i	−1.43259	−	0.363441i
$393$	−17.0466	+	13.1899i	−0.859889	+	0.665340i
$394$	−5.54266	−	9.60017i	−0.279235	−	0.483650i
$395$	6.65907	+	11.5338i	0.335054	+	0.580331i
$396$	−4.50114	−	16.2726i	−0.226191	−	0.817728i
$397$	17.6893	−	10.2130i	0.887803	−	0.512573i	0.0145798	−	0.999894i	$-0.495359\pi$
$397$	17.6893	−	10.2130i	0.887803	−	0.512573i	0.873223	+	0.487320i	$0.162026\pi$
$398$	21.0089			1.05308
$399$	10.4770	+	10.2551i	0.524506	+	0.513395i
$400$	0.195281	+	0.338236i	0.00976404	+	0.0169118i
$401$		−	32.5300i		−	1.62447i	−0.583330	−	0.812235i	$-0.698251\pi$
$401$		−	32.5300i		−	1.62447i	0.583330	−	0.812235i	$-0.301749\pi$
$402$	−17.6163	−	22.7674i	−0.878620	−	1.13553i
$403$	9.40996	−	2.39508i	0.468743	−	0.119308i
$404$	32.7876	−	56.7897i	1.63124	−	2.82539i
$405$	17.3148	+	9.62788i	0.860380	+	0.478413i
$406$	2.13906	−	5.26322i	0.106160	−	0.261209i
$407$	13.0774	+	7.55024i	0.648223	+	0.374252i
$408$	13.4647	−	32.8808i	0.666600	−	1.62784i
$409$			26.4267i			1.30672i	0.757049	+	0.653358i	$0.226640\pi$
$409$			26.4267i			1.30672i	−0.757049	+	0.653358i	$0.773360\pi$
$410$		−	52.6102i		−	2.59823i
$411$	6.19919	−	15.1385i	0.305784	−	0.746727i
$412$	−10.3504	−	5.97578i	−0.509926	−	0.294406i
$413$	−22.4971	−	28.9171i	−1.10701	−	1.42292i
$414$	−25.3403	−	24.9349i	−1.24541	−	1.22549i
$415$	3.01917	−	5.22936i	0.148205	−	0.256699i
$416$	−2.24236	+	7.96682i	−0.109941	+	0.390605i
$417$	−4.77797	−	6.17507i	−0.233978	−	0.302394i
$418$			11.5251i			0.563709i
$419$	−7.22669	−	12.5170i	−0.353047	−	0.611495i	0.633735	−	0.773550i	$-0.281521\pi$
$419$	−7.22669	−	12.5170i	−0.353047	−	0.611495i	−0.986782	+	0.162055i	$0.948188\pi$
$420$	36.5855	+	9.38449i	1.78519	+	0.457916i
$421$	−29.6577			−1.44543			−0.722713	−	0.691148i	$-0.757105\pi$
$421$	−29.6577			−1.44543			−0.722713	+	0.691148i	$0.757105\pi$
$422$	2.05197	−	1.18471i	0.0998884	−	0.0576706i
$423$	−0.955423	+	0.264278i	−0.0464543	+	0.0128497i
$424$	−12.9392	−	22.4113i	−0.628381	−	1.08839i
$425$	−0.378670	−	0.655875i	−0.0183682	−	0.0318146i
$426$	−52.8364	+	40.8822i	−2.55993	+	1.98075i
$427$	−6.93132	−	2.81700i	−0.335430	−	0.136324i
$428$		−	7.70874i		−	0.372616i
$429$	3.51803	+	8.70262i	0.169852	+	0.420166i
$430$	7.49971	−	4.32996i	0.361668	−	0.208809i
$431$	−10.4396	−	6.02731i	−0.502858	−	0.290325i	0.227035	−	0.973887i	$-0.427097\pi$
$431$	−10.4396	−	6.02731i	−0.502858	−	0.290325i	−0.729893	+	0.683561i	$0.760430\pi$
$432$	5.17870	+	12.0870i	0.249160	+	0.581535i
$433$	−23.4870	−	13.5603i	−1.12872	−	0.651664i	−0.185104	−	0.982719i	$-0.559262\pi$
$433$	−23.4870	−	13.5603i	−1.12872	−	0.651664i	−0.943612	+	0.331055i	$0.892595\pi$
$434$	−6.42964	+	15.8203i	−0.308632	+	0.759399i
$435$	−1.29452	+	3.16123i	−0.0620676	+	0.151570i
$436$	−9.51634	−	16.4828i	−0.455750	−	0.789382i
$437$	7.90914	+	13.6990i	0.378345	+	0.655313i
$438$	1.85092	+	13.6342i	0.0884403	+	0.651467i
$439$		−	4.20603i		−	0.200743i	−0.994950	−	0.100371i	$-0.967997\pi$
$439$		−	4.20603i		−	0.200743i	0.994950	−	0.100371i	$-0.0320031\pi$
$440$	6.91583	+	11.9786i	0.329699	+	0.571056i
$441$	−17.9576	+	10.8869i	−0.855123	+	0.518424i
$442$	−11.4891	+	40.8193i	−0.546481	+	1.94157i
$443$	10.9258	+	6.30802i	0.519101	+	0.299703i	0.736567	−	0.676365i	$-0.236446\pi$
$443$	10.9258	+	6.30802i	0.519101	+	0.299703i	−0.217466	+	0.976068i	$0.569779\pi$
$444$	−60.2923	−	24.6896i	−2.86135	−	1.17172i
$445$	−13.9008	+	24.0769i	−0.658960	+	1.14135i
$446$	25.4639	+	44.1048i	1.20575	+	2.08842i
$447$	−32.3366	+	4.38988i	−1.52947	+	0.207634i
$448$	−17.1604	−	22.0575i	−0.810753	−	1.04212i
$449$	5.18515	+	2.99365i	0.244702	+	0.141279i	0.617336	−	0.786699i	$-0.288212\pi$
$449$	5.18515	+	2.99365i	0.244702	+	0.141279i	−0.372634	+	0.927979i	$0.621545\pi$
$450$	1.07414	+	0.278553i	0.0506353	+	0.0131311i
$451$			14.9887i			0.705790i
$452$	13.9369	+	8.04649i	0.655538	+	0.378475i
$453$	−1.92018	−	14.1444i	−0.0902177	−	0.664560i
$454$		−	9.55287i		−	0.448338i
$455$	−20.8028	−	2.86353i	−0.975250	−	0.134244i
$456$	−3.11607	−	22.9536i	−0.145923	−	1.07490i
$457$	37.7688			1.76675			0.883374	−	0.468669i	$-0.155266\pi$
$457$	37.7688			1.76675			0.883374	+	0.468669i	$0.155266\pi$
$458$	1.81555	−	3.14463i	0.0848353	−	0.146939i
$459$	−10.0420	−	23.4379i	−0.468722	−	1.09399i
$460$	35.2926	+	20.3762i	1.64553	+	0.950045i
$461$	7.86795	−	13.6277i	0.366447	−	0.634705i	−0.622560	−	0.782572i	$-0.713907\pi$
$461$	7.86795	−	13.6277i	0.366447	−	0.634705i	0.989007	+	0.147867i	$0.0472408\pi$
$462$	−15.9909	−	4.10180i	−0.743964	−	0.190833i
$463$	−23.9163			−1.11148			−0.555742	−	0.831355i	$-0.687566\pi$
$463$	−23.9163			−1.11148			−0.555742	+	0.831355i	$0.687566\pi$
$464$	−1.96357	+	1.13367i	−0.0911565	+	0.0526292i
$465$	3.89111	−	9.50212i	0.180446	−	0.440650i
$466$	8.11995	−	14.0642i	0.376149	−	0.651510i
$467$	11.4121	−	19.7663i	0.528087	−	0.914674i	−0.471377	−	0.881932i	$-0.656243\pi$
$467$	11.4121	−	19.7663i	0.528087	−	0.914674i	0.999464	−	0.0327419i	$-0.0104239\pi$
$468$	−20.0917	−	35.1647i	−0.928740	−	1.62549i
$469$	−18.1738	+	2.51612i	−0.839188	+	0.116184i
$470$	1.50975	−	0.871657i	0.0696398	−	0.0402066i
$471$	23.9307	−	3.24873i	1.10267	−	0.149693i
$472$			57.8883i			2.66452i
$473$	−2.13667	+	1.23361i	−0.0982443	+	0.0567214i
$474$	15.3696	+	19.8637i	0.705947	+	0.912369i
$475$	−0.427592	−	0.246871i	−0.0196193	−	0.0113272i
$476$	−29.8497	−	38.3680i	−1.36816	−	1.75860i
$477$	−17.9768	−	4.66186i	−0.823100	−	0.213452i
$478$	−37.0134			−1.69295
$479$	−1.19588	+	2.07132i	−0.0546411	+	0.0946412i	−0.892052	−	0.451932i	$-0.850735\pi$
$479$	−1.19588	+	2.07132i	−0.0546411	+	0.0946412i	0.837411	+	0.546574i	$0.184068\pi$
$480$	5.35581	+	6.92187i	0.244458	+	0.315939i
$481$	34.8676	+	9.81393i	1.58983	+	0.447476i
$482$	−16.8706			−0.768435
$483$	−21.8222	+	6.09832i	−0.992942	+	0.277483i
$484$	16.3635	+	28.3424i	0.743796	+	1.28829i
$485$	−25.4668	+	14.7033i	−1.15639	+	0.667641i
$486$	34.7982	+	13.5989i	1.57848	+	0.616858i
$487$	40.0884			1.81658			0.908290	−	0.418340i	$-0.137388\pi$
$487$	40.0884			1.81658			0.908290	+	0.418340i	$0.137388\pi$
$488$	5.91077	+	10.2378i	0.267568	+	0.463442i
$489$	−2.61724	−	19.2791i	−0.118356	−	0.871829i
$490$	25.7632	−	26.4603i	1.16386	−	1.19535i
$491$	3.37799	−	1.95028i	0.152447	−	0.0880151i	−0.421836	−	0.906672i	$-0.638614\pi$
$491$	3.37799	−	1.95028i	0.152447	−	0.0880151i	0.574283	+	0.818657i	$0.305281\pi$
$492$	−8.69942	−	64.0816i	−0.392200	−	2.88902i
$493$	3.80756	−	2.19830i	0.171484	−	0.0990064i
$494$	6.81917	+	26.7916i	0.306809	+	1.20541i
$495$	9.60838	+	2.49171i	0.431865	+	0.111994i
$496$	5.90215	−	3.40761i	0.265014	−	0.153006i
$497$	5.83918	+	42.1761i	0.261923	+	1.89186i
$498$	4.31524	−	10.5379i	0.193371	−	0.472213i
$499$	16.3007	−	28.2336i	0.729718	−	1.26391i	−0.227284	−	0.973829i	$-0.572984\pi$
$499$	16.3007	−	28.2336i	0.729718	−	1.26391i	0.957002	−	0.290081i	$-0.0936822\pi$
$500$	−42.4824			−1.89987
$501$	−1.30777	−	9.63328i	−0.0584269	−	0.430383i
$502$	7.02736	+	4.05725i	0.313646	+	0.181084i
$503$	−6.79105	+	11.7625i	−0.302798	+	0.524462i	−0.976769	−	0.214296i	$-0.931254\pi$
$503$	−6.79105	+	11.7625i	−0.302798	+	0.524462i	0.673971	+	0.738758i	$0.264587\pi$
$504$	32.9568	+	3.84573i	1.46801	+	0.171302i
$505$	19.2764	+	33.3877i	0.857789	+	1.48573i
$506$	−15.4258	−	8.90609i	−0.685760	−	0.395924i
$507$	13.3273	+	18.1489i	0.591888	+	0.806020i
$508$	33.1094	+	57.3472i	1.46899	+	2.54437i
$509$	−15.4269			−0.683787			−0.341894	−	0.939739i	$-0.611068\pi$
$509$	−15.4269			−0.683787			−0.341894	+	0.939739i	$0.611068\pi$
$510$	27.4413	+	35.4653i	1.21512	+	1.57043i
$511$	8.12406	+	3.30175i	0.359387	+	0.146061i
$512$			26.9670i			1.19179i
$513$	−13.3098	−	9.95957i	−0.587641	−	0.439726i
$514$		−	49.4195i		−	2.17980i
$515$	6.08517	−	3.51327i	0.268145	−	0.154813i
$516$	8.41899	−	6.51420i	0.370625	−	0.286772i
$517$	−0.430130	+	0.248336i	−0.0189171	+	0.0109218i
$518$	−50.2802	+	39.1172i	−2.20918	+	1.71871i
$519$	5.57022	+	41.0313i	0.244506	+	1.80107i
$520$	23.1643	+	23.7539i	1.01582	+	1.04168i
$521$	8.81691	+	15.2713i	0.386276	+	0.669050i	0.991945	−	0.126667i	$-0.0404279\pi$
$521$	8.81691	+	15.2713i	0.386276	+	0.669050i	−0.605669	+	0.795716i	$0.707095\pi$
$522$	−1.61709	+	6.23571i	−0.0707780	+	0.272930i
$523$			16.0990i			0.703958i	0.936008	+	0.351979i	$0.114491\pi$
$523$			16.0990i			0.703958i	−0.936008	+	0.351979i	$0.885509\pi$
$524$	23.2964	−	40.3506i	1.01771	−	1.76273i
$525$	0.494712	−	0.505418i	0.0215910	−	0.0220583i
$526$	−6.65022	+	11.5185i	−0.289964	+	0.502232i
$527$	−11.4449	+	6.60770i	−0.498547	+	0.287836i
$528$	4.03179	+	5.21071i	0.175461	+	0.226767i
$529$	−1.44743			−0.0629317
$530$	32.6599			1.41866
$531$	29.6113	+	29.1377i	1.28502	+	1.26447i
$532$	−29.3600	−	11.9324i	−1.27292	−	0.517334i
$533$	8.86854	+	34.8433i	0.384139	+	1.50923i
$534$	−19.8681	+	48.5181i	−0.859778	+	2.09959i
$535$	3.92493	+	2.26606i	0.169689	+	0.0979702i
$536$	25.1051	+	14.4944i	1.08438	+	0.626064i
$537$	−20.7398	−	26.8043i	−0.894990	−	1.15669i
$538$		−	21.9723i		−	0.947294i
$539$	−7.33996	+	7.53856i	−0.316155	+	0.324709i
$540$	−42.5252	−	5.07619i	−1.82999	−	0.218444i
$541$	−11.6387	+	20.1589i	−0.500388	+	0.866697i	0.499612	+	0.866249i	$0.333476\pi$
$541$	−11.6387	+	20.1589i	−0.500388	+	0.866697i	−1.00000		0.000447572i	$0.999858\pi$
$542$	16.3561			0.702555
$543$	1.00310	−	2.44957i	0.0430470	−	0.105121i
$544$		−	11.2642i		−	0.482951i
$545$	11.1897			0.479313
$546$	−39.6000	−	0.0736874i	−1.69472	−	0.00315353i
$547$	32.4180			1.38609			0.693046	−	0.720893i	$-0.256268\pi$
$547$	32.4180			1.38609			0.693046	+	0.720893i	$0.256268\pi$
$548$			35.3627i			1.51062i
$549$	8.21202	+	2.12960i	0.350481	+	0.0908891i
$550$	0.555977			0.0237070
$551$	1.43316	−	2.48231i	0.0610548	−	0.105750i
$552$	33.1303	+	13.5668i	1.41012	+	0.577443i
$553$	15.8560	−	2.19522i	0.674264	−	0.0933503i
$554$			7.11132i			0.302131i
$555$	30.2943	−	23.4402i	1.28592	−	0.994983i
$556$	14.6168	+	8.43904i	0.619892	+	0.357895i
$557$	−7.16449	−	4.13642i	−0.303569	−	0.175266i	0.340476	−	0.940253i	$-0.389412\pi$
$557$	−7.16449	−	4.13642i	−0.303569	−	0.175266i	−0.644045	+	0.764987i	$0.722745\pi$
$558$	4.86068	−	18.7435i	0.205769	−	0.793474i
$559$	−4.23709	+	4.13193i	−0.179210	+	0.174762i
$560$	−14.5994	+	2.02126i	−0.616939	+	0.0854137i
$561$	−7.81806	−	10.1041i	−0.330079	−	0.426595i
$562$	−62.2407			−2.62547
$563$	−41.4857			−1.74841			−0.874206	−	0.485555i	$-0.838617\pi$
$563$	−41.4857			−1.74841			−0.874206	+	0.485555i	$0.838617\pi$
$564$	1.69481	−	1.31136i	0.0713645	−	0.0552184i
$565$	−8.19378	+	4.73068i	−0.344715	+	0.199021i
$566$	−13.0569	+	22.6152i	−0.548821	+	0.950586i
$567$	18.5558	−	14.9225i	0.779270	−	0.626688i
$568$	33.6374	−	58.2616i	1.41139	−	2.44460i
$569$		−	15.4494i		−	0.647673i	−0.946113	−	0.323837i	$-0.895027\pi$
$569$		−	15.4494i		−	0.647673i	0.946113	−	0.323837i	$-0.104973\pi$
$570$	27.0540	+	11.0786i	1.13317	+	0.464031i
$571$	−16.0896	−	27.8680i	−0.673329	−	1.16624i	−0.976954	−	0.213449i	$-0.931530\pi$
$571$	−16.0896	−	27.8680i	−0.673329	−	1.16624i	0.303625	−	0.952792i	$-0.401803\pi$
$572$	−14.1669	−	14.5275i	−0.592349	−	0.607425i
$573$	10.5966	−	1.43854i	0.442679	−	0.0600961i
$574$	−58.5797	−	23.8078i	−2.44507	−	0.993716i
$575$	0.660852	−	0.381543i	0.0275594	−	0.0159114i
$576$	22.5871	+	22.2258i	0.941128	+	0.926075i
$577$	−19.3075	+	11.1472i	−0.803783	+	0.464064i	−0.844792	−	0.535094i	$-0.820276\pi$
$577$	−19.3075	+	11.1472i	−0.803783	+	0.464064i	0.0410092	+	0.999159i	$0.486943\pi$
$578$		−	16.9702i		−	0.705866i
$579$	−14.3248	+	11.0838i	−0.595317	+	0.460627i
$580$		−	7.38447i		−	0.306623i
$581$	−4.45644	−	5.72819i	−0.184884	−	0.237645i
$582$	−43.8592	+	33.9361i	−1.81802	+	1.40670i
$583$	−9.30484			−0.385367
$584$	−6.92790	−	11.9995i	−0.286679	−	0.496542i
$585$	23.8103	+	0.107225i	0.984436	+	0.00443319i
$586$	−23.6789	−	13.6710i	−0.978165	−	0.564744i
$587$	19.0213	+	32.9459i	0.785094	+	1.35982i	0.928943	+	0.370223i	$0.120719\pi$
$587$	19.0213	+	32.9459i	0.785094	+	1.35982i	−0.143849	+	0.989600i	$0.545948\pi$
$588$	27.0054	−	36.4899i	1.11368	−	1.50482i
$589$	−4.30784	+	7.46139i	−0.177501	+	0.307441i
$590$	−63.2704	−	36.5292i	−2.60480	−	1.50388i
$591$	7.93832	−	1.07767i	0.326539	−	0.0443294i
$592$	25.4237			1.04491
$593$	−0.484442	+	0.839079i	−0.0198937	+	0.0344568i	−0.875801	−	0.482673i	$-0.839666\pi$
$593$	−0.484442	+	0.839079i	−0.0198937	+	0.0344568i	0.855907	+	0.517129i	$0.172999\pi$
$594$	18.5870	+	2.21872i	0.762635	+	0.0910350i
$595$	28.3098	−	3.91942i	1.16059	−	0.160681i
$596$	61.0928	−	35.2719i	2.50246	−	1.44479i
$597$	−5.75358	+	14.0503i	−0.235478	+	0.575040i
$598$	−41.1290	−	11.5763i	−1.68189	−	0.473389i
$599$	−32.1172	+	18.5429i	−1.31228	+	0.757642i	−0.982472	−	0.186408i	$-0.940315\pi$
$599$	−32.1172	+	18.5429i	−1.31228	+	0.757642i	−0.329803	+	0.944050i	$0.606982\pi$
$600$	−1.10730	+	0.150322i	−0.0452052	+	0.00613686i
$601$	−9.42183	+	5.43970i	−0.384324	+	0.221890i	−0.679698	−	0.733492i	$-0.737889\pi$
$601$	−9.42183	+	5.43970i	−0.384324	+	0.221890i	0.295374	+	0.955382i	$0.404556\pi$
$602$	−1.42741	−	10.3101i	−0.0581769	−	0.420209i
$603$	20.0508	−	5.54622i	0.816530	−	0.225859i
$604$	15.4283	+	26.7226i	0.627768	+	1.08733i
$605$	−19.2408			−0.782251
$606$	44.4912	+	57.5007i	1.80733	+	2.33580i
$607$	14.0368	−	8.10415i	0.569736	−	0.328937i	−0.187308	−	0.982301i	$-0.559976\pi$
$607$	14.0368	−	8.10415i	0.569736	−	0.328937i	0.757044	+	0.653364i	$0.226643\pi$
$608$	−3.67182	−	6.35977i	−0.148912	−	0.257923i
$609$	2.93411	+	2.87196i	0.118896	+	0.116378i
$610$	−14.9195			−0.604072
$611$	−0.852962	+	0.831792i	−0.0345072	+	0.0336507i
$612$	39.2892	+	38.6607i	1.58817	+	1.56277i
$613$	16.3691	−	28.3521i	0.661142	−	1.14513i	−0.319174	−	0.947696i	$-0.603406\pi$
$613$	16.3691	−	28.3521i	0.661142	−	1.14513i	0.980316	−	0.197435i	$-0.0632611\pi$
$614$	2.78398			0.112352
$615$	35.1846	+	14.4080i	1.41878	+	0.580988i
$616$	16.4674	−	2.27987i	0.663489	−	0.0918584i
$617$	33.8949	+	19.5692i	1.36456	+	0.787828i	0.990227	−	0.139467i	$-0.0445389\pi$
$617$	33.8949	+	19.5692i	1.36456	+	0.787828i	0.374331	+	0.927295i	$0.377872\pi$
$618$	10.4799	−	8.10886i	0.421565	−	0.326186i
$619$	−4.41436	+	2.54863i	−0.177428	+	0.102438i	−0.586084	−	0.810250i	$-0.699331\pi$
$619$	−4.41436	+	2.54863i	−0.177428	+	0.102438i	0.408656	+	0.912689i	$0.365998\pi$
$620$			22.1964i			0.891430i
$621$	23.6157	−	10.1182i	0.947666	−	0.406031i
$622$	14.4887	−	8.36504i	0.580943	−	0.335407i
$623$	20.5182	+	26.3736i	0.822045	+	1.05663i
$624$	12.4555	+	9.72748i	0.498621	+	0.389411i
$625$	12.1023	−	20.9617i	0.484090	−	0.838469i
$626$	23.7017	−	41.0526i	0.947312	−	1.64079i
$627$	−7.70770	−	3.15630i	−0.307816	−	0.126050i
$628$	−45.2117	+	26.1030i	−1.80414	+	1.04162i
$629$	−49.2991			−1.96569
$630$	−25.0000	+	33.5942i	−0.996025	+	1.33843i
$631$	24.5250	−	42.4785i	0.976324	−	1.69104i	0.300828	−	0.953678i	$-0.402737\pi$
$631$	24.5250	−	42.4785i	0.976324	−	1.69104i	0.675496	−	0.737364i	$-0.263930\pi$
$632$	−21.9033	−	12.6459i	−0.871266	−	0.503026i
$633$	0.230345	+	1.69676i	0.00915538	+	0.0674402i
$634$	8.82643	−	15.2878i	0.350542	−	0.607157i
$635$	−38.9313			−1.54494
$636$	39.7812	−	5.40052i	1.57743	−	0.214145i
$637$	−12.6023	+	21.8674i	−0.499323	+	0.866416i
$638$			3.22763i			0.127783i
$639$	−12.8712	−	46.5320i	−0.509175	−	1.84078i
$640$	−39.5098	−	22.8110i	−1.56176	−	0.901683i
$641$			25.8865i			1.02246i	0.859445	+	0.511228i	$0.170809\pi$
$641$			25.8865i			1.02246i	−0.859445	+	0.511228i	$0.829191\pi$
$642$	7.90926	+	3.23883i	0.312154	+	0.127827i
$643$	19.3103	+	11.1488i	0.761526	+	0.439667i	0.829843	−	0.557997i	$-0.188430\pi$
$643$	19.3103	+	11.1488i	0.761526	+	0.439667i	−0.0683177	+	0.997664i	$0.521763\pi$
$644$	38.6592	−	30.0762i	1.52338	−	1.18517i
$645$	0.841882	+	6.20146i	0.0331491	+	0.244182i
$646$	−18.8131	−	32.5853i	−0.740193	−	1.28205i
$647$	9.84729	−	17.0560i	0.387137	−	0.670541i	−0.604926	−	0.796282i	$-0.706797\pi$
$647$	9.84729	−	17.0560i	0.387137	−	0.670541i	0.992063	+	0.125741i	$0.0401307\pi$
$648$	−37.6182	+	0.606599i	−1.47778	+	0.0238295i
$649$	18.0258	+	10.4072i	0.707575	+	0.408518i
$650$	1.29245	−	0.328962i	0.0506939	−	0.0129029i
$651$	−8.81943	−	8.63261i	−0.345661	−	0.338339i
$652$	21.0291	+	36.4234i	0.823562	+	1.42645i
$653$		−	9.34844i		−	0.365833i	−0.983128	−	0.182916i	$-0.941446\pi$
$653$		−	9.34844i		−	0.365833i	0.983128	−	0.182916i	$-0.0585538\pi$
$654$	20.9098	−	2.83862i	0.817639	−	0.110999i
$655$	13.6964	+	23.7229i	0.535163	+	0.926930i
$656$	12.6177	+	21.8546i	0.492640	+	0.853277i
$657$	−9.62516	−	2.49606i	−0.375513	−	0.0973807i
$658$	−0.287350	−	2.07551i	−0.0112021	−	0.0809119i
$659$	−12.6857	−	7.32409i	−0.494165	−	0.285306i	0.232136	−	0.972683i	$-0.425429\pi$
$659$	−12.6857	−	7.32409i	−0.494165	−	0.285306i	−0.726301	+	0.687377i	$0.758762\pi$
$660$	−21.2626	+	2.88652i	−0.827646	+	0.112358i
$661$	−1.74192	−	1.00570i	−0.0677529	−	0.0391172i	0.465741	−	0.884921i	$-0.345788\pi$
$661$	−1.74192	−	1.00570i	−0.0677529	−	0.0391172i	−0.533494	+	0.845804i	$0.679121\pi$
$662$	−4.78526	+	2.76277i	−0.185984	+	0.107378i
$663$	−24.1526	−	18.8626i	−0.938009	−	0.732562i
$664$			11.4671i			0.445009i
$665$	14.7060	−	11.4411i	0.570276	−	0.443666i
$666$	50.6637	−	51.4873i	1.96318	−	1.99509i
$667$	2.21498	+	3.83646i	0.0857643	+	0.148548i
$668$	10.5077	+	18.1999i	0.406556	+	0.704176i
$669$	−36.4699	+	4.95099i	−1.41001	+	0.191417i
$670$	−31.6841	+	18.2928i	−1.22406	+	0.706714i
$671$	4.25057			0.164092
$672$	10.1309	−	2.83114i	0.390809	−	0.109214i
$673$	−3.60802	−	6.24928i	−0.139079	−	0.240892i	0.788069	−	0.615587i	$-0.211081\pi$
$673$	−3.60802	−	6.24928i	−0.139079	−	0.240892i	−0.927148	+	0.374695i	$0.877748\pi$
$674$			23.9533i			0.922646i
$675$	−0.480457	+	0.642074i	−0.0184928	+	0.0247134i
$676$	−41.5286	−	25.3889i	−1.59726	−	0.976494i
$677$	12.2214	−	21.1681i	0.469706	−	0.813554i	−0.529694	−	0.848189i	$-0.677693\pi$
$677$	12.2214	−	21.1681i	0.469706	−	0.813554i	0.999400	+	0.0346344i	$0.0110267\pi$
$678$	−14.1114	+	10.9187i	−0.541945	+	0.419331i
$679$	4.84706	+	35.0101i	0.186013	+	1.34356i
$680$	−39.1069	−	22.5784i	−1.49968	−	0.865841i
$681$	6.38875	+	2.61619i	0.244817	+	0.100252i
$682$		−	9.70168i		−	0.371496i
$683$		−	6.35051i		−	0.242995i	−0.992592	−	0.121498i	$-0.961230\pi$
$683$		−	6.35051i		−	0.242995i	0.992592	−	0.121498i	$-0.0387697\pi$
$684$	34.7849	+	9.02065i	1.33003	+	0.344913i
$685$	−18.0050	−	10.3952i	−0.687935	−	0.397180i
$686$	−17.8040	−	40.6606i	−0.679758	−	1.55243i
$687$	1.60585	+	2.07540i	0.0612669	+	0.0791816i
$688$	−2.07694	+	3.59737i	−0.0791828	+	0.137149i
$689$	−21.6304	+	5.50551i	−0.824053	+	0.209743i
$690$	−35.7344	+	27.6495i	−1.36039	+	1.05260i
$691$			5.74331i			0.218486i	0.994015	+	0.109243i	$0.0348427\pi$
$691$			5.74331i			0.218486i	−0.994015	+	0.109243i	$0.965157\pi$
$692$	−44.7558	−	77.5193i	−1.70136	−	2.94684i
$693$	7.12253	−	9.57103i	0.270562	−	0.363573i
$694$	72.6265			2.75686
$695$	−8.59352	+	4.96147i	−0.325971	+	0.188199i
$696$	−0.872665	−	6.42821i	−0.0330783	−	0.243661i
$697$	−24.4671	−	42.3782i	−0.926757	−	1.60519i
$698$	−26.0002	−	45.0337i	−0.984122	−	1.70455i
$699$	7.18204	+	9.28211i	0.271650	+	0.351082i
$700$	−0.575627	+	1.41635i	−0.0217567	+	0.0535329i
$701$		−	14.7876i		−	0.558520i	−0.960216	−	0.279260i	$-0.909911\pi$
$701$		−	14.7876i		−	0.558520i	0.960216	−	0.279260i	$-0.0900891\pi$
$702$	44.5209	−	5.83990i	1.68033	−	0.220413i
$703$	−27.8342	+	16.0701i	−1.04979	+	0.606095i
$704$	13.7498	+	7.93846i	0.518215	+	0.299192i
$705$	0.169478	+	1.24841i	0.00638291	+	0.0470177i
$706$	32.7160	+	18.8886i	1.23128	+	0.710882i
$707$	45.8993	−	6.35464i	1.72622	−	0.238991i
$708$	−83.1065	−	34.0320i	−3.12333	−	1.27900i
$709$	24.3473	+	42.1707i	0.914381	+	1.58375i	0.807805	+	0.589450i	$0.200655\pi$
$709$	24.3473	+	42.1707i	0.914381	+	1.58375i	0.106576	+	0.994305i	$0.466011\pi$
$710$	42.4523	+	73.5296i	1.59321	+	2.75952i
$711$	−17.4936	+	4.83887i	−0.656060	+	0.181472i
$712$		−	52.7964i		−	1.97863i
$713$	−6.65784	−	11.5317i	−0.249338	−	0.431866i
$714$	51.9075	−	14.5058i	1.94259	−	0.542867i
$715$	11.5612	−	2.94263i	0.432365	−	0.110048i
$716$	63.4476	+	36.6315i	2.37115	+	1.36898i
$717$	10.1366	−	24.7538i	0.378560	−	0.924446i
$718$	8.14751	−	14.1119i	0.304062	−	0.526651i
$719$	14.8764	+	25.7667i	0.554796	+	0.960935i	0.997919	+	0.0644743i	$0.0205371\pi$
$719$	14.8764	+	25.7667i	0.554796	+	0.960935i	−0.443123	+	0.896461i	$0.646130\pi$
$720$	16.1073	−	4.45541i	0.600282	−	0.166043i
$721$	−1.15818	−	8.36549i	−0.0431330	−	0.311547i
$722$	18.1928	+	10.5036i	0.677068	+	0.390905i
$723$	4.62025	−	11.2827i	0.171829	−	0.419608i
$724$			5.72206i			0.212659i
$725$	−0.119749	−	0.0691369i	−0.00444735	−	0.00256768i
$726$	−35.9548	+	4.88106i	−1.33441	+	0.181153i
$727$			40.6361i			1.50711i	0.657385	+	0.753555i	$0.271663\pi$
$727$			40.6361i			1.50711i	−0.657385	+	0.753555i	$0.728337\pi$
$728$	36.9317	−	15.0433i	1.36878	−	0.557542i
$729$	−18.6246	+	19.5480i	−0.689800	+	0.724000i
$730$	17.4868			0.647217
$731$	4.02741	−	6.97568i	0.148959	−	0.258005i
$732$	−18.1726	+	2.46703i	−0.671678	+	0.0911840i
$733$	−24.6541	−	14.2340i	−0.910619	−	0.525746i	−0.0299887	−	0.999550i	$-0.509547\pi$
$733$	−24.6541	−	14.2340i	−0.910619	−	0.525746i	−0.880630	+	0.473804i	$0.842880\pi$
$734$	−19.4718	+	33.7261i	−0.718716	+	1.24485i
$735$	10.6404	+	24.4764i	0.392479	+	0.902826i
$736$	11.3497			0.418356
$737$	9.02683	−	5.21164i	0.332508	−	0.191973i
$738$	69.4035	+	17.9982i	2.55478	+	0.662523i
$739$	−15.6689	+	27.1393i	−0.576389	+	0.998335i	0.419500	+	0.907755i	$0.362205\pi$
$739$	−15.6689	+	27.1393i	−0.576389	+	0.998335i	−0.995889	+	0.0905800i	$0.971128\pi$
$740$	−41.4011	+	71.7088i	−1.52193	+	2.63607i
$741$	−19.7852	−	2.77674i	−0.726826	−	0.102006i
$742$	14.7796	−	36.3657i	0.542577	−	1.33503i
$743$	11.8552	−	6.84459i	0.434924	−	0.251104i	−0.266518	−	0.963830i	$-0.585873\pi$
$743$	11.8552	−	6.84459i	0.434924	−	0.251104i	0.701442	+	0.712726i	$0.252540\pi$
$744$	2.62308	+	19.3221i	0.0961667	+	0.708382i
$745$			41.4741i			1.51949i
$746$	27.7158	−	16.0017i	1.01475	−	0.585865i
$747$	5.86570	+	5.77188i	0.214615	+	0.211182i
$748$	23.9171	+	13.8086i	0.874497	+	0.504891i
$749$	4.29933	−	3.34481i	0.157094	−	0.122217i
$750$	17.8490	−	43.5874i	0.651753	−	1.59159i
$751$	38.3433			1.39917			0.699583	−	0.714551i	$-0.253369\pi$
$751$	38.3433			1.39917			0.699583	+	0.714551i	$0.253369\pi$
$752$	−0.418107	+	0.724182i	−0.0152468	+	0.0264082i
$753$	−4.63794	+	3.58861i	−0.169016	+	0.130776i
$754$	1.90973	+	7.50307i	0.0695482	+	0.273246i
$755$	−18.1412			−0.660225
$756$	−24.8961	+	45.0532i	−0.905463	+	1.63857i
$757$	−3.23204	−	5.59806i	−0.117471	−	0.203465i	0.801294	−	0.598271i	$-0.204145\pi$
$757$	−3.23204	−	5.59806i	−0.117471	−	0.203465i	−0.918765	+	0.394806i	$0.870812\pi$
$758$	−49.5807	+	28.6254i	−1.80085	+	1.03972i
$759$	10.1808	−	7.87738i	0.369538	−	0.285931i
$760$	−29.4396			−1.06789
$761$	−6.91097	−	11.9702i	−0.250523	−	0.433918i	0.713147	−	0.701014i	$-0.247269\pi$
$761$	−6.91097	−	11.9702i	−0.250523	−	0.433918i	−0.963670	+	0.267096i	$0.913936\pi$
$762$	−72.7499	+	9.87620i	−2.63545	+	0.357777i
$763$	5.06367	−	12.4593i	0.183317	−	0.451057i
$764$	−20.0199	+	11.5585i	−0.724293	+	0.418171i
$765$	−31.2336	+	8.63949i	−1.12925	+	0.312362i
$766$	3.31629	−	1.91466i	0.119822	−	0.0691795i
$767$	48.0612	+	13.5274i	1.73539	+	0.488448i
$768$	−45.7560	−	18.7370i	−1.65108	−	0.676114i
$769$	1.89305	−	1.09295i	0.0682650	−	0.0394128i	−0.465479	−	0.885059i	$-0.654118\pi$
$769$	1.89305	−	1.09295i	0.0682650	−	0.0394128i	0.533744	+	0.845646i	$0.320785\pi$
$770$	−7.89955	+	19.4371i	−0.284680	+	0.700463i
$771$	33.0507	+	13.5342i	1.19029	+	0.487423i
$772$	19.5767	−	33.9078i	0.704579	−	1.22037i
$773$	−8.34018			−0.299975			−0.149988	−	0.988688i	$-0.547923\pi$
$773$	−8.34018			−0.299975			−0.149988	+	0.988688i	$0.547923\pi$
$774$	3.14641	+	11.3749i	0.113095	+	0.408863i
$775$	0.359943	+	0.207813i	0.0129295	+	0.00746487i
$776$	27.9222	−	48.3626i	1.00235	−	1.73612i
$777$	−12.3908	−	44.3391i	−0.444517	−	1.59066i
$778$	−26.8424	−	46.4923i	−0.962345	−	1.66683i
$779$	−27.6281	−	15.9511i	−0.989881	−	0.571508i
$780$	−47.7200	+	19.2908i	−1.70865	+	0.690722i
$781$	−12.0947	−	20.9486i	−0.432783	−	0.749602i
$782$	58.1521			2.07951
$783$	−3.72744	−	2.78921i	−0.133208	−	0.0996782i
$784$	−4.35609	+	17.1706i	−0.155575	+	0.613237i
$785$		−	30.6929i		−	1.09548i
$786$	31.6122	+	40.8558i	1.12757	+	1.45728i
$787$			5.94642i			0.211967i	0.994368	+	0.105983i	$0.0337991\pi$
$787$			5.94642i			0.211967i	−0.994368	+	0.105983i	$0.966201\pi$
$788$	−14.9977	+	8.65890i	−0.534270	+	0.308461i
$789$	−5.88208	−	7.60203i	−0.209408	−	0.270640i
$790$	27.6432	−	15.9598i	0.983502	−	0.567825i
$791$	1.55951	+	11.2643i	0.0554498	+	0.400511i
$792$	−18.1681	+	5.02545i	−0.645575	+	0.178572i
$793$	9.88105	−	2.51499i	0.350886	−	0.0893099i
$794$	−24.4774	−	42.3962i	−0.868672	−	1.50458i
$795$	−8.94438	+	21.8423i	−0.317224	+	0.774665i
$796$		−	32.8207i		−	1.16330i
$797$	12.4919	−	21.6366i	0.442486	−	0.766409i	−0.555387	−	0.831592i	$-0.687430\pi$
$797$	12.4919	−	21.6366i	0.442486	−	0.766409i	0.997873	+	0.0651832i	$0.0207632\pi$
$798$	24.5784	−	25.1103i	0.870065	−	0.888894i
$799$	0.810752	−	1.40426i	0.0286823	−	0.0496793i
$800$	−0.306800	+	0.177131i	−0.0108470	+	0.00626254i
$801$	−27.0067	−	26.5747i	−0.954235	−	0.938972i
$802$	−77.9648			−2.75303
$803$	−4.98202			−0.175812
$804$	−35.5678	+	27.5206i	−1.25438	+	0.970578i
$805$	3.94916	+	28.5246i	0.139190	+	1.00536i
$806$	−5.74031	−	22.5529i	−0.202194	−	0.794392i
$807$	14.6946	+	6.01743i	0.517275	+	0.211823i
$808$	−63.4048	−	36.6068i	−2.23057	−	1.28782i
$809$	−19.3679	−	11.1821i	−0.680939	−	0.393140i	0.119270	−	0.992862i	$-0.461945\pi$
$809$	−19.3679	−	11.1821i	−0.680939	−	0.393140i	−0.800209	+	0.599722i	$0.795278\pi$
$810$	23.0752	−	41.4986i	0.810780	−	1.45811i
$811$		−	27.6233i		−	0.969986i	−0.874518	−	0.484993i	$-0.838822\pi$
$811$		−	27.6233i		−	0.969986i	0.874518	−	0.484993i	$-0.161178\pi$
$812$	−8.22235	−	3.34170i	−0.288548	−	0.117271i
$813$	−4.47935	+	10.9386i	−0.157098	+	0.383634i
$814$	18.0957	−	31.3427i	0.634255	−	1.09856i
$815$	−24.7268			−0.866141
$816$	−19.9051	−	8.15110i	−0.696817	−	0.285346i
$817$		−	5.25127i		−	0.183719i
$818$	63.3370			2.21453
$819$	10.8943	−	26.4635i	0.380678	−	0.924708i
$820$	−82.1892			−2.87017
$821$			13.4264i			0.468586i	0.972166	+	0.234293i	$0.0752775\pi$
$821$			13.4264i			0.468586i	−0.972166	+	0.234293i	$0.924723\pi$
$822$	−36.2825	−	14.8577i	−1.26550	−	0.518220i
$823$	6.11903			0.213296			0.106648	−	0.994297i	$-0.465988\pi$
$823$	6.11903			0.213296			0.106648	+	0.994297i	$0.465988\pi$
$824$	−6.67187	+	11.5560i	−0.232426	+	0.402573i
$825$	−0.152262	+	0.371826i	−0.00530109	+	0.0129453i
$826$	−69.3058	+	53.9189i	−2.41146	+	1.87608i
$827$			32.0820i			1.11560i	0.829975	+	0.557801i	$0.188355\pi$
$827$			32.0820i			1.11560i	−0.829975	+	0.557801i	$0.811645\pi$
$828$	−38.9541	+	39.5873i	−1.35375	+	1.37575i
$829$	−33.3697	−	19.2660i	−1.15898	−	0.669136i	−0.207919	−	0.978146i	$-0.566669\pi$
$829$	−33.3697	−	19.2660i	−1.15898	−	0.669136i	−0.951059	+	0.309010i	$0.900002\pi$
$830$	−12.5332	−	7.23606i	−0.435035	−	0.251167i
$831$	−4.75589	−	1.94753i	−0.164980	−	0.0675592i
$832$	36.6604	+	10.3185i	1.27097	+	0.357731i
$833$	8.44691	−	33.2956i	0.292668	−	1.15363i
$834$	−14.7998	+	11.4514i	−0.512476	+	0.396529i
$835$	−12.3554			−0.427575
$836$	18.0048			0.622708
$837$	11.2040	+	8.38387i	0.387268	+	0.289789i
$838$	−29.9996	+	17.3203i	−1.03632	+	0.598319i
$839$	−20.9048	+	36.2081i	−0.721713	+	1.25004i	0.238599	+	0.971118i	$0.423312\pi$
$839$	−20.9048	+	36.2081i	−0.721713	+	1.25004i	−0.960313	+	0.278926i	$0.910022\pi$
$840$	10.4776	−	40.8471i	0.361513	−	1.40936i
$841$	−14.0986	+	24.4196i	−0.486160	+	0.842054i
$842$			71.0807i			2.44960i
$843$	17.0455	−	41.6252i	0.587078	−	1.43365i
$844$	−1.85078	−	3.20565i	−0.0637065	−	0.110343i
$845$	25.1345	−	13.6811i	0.864654	−	0.470645i
$846$	0.633398	+	2.28987i	0.0217767	+	0.0787273i
$847$	−8.70707	+	21.4240i	−0.299178	+	0.736137i
$848$	−13.5671	+	7.83297i	−0.465896	+	0.268985i
$849$	−11.5487	−	14.9256i	−0.396351	−	0.512246i
$850$	−1.57194	+	0.907560i	−0.0539171	+	0.0311291i
$851$		−	49.6732i		−	1.70278i
$852$	63.8674	+	82.5425i	2.18806	+	2.82786i
$853$		−	22.5503i		−	0.772109i	−0.922476	−	0.386054i	$-0.873838\pi$
$853$		−	22.5503i		−	0.772109i	0.922476	−	0.386054i	$-0.126162\pi$
$854$	−6.75153	+	16.6123i	−0.231033	+	0.568462i
$855$	−14.8182	+	15.0591i	−0.506772	+	0.515010i
$856$	−8.60669			−0.294171
$857$	−7.35349	−	12.7366i	−0.251191	−	0.435075i	0.712663	−	0.701506i	$-0.247489\pi$
$857$	−7.35349	−	12.7366i	−0.251191	−	0.435075i	−0.963854	+	0.266431i	$0.914155\pi$
$858$	20.8576	−	8.43169i	0.712067	−	0.287853i
$859$	−13.1023	−	7.56462i	−0.447045	−	0.258101i	0.259537	−	0.965733i	$-0.416430\pi$
$859$	−13.1023	−	7.56462i	−0.447045	−	0.258101i	−0.706581	+	0.707632i	$0.749764\pi$
$860$	−6.76439	−	11.7163i	−0.230664	−	0.399521i
$861$	31.9650	−	32.6567i	1.08936	−	1.11294i
$862$	−14.4457	+	25.0207i	−0.492023	+	0.852208i
$863$	29.5253	+	17.0464i	1.00505	+	0.580267i	0.909739	−	0.415180i	$-0.136282\pi$
$863$	29.5253	+	17.0464i	1.00505	+	0.580267i	0.0953128	+	0.995447i	$0.469615\pi$
$864$	−10.9636	+	4.69739i	−0.372989	+	0.159808i
$865$	52.6256			1.78932
$866$	−32.4999	+	56.2916i	−1.10439	+	1.91287i
$867$	11.3493	+	4.64752i	0.385442	+	0.157838i
$868$	24.7149	+	10.0446i	0.838880	+	0.340935i
$869$	−7.87558	+	4.54697i	−0.267161	+	0.154245i
$870$	7.57655	+	3.10259i	0.256869	+	0.105188i
$871$	17.9005	−	17.4562i	0.606535	−	0.591481i
$872$	−18.4028	+	10.6248i	−0.623197	+	0.359803i
$873$	−10.6843	−	38.6259i	−0.361608	−	1.30729i
$874$	32.8326	−	18.9559i	1.11058	−	0.641192i
$875$	−18.4330	−	23.6933i	−0.623150	−	0.800980i
$876$	21.2997	−	2.89156i	0.719651	−	0.0976966i
$877$	−19.5195	−	33.8088i	−0.659128	−	1.14164i	−0.980842	−	0.194806i	$-0.937592\pi$
$877$	−19.5195	−	33.8088i	−0.659128	−	1.14164i	0.321714	−	0.946837i	$-0.395741\pi$
$878$	−10.0806			−0.340205
$879$	15.6277	−	12.0919i	0.527108	−	0.407850i
$880$	7.25147	−	4.18664i	0.244447	−	0.141131i
$881$	12.3427	+	21.3781i	0.415835	+	0.720248i	0.995516	−	0.0945959i	$-0.0301559\pi$
$881$	12.3427	+	21.3781i	0.415835	+	0.720248i	−0.579680	+	0.814844i	$0.696823\pi$
$882$	26.0927	+	43.0391i	0.878588	+	1.44920i
$883$	17.3258			0.583059			0.291529	−	0.956562i	$-0.405836\pi$
$883$	17.3258			0.583059			0.291529	+	0.956562i	$0.405836\pi$
$884$	63.7690	+	17.9486i	2.14478	+	0.603677i
$885$	41.7574	−	32.3099i	1.40366	−	1.08608i
$886$	15.1185	−	26.1860i	0.507915	−	0.879735i
$887$	−20.6414			−0.693070			−0.346535	−	0.938037i	$-0.612642\pi$
$887$	−20.6414			−0.693070			−0.346535	+	0.938037i	$0.612642\pi$
$888$	−27.5656	+	67.3154i	−0.925041	+	2.25896i
$889$	−17.6176	+	43.3487i	−0.590876	+	1.45387i
$890$	57.7052	+	33.3161i	1.93428	+	1.11676i
$891$	−6.57414	+	11.8230i	−0.220242	+	0.396084i
$892$	68.9017	−	39.7804i	2.30700	−	1.33195i
$893$		−	1.05713i		−	0.0353754i
$894$	10.5212	+	77.5015i	0.351883	+	2.59204i
$895$	−37.3021	+	21.5364i	−1.24687	+	0.719881i
$896$	−43.2786	+	33.6701i	−1.44584	+	1.12484i
$897$	19.0057	−	24.3358i	0.634582	−	0.812550i
$898$	7.17490	−	12.4273i	0.239429	−	0.414704i
$899$	−1.20642	+	2.08959i	−0.0402364	+	0.0696916i
$900$	0.435163	−	1.67805i	0.0145054	−	0.0559349i
$901$	26.3080	−	15.1889i	0.876447	−	0.506017i
$902$	35.9235			1.19612
$903$	7.28609	+	1.86895i	0.242466	+	0.0621946i
$904$	8.98378	−	15.5604i	0.298796	−	0.517530i
$905$	−2.91340	−	1.68205i	−0.0968447	−	0.0559133i
$906$	−33.8999	+	4.60210i	−1.12625	+	0.152894i
$907$	−21.6610	+	37.5179i	−0.719242	+	1.24576i	0.242059	+	0.970262i	$0.422177\pi$
$907$	−21.6610	+	37.5179i	−0.719242	+	1.24576i	−0.961301	+	0.275501i	$0.911156\pi$
$908$	−14.9238			−0.495263
$909$	−50.6397	+	14.0074i	−1.67961	+	0.464596i
$910$	−6.86303	+	49.8582i	−0.227507	+	1.65278i
$911$			13.2577i			0.439246i	0.975585	+	0.219623i	$0.0704827\pi$
$911$			13.2577i			0.439246i	−0.975585	+	0.219623i	$0.929517\pi$
$912$	−13.8954	+	1.88638i	−0.460122	+	0.0624641i
$913$	3.57073	+	2.06156i	0.118174	+	0.0682277i
$914$		−	90.5206i		−	2.99416i
$915$	4.08591	−	9.97783i	0.135076	−	0.329857i
$916$	−4.91263	−	2.83631i	−0.162318	−	0.0937143i
$917$	32.6127	−	4.51515i	1.07697	−	0.149103i
$918$	−56.1737	+	24.0678i	−1.85401	+	0.794356i
$919$	5.47411	+	9.48144i	0.180574	+	0.312764i	0.942076	−	0.335399i	$-0.108871\pi$
$919$	5.47411	+	9.48144i	0.180574	+	0.312764i	−0.761502	+	0.648163i	$0.775538\pi$
$920$	22.7497	−	39.4036i	0.750035	−	1.29910i
$921$	−0.762431	+	1.86186i	−0.0251230	+	0.0613505i
$922$	−32.6616	−	18.8572i	−1.07565	−	0.621028i
$923$	−40.5108	−	41.5418i	−1.33343	−	1.36737i
$924$	−6.40796	+	24.9814i	−0.210806	+	0.821829i
$925$	0.775233	+	1.34274i	0.0254895	+	0.0441491i
$926$			57.3203i			1.88366i
$927$	2.55295	+	9.22948i	0.0838500	+	0.303136i
$928$	−1.02830	−	1.78107i	−0.0337557	−	0.0584666i
$929$	−8.02130	−	13.8933i	−0.263170	−	0.455824i	0.703912	−	0.710287i	$-0.251435\pi$
$929$	−8.02130	−	13.8933i	−0.263170	−	0.455824i	−0.967083	+	0.254463i	$0.918101\pi$
$930$	−22.7738	−	9.32584i	−0.746782	−	0.305806i
$931$	−6.08430	−	21.5521i	−0.199405	−	0.706342i
$932$	−21.9714	−	12.6852i	−0.719698	−	0.415518i
$933$	1.62643	+	11.9806i	0.0532469	+	0.392227i
$934$	−47.3740	−	27.3514i	−1.55012	−	0.894964i
$935$	−14.0613	+	8.11832i	−0.459855	+	0.265497i
$936$	−39.2608	+	22.4321i	−1.28328	+	0.733216i
$937$		−	22.6768i		−	0.740820i	−0.928868	−	0.370410i	$-0.879217\pi$
$937$		−	22.6768i		−	0.740820i	0.928868	−	0.370410i	$-0.120783\pi$
$938$	6.03040	+	43.5572i	0.196899	+	1.42219i
$939$	20.9640	+	27.0940i	0.684136	+	0.884181i
$940$	−1.36173	−	2.35858i	−0.0444147	−	0.0769285i
$941$	8.19499	+	14.1941i	0.267149	+	0.462716i	0.968124	−	0.250470i	$-0.0805851\pi$
$941$	8.19499	+	14.1941i	0.267149	+	0.462716i	−0.700975	+	0.713185i	$0.747252\pi$
$942$	−7.78625	−	57.3549i	−0.253690	−	1.86872i
$943$	42.6998	−	24.6527i	1.39050	−	0.802803i
$944$	35.0438			1.14058
$945$	−15.6205	−	25.9197i	−0.508135	−	0.843168i
$946$	2.95660	+	5.12098i	0.0961273	+	0.166497i
$947$		−	16.4860i		−	0.535723i	−0.963457	−	0.267861i	$-0.913683\pi$
$947$		−	16.4860i		−	0.535723i	0.963457	−	0.267861i	$-0.0863169\pi$
$948$	31.0316	−	24.0108i	1.00786	−	0.779833i
$949$	−11.5814	+	2.94777i	−0.375948	+	0.0956886i
$950$	−0.591676	+	1.02481i	−0.0191965	+	0.0332493i
$951$	7.80692	+	10.0897i	0.253157	+	0.327181i
$952$	−42.8373	+	33.3268i	−1.38837	+	1.08013i
$953$	2.87033	+	1.65718i	0.0929790	+	0.0536815i	0.545769	−	0.837936i	$-0.316238\pi$
$953$	2.87033	+	1.65718i	0.0929790	+	0.0536815i	−0.452790	+	0.891617i	$0.649571\pi$
$954$	−11.1731	+	43.0851i	−0.361743	+	1.39493i
$955$		−	13.5909i		−	0.439791i
$956$			57.8234i			1.87014i
$957$	−2.15857	−	0.883930i	−0.0697765	−	0.0285734i
$958$	4.96436	+	2.86617i	0.160391	+	0.0926018i
$959$	−19.7225	+	15.3438i	−0.636873	+	0.495477i
$960$	31.8519	−	24.6455i	1.02802	−	0.795429i
$961$	−11.8737	+	20.5659i	−0.383023	+	0.663415i
$962$	23.5211	−	83.5674i	0.758351	−	2.69432i
$963$	−4.33212	+	4.40254i	−0.139601	+	0.141870i
$964$			26.3557i			0.848861i
$965$	11.5095	+	19.9350i	0.370503	+	0.641731i
$966$	14.6159	+	52.3013i	0.470259	+	1.68277i
$967$	18.2322			0.586308			0.293154	−	0.956065i	$-0.405295\pi$
$967$	18.2322			0.586308			0.293154	+	0.956065i	$0.405295\pi$
$968$	31.6439	−	18.2696i	1.01707	−	0.587207i
$969$	26.9446	−	3.65788i	0.865585	−	0.117508i
$970$	35.2394	+	61.0365i	1.13147	+	1.95976i
$971$	−6.65694	−	11.5302i	−0.213631	−	0.370020i	0.739217	−	0.673467i	$-0.235196\pi$
$971$	−6.65694	−	11.5302i	−0.213631	−	0.370020i	−0.952848	+	0.303447i	$0.901862\pi$
$972$	21.2446	−	54.3627i	0.681420	−	1.74368i
$973$	1.63559	+	11.8138i	0.0524347	+	0.378733i
$974$		−	96.0803i		−	3.07861i
$975$	−0.133952	+	0.954451i	−0.00428990	+	0.0305669i
$976$	6.19763	−	3.57820i	0.198381	−	0.114536i
$977$	27.7242	+	16.0066i	0.886977	+	0.512096i	0.872952	−	0.487805i	$-0.162202\pi$
$977$	27.7242	+	16.0066i	0.886977	+	0.512096i	0.0140243	+	0.999902i	$0.495536\pi$
$978$	−46.2062	+	6.27275i	−1.47751	+	0.200580i
$979$	−16.4402	−	9.49178i	−0.525433	−	0.303359i
$980$	−41.3370	−	40.2481i	−1.32046	−	1.28568i
$981$	−3.82804	+	14.7614i	−0.122220	+	0.471296i
$982$	−4.67426	−	8.09605i	−0.149162	−	0.258355i
$983$	6.83560	+	11.8396i	0.218022	+	0.377625i	0.954203	−	0.299159i	$-0.0967062\pi$
$983$	6.83560	+	11.8396i	0.218022	+	0.377625i	−0.736181	+	0.676784i	$0.763373\pi$
$984$	−71.5461	+	9.71277i	−2.28081	+	0.309632i
$985$		−	10.1815i		−	0.324408i
$986$	−5.26868	−	9.12562i	−0.167789	−	0.290619i
$987$	1.46675	+	0.376235i	0.0466872	+	0.0119757i
$988$	41.8546	−	10.6531i	1.33157	−	0.338920i
$989$	7.02861	+	4.05797i	0.223497	+	0.129036i
$990$	5.97190	−	23.0285i	0.189800	−	0.731893i
$991$	7.32083	−	12.6801i	0.232554	−	0.402795i	−0.726005	−	0.687689i	$-0.758625\pi$
$991$	7.32083	−	12.6801i	0.232554	−	0.402795i	0.958559	+	0.284894i	$0.0919585\pi$
$992$	3.09090	+	5.35360i	0.0981362	+	0.169977i
$993$	−0.537171	−	3.95690i	−0.0170466	−	0.125568i
$994$	101.084	−	13.9948i	3.20618	−	0.443888i
$995$	16.7107	+	9.64795i	0.529766	+	0.305861i
$996$	−16.4626	−	6.74140i	−0.521636	−	0.213609i
$997$		−	46.0995i		−	1.45999i	−0.683454	−	0.729994i	$-0.739523\pi$
$997$		−	46.0995i		−	1.45999i	0.683454	−	0.729994i	$-0.260477\pi$
$998$	−67.6677	−	39.0679i	−2.14198	−	1.23667i
$999$	20.5586	+	47.9833i	0.650445	+	1.51812i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	273.2.r.b.68.3	✓	64
3.2	odd	2	inner	273.2.r.b.68.30	yes	64
7.3	odd	6		273.2.bf.b.185.30	yes	64
13.9	even	3		273.2.bf.b.152.3	yes	64
21.17	even	6		273.2.bf.b.185.3	yes	64
39.35	odd	6		273.2.bf.b.152.30	yes	64
91.87	odd	6	inner	273.2.r.b.269.3	yes	64
273.269	even	6	inner	273.2.r.b.269.30	yes	64

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
273.2.r.b.68.3	✓	64	1.1	even	1	trivial
273.2.r.b.68.30	yes	64	3.2	odd	2	inner
273.2.r.b.269.3	yes	64	91.87	odd	6	inner
273.2.r.b.269.30	yes	64	273.269	even	6	inner
273.2.bf.b.152.3	yes	64	13.9	even	3
273.2.bf.b.152.30	yes	64	39.35	odd	6
273.2.bf.b.185.3	yes	64	21.17	even	6
273.2.bf.b.185.30	yes	64	7.3	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:	\( N \)	\(=\)	\( 273 = 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	273.r (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-2.39671i q^{2} +(1.60287 + 0.656371i) q^{3} -3.74420 q^{4} +(1.10064 - 1.90637i) q^{5} +(1.57313 - 3.84160i) q^{6} +(-1.62460 - 2.08822i) q^{7} +4.18035i q^{8} +(2.13835 + 2.10415i) q^{9} +(-4.56901 - 2.63792i) q^{10} +(1.30172 + 0.751546i) q^{11} +(-6.00145 - 2.45759i) q^{12} +(3.47069 + 0.976871i) q^{13} +(-5.00485 + 3.89370i) q^{14} +(3.01547 - 2.33322i) q^{15} +2.53065 q^{16} -4.90720 q^{17} +(5.04303 - 5.12501i) q^{18} +(-2.77060 + 1.59960i) q^{19} +(-4.12104 + 7.13784i) q^{20} +(-1.23337 - 4.41348i) q^{21} +(1.80123 - 3.11983i) q^{22} -4.94443i q^{23} +(-2.74386 + 6.70053i) q^{24} +(0.0771661 + 0.133656i) q^{25} +(2.34127 - 8.31824i) q^{26} +(2.04639 + 4.77622i) q^{27} +(6.08284 + 7.81872i) q^{28} +(-0.775914 + 0.447974i) q^{29} +(-5.59206 - 7.22720i) q^{30} +(2.33226 - 1.34653i) q^{31} +2.29545i q^{32} +(1.59318 + 2.05904i) q^{33} +11.7611i q^{34} +(-5.76903 + 0.798709i) q^{35} +(-8.00643 - 7.87837i) q^{36} +10.0463 q^{37} +(3.83378 + 6.64031i) q^{38} +(4.92187 + 3.84386i) q^{39} +(7.96929 + 4.60107i) q^{40} +(4.98596 + 8.63593i) q^{41} +(-10.5778 + 2.95603i) q^{42} +(-0.820714 + 1.42152i) q^{43} +(-4.87389 - 2.81394i) q^{44} +(6.36486 - 1.76057i) q^{45} -11.8504 q^{46} +(-0.165217 + 0.286164i) q^{47} +(4.05630 + 1.66105i) q^{48} +(-1.72133 + 6.78506i) q^{49} +(0.320334 - 0.184945i) q^{50} +(-7.86558 - 3.22095i) q^{51} +(-12.9950 - 3.65760i) q^{52} +(-5.36111 + 3.09524i) q^{53} +(11.4472 - 4.90459i) q^{54} +(2.86545 - 1.65437i) q^{55} +(8.72948 - 6.79140i) q^{56} +(-5.49083 + 0.745410i) q^{57} +(1.07366 + 1.85964i) q^{58} +13.8477 q^{59} +(-11.2905 + 8.73607i) q^{60} +(2.44902 - 1.41394i) q^{61} +(-3.22724 - 5.58975i) q^{62} +(0.919954 - 7.88376i) q^{63} +10.5628 q^{64} +(5.68228 - 5.54125i) q^{65} +(4.93490 - 3.81839i) q^{66} +(3.46728 - 6.00551i) q^{67} +18.3736 q^{68} +(3.24539 - 7.92526i) q^{69} +(1.91427 + 13.8267i) q^{70} +(-13.9370 - 8.04655i) q^{71} +(-8.79607 + 8.93905i) q^{72} +(-2.87045 + 1.65726i) q^{73} -24.0780i q^{74} +(0.0359591 + 0.264882i) q^{75} +(10.3737 - 5.98924i) q^{76} +(-0.545377 - 3.93923i) q^{77} +(9.21260 - 11.7963i) q^{78} +(-3.02508 + 5.23959i) q^{79} +(2.78535 - 4.82437i) q^{80} +(0.145107 + 8.99883i) q^{81} +(20.6978 - 11.9499i) q^{82} +2.74309 q^{83} +(4.61799 + 16.5250i) q^{84} +(-5.40108 + 9.35495i) q^{85} +(3.40696 + 1.96701i) q^{86} +(-1.53772 + 0.208754i) q^{87} +(-3.14172 + 5.44162i) q^{88} -12.6297 q^{89} +(-4.21958 - 15.2547i) q^{90} +(-3.59858 - 8.83460i) q^{91} +18.5130i q^{92} +(4.62213 - 0.627479i) q^{93} +(0.685851 + 0.395976i) q^{94} +7.04238i q^{95} +(-1.50667 + 3.67930i) q^{96} +(-11.5690 - 6.67939i) q^{97} +(16.2618 + 4.12552i) q^{98} +(1.20216 + 4.34607i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 64 q - 64 q^{4} + 12 q^{6} - 10 q^{7} - 4 q^{9} - 6 q^{10} + 6 q^{12} + 12 q^{13} - 9 q^{15} + 32 q^{16} + 2 q^{18} - 36 q^{19} + 10 q^{21} + 10 q^{22} - 18 q^{24} - 24 q^{25} - 14 q^{28} + 8 q^{30} - 24 q^{31}+ \cdots + 22 q^{99}+O(q^{100}) \) 64 * q - 64 * q^4 + 12 * q^6 - 10 * q^7 - 4 * q^9 - 6 * q^10 + 6 * q^12 + 12 * q^13 - 9 * q^15 + 32 * q^16 + 2 * q^18 - 36 * q^19 + 10 * q^21 + 10 * q^22 - 18 * q^24 - 24 * q^25 - 14 * q^28 + 8 * q^30 - 24 * q^31 - 45 * q^33 + 33 * q^39 + 90 * q^40 + 3 * q^42 - 20 * q^43 - 6 * q^48 - 6 * q^49 - 10 * q^51 - 48 * q^52 - 18 * q^55 + 4 * q^57 + 30 * q^58 + 55 * q^60 - 18 * q^61 + 31 * q^63 - 84 * q^64 + 75 * q^66 + 44 * q^67 + 33 * q^69 + 20 * q^70 + 17 * q^72 + 84 * q^73 - 18 * q^76 - 71 * q^78 + 20 * q^79 + 16 * q^81 - 18 * q^82 - 135 * q^84 - 2 * q^85 - 46 * q^88 - 10 * q^91 - 56 * q^93 + 36 * q^94 + 30 * q^96 - 24 * q^97 + 22 * q^99

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