LMFDB - Embedded newform 680.2.cf.a.37.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [680,2,Mod(37,680)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(680, base_ring=CyclotomicField(16)) chi = DirichletCharacter(H, H._module([0, 8, 4, 1])) N = Newforms(chi, 2, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("680.37"); S:= CuspForms(chi, 2); N := Newforms(S);

Level:	$ N $	$=$	$ 680 = 2^{3} \cdot 5 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	680.cf (of order $16$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$5.42982733745$
Analytic rank:	$0$
Dimension:	$832$
Relative dimension:	$104$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			37.12
Character	$\chi$	$=$	680.37
Dual form			680.2.cf.a.533.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.34139 + 0.447975i) q^{2} +(-0.672289 - 1.00615i) q^{3} +(1.59864 - 1.20182i) q^{4} +(2.23426 + 0.0898960i) q^{5} +(1.35253 + 1.04847i) q^{6} +(2.33408 - 0.464277i) q^{7} +(-1.60601 + 2.32825i) q^{8} +(0.587682 - 1.41879i) q^{9} +(-3.03728 + 0.880308i) q^{10} +(5.28016 - 1.05029i) q^{11} +(-2.28395 - 0.800503i) q^{12} +4.10579i q^{13} +(-2.92291 + 1.66838i) q^{14} +(-1.41162 - 2.30844i) q^{15} +(1.11128 - 3.84253i) q^{16} +(2.98518 + 2.84407i) q^{17} +(-0.152726 + 2.16641i) q^{18} +(-2.96469 + 1.22802i) q^{19} +(3.67981 - 2.54146i) q^{20} +(-2.03631 - 2.03631i) q^{21} +(-6.61224 + 3.77423i) q^{22} +(0.120801 - 0.180792i) q^{23} +(3.42227 + 0.0506294i) q^{24} +(4.98384 + 0.401702i) q^{25} +(-1.83929 - 5.50745i) q^{26} +(-5.38312 + 1.07077i) q^{27} +(3.17336 - 3.54734i) q^{28} +(-7.32694 + 4.89570i) q^{29} +(2.92765 + 2.46414i) q^{30} +(0.513010 - 2.57908i) q^{31} +(0.230706 + 5.65215i) q^{32} +(-4.60654 - 4.60654i) q^{33} +(-5.27835 - 2.47771i) q^{34} +(5.25667 - 0.827490i) q^{35} +(-0.765634 - 2.97442i) q^{36} +(-2.88079 + 1.92488i) q^{37} +(3.42668 - 2.97535i) q^{38} +(4.13105 - 2.76028i) q^{39} +(-3.79754 + 5.05754i) q^{40} +(3.19616 - 4.78340i) q^{41} +(3.64369 + 1.81926i) q^{42} +(2.87440 + 6.93943i) q^{43} +(7.17881 - 8.02481i) q^{44} +(1.44058 - 3.11712i) q^{45} +(-0.0810508 + 0.296627i) q^{46} -6.77633i q^{47} +(-4.61327 + 1.46518i) q^{48} +(-1.23480 + 0.511471i) q^{49} +(-6.86521 + 1.69380i) q^{50} +(0.854664 - 4.91557i) q^{51} +(4.93441 + 6.56367i) q^{52} +(4.13689 + 1.71356i) q^{53} +(6.74117 - 3.84782i) q^{54} +(11.8917 - 1.87195i) q^{55} +(-2.66759 + 6.17994i) q^{56} +(3.22870 + 2.15735i) q^{57} +(7.63510 - 9.84932i) q^{58} +(5.56300 - 13.4303i) q^{59} +(-5.03099 - 1.99385i) q^{60} +(-4.86588 + 7.28231i) q^{61} +(0.467217 + 3.68936i) q^{62} +(0.712984 - 3.58441i) q^{63} +(-2.84149 - 7.47837i) q^{64} +(-0.369094 + 9.17341i) q^{65} +(8.24277 + 4.11554i) q^{66} +(-2.81514 - 2.81514i) q^{67} +(8.19026 + 0.959002i) q^{68} -0.263117 q^{69} +(-6.68053 + 3.46484i) q^{70} +(2.46762 + 0.490841i) q^{71} +(2.35948 + 3.64686i) q^{72} +(-1.59686 - 0.317635i) q^{73} +(3.00196 - 3.87254i) q^{74} +(-2.94640 - 5.28455i) q^{75} +(-3.26362 + 5.52617i) q^{76} +(11.8367 - 4.90291i) q^{77} +(-4.30480 + 5.55321i) q^{78} +(11.3771 - 2.26304i) q^{79} +(2.82831 - 8.48532i) q^{80} +(1.43868 + 1.43868i) q^{81} +(-2.14445 + 7.84818i) q^{82} +(3.37733 - 8.15361i) q^{83} +(-5.70258 - 0.808048i) q^{84} +(6.41399 + 6.62275i) q^{85} +(-6.96438 - 8.02079i) q^{86} +(9.85163 + 4.08068i) q^{87} +(-6.03464 + 13.9803i) q^{88} +(0.681248 + 0.681248i) q^{89} +(-0.535982 + 4.82660i) q^{90} +(1.90622 + 9.58323i) q^{91} +(-0.0241612 - 0.434201i) q^{92} +(-2.93983 + 1.21772i) q^{93} +(3.03563 + 9.08967i) q^{94} +(-6.73429 + 2.47719i) q^{95} +(5.53181 - 4.03200i) q^{96} +(-11.6951 - 2.32630i) q^{97} +(1.42722 - 1.23924i) q^{98} +(1.61292 - 8.10868i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) $ 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/680\mathbb{Z}\right)^\times$.

$n$	$137$	$241$	$341$	$511$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{16}\right)$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.34139	+	0.447975i	−0.948504	+	0.316766i
$2$	−1.34139	+	0.447975i	−0.948504	+	0.316766i
$3$	−0.672289	−	1.00615i	−0.388146	−	0.580902i	0.585016	−	0.811022i	$-0.301088\pi$
$3$	−0.672289	−	1.00615i	−0.388146	−	0.580902i	−0.973162	+	0.230120i	$0.926088\pi$
$4$	1.59864	−	1.20182i	0.799318	−	0.600908i
$5$	2.23426	+	0.0898960i	0.999192	+	0.0402027i
$5$	2.23426	+	0.0898960i	0.999192	+	0.0402027i
$6$	1.35253	+	1.04847i	0.552168	+	0.428036i
$7$	2.33408	−	0.464277i	0.882198	−	0.175480i	0.266852	−	0.963737i	$-0.414016\pi$
$7$	2.33408	−	0.464277i	0.882198	−	0.175480i	0.615346	+	0.788257i	$0.289016\pi$
$8$	−1.60601	+	2.32825i	−0.567809	+	0.823160i
$9$	0.587682	−	1.41879i	0.195894	−	0.472930i
$10$	−3.03728	+	0.880308i	−0.960472	+	0.278378i
$11$	5.28016	−	1.05029i	1.59203	−	0.316674i	0.682042	−	0.731313i	$-0.261092\pi$
$11$	5.28016	−	1.05029i	1.59203	−	0.316674i	0.909986	+	0.414638i	$0.136092\pi$
$12$	−2.28395	−	0.800503i	−0.659321	−	0.231085i
$13$			4.10579i			1.13874i	0.822081	+	0.569371i	$0.192813\pi$
$13$			4.10579i			1.13874i	−0.822081	+	0.569371i	$0.807187\pi$
$14$	−2.92291	+	1.66838i	−0.781182	+	0.445894i
$15$	−1.41162	−	2.30844i	−0.364478	−	0.596037i
$16$	1.11128	−	3.84253i	0.277819	−	0.960633i
$17$	2.98518	+	2.84407i	0.724011	+	0.689788i
$17$	2.98518	+	2.84407i	0.724011	+	0.689788i
$18$	−0.152726	+	2.16641i	−0.0359979	+	0.510628i
$19$	−2.96469	+	1.22802i	−0.680147	+	0.281726i	−0.695888	−	0.718150i	$-0.744989\pi$
$19$	−2.96469	+	1.22802i	−0.680147	+	0.281726i	0.0157412	+	0.999876i	$0.494989\pi$
$20$	3.67981	−	2.54146i	0.822830	−	0.568287i
$21$	−2.03631	−	2.03631i	−0.444358	−	0.444358i
$22$	−6.61224	+	3.77423i	−1.40973	+	0.804668i
$23$	0.120801	−	0.180792i	0.0251888	−	0.0376977i	−0.818662	−	0.574276i	$-0.805284\pi$
$23$	0.120801	−	0.180792i	0.0251888	−	0.0376977i	0.843850	+	0.536579i	$0.180284\pi$
$24$	3.42227	+	0.0506294i	0.698568	+	0.0103347i
$25$	4.98384	+	0.401702i	0.996767	+	0.0803405i
$26$	−1.83929	−	5.50745i	−0.360715	−	1.08010i
$27$	−5.38312	+	1.07077i	−1.03598	+	0.206070i
$28$	3.17336	−	3.54734i	0.599709	−	0.670384i
$29$	−7.32694	+	4.89570i	−1.36058	+	0.909109i	−0.999724	−	0.0235130i	$-0.992515\pi$
$29$	−7.32694	+	4.89570i	−1.36058	+	0.909109i	−0.360854	+	0.932622i	$0.617515\pi$
$30$	2.92765	+	2.46414i	0.534513	+	0.449888i
$31$	0.513010	−	2.57908i	0.0921394	−	0.463216i	−0.906977	−	0.421181i	$-0.861616\pi$
$31$	0.513010	−	2.57908i	0.0921394	−	0.463216i	0.999116	−	0.0420352i	$-0.0133842\pi$
$32$	0.230706	+	5.65215i	0.0407835	+	0.999168i
$33$	−4.60654	−	4.60654i	−0.801896	−	0.801896i
$34$	−5.27835	−	2.47771i	−0.905229	−	0.424924i
$35$	5.25667	−	0.827490i	0.888539	−	0.139871i
$36$	−0.765634	−	2.97442i	−0.127606	−	0.495736i
$37$	−2.88079	+	1.92488i	−0.473599	+	0.316449i	−0.769363	−	0.638812i	$-0.779426\pi$
$37$	−2.88079	+	1.92488i	−0.473599	+	0.316449i	0.295763	+	0.955261i	$0.404426\pi$
$38$	3.42668	−	2.97535i	0.555881	−	0.482666i
$39$	4.13105	−	2.76028i	0.661497	−	0.441998i
$40$	−3.79754	+	5.05754i	−0.600443	+	0.799667i
$41$	3.19616	−	4.78340i	0.499157	−	0.747041i	−0.493270	−	0.869876i	$-0.664199\pi$
$41$	3.19616	−	4.78340i	0.499157	−	0.747041i	0.992427	+	0.122835i	$0.0391987\pi$
$42$	3.64369	+	1.81926i	0.562233	+	0.280718i
$43$	2.87440	+	6.93943i	0.438343	+	1.05825i	0.976521	+	0.215422i	$0.0691126\pi$
$43$	2.87440	+	6.93943i	0.438343	+	1.05825i	−0.538179	+	0.842831i	$0.680887\pi$
$44$	7.17881	−	8.02481i	1.08225	−	1.20979i
$45$	1.44058	−	3.11712i	0.214749	−	0.464672i
$46$	−0.0810508	+	0.296627i	−0.0119503	+	0.0437353i
$47$		−	6.77633i		−	0.988429i	−0.869340	−	0.494214i	$-0.835456\pi$
$47$		−	6.77633i		−	0.988429i	0.869340	−	0.494214i	$-0.164544\pi$
$48$	−4.61327	+	1.46518i	−0.665868	+	0.211480i
$49$	−1.23480	+	0.511471i	−0.176400	+	0.0730673i
$50$	−6.86521	+	1.69380i	−0.970887	+	0.239539i
$51$	0.854664	−	4.91557i	0.119677	−	0.688318i
$52$	4.93441	+	6.56367i	0.684279	+	0.910217i
$53$	4.13689	+	1.71356i	0.568246	+	0.235375i	0.648261	−	0.761419i	$-0.275497\pi$
$53$	4.13689	+	1.71356i	0.568246	+	0.235375i	−0.0800148	+	0.996794i	$0.525497\pi$
$54$	6.74117	−	3.84782i	0.917356	−	0.523622i
$55$	11.8917	−	1.87195i	1.60347	−	0.252414i
$56$	−2.66759	+	6.17994i	−0.356472	+	0.825829i
$57$	3.22870	+	2.15735i	0.427652	+	0.285748i
$58$	7.63510	−	9.84932i	1.00254	−	1.29328i
$59$	5.56300	−	13.4303i	0.724241	−	1.74847i	0.0633477	−	0.997992i	$-0.479822\pi$
$59$	5.56300	−	13.4303i	0.724241	−	1.74847i	0.660893	−	0.750480i	$-0.270178\pi$
$60$	−5.03099	−	1.99385i	−0.649497	−	0.257405i
$61$	−4.86588	+	7.28231i	−0.623012	+	0.932404i	0.376969	+	0.926226i	$0.376966\pi$
$61$	−4.86588	+	7.28231i	−0.623012	+	0.932404i	−0.999981	+	0.00617776i	$0.998034\pi$
$62$	0.467217	+	3.68936i	0.0593366	+	0.468549i
$63$	0.712984	−	3.58441i	0.0898275	−	0.451593i
$64$	−2.84149	−	7.47837i	−0.355186	−	0.934796i
$65$	−0.369094	+	9.17341i	−0.0457805	+	1.13782i
$66$	8.24277	+	4.11554i	1.01462	+	0.506588i
$67$	−2.81514	−	2.81514i	−0.343924	−	0.343924i	0.513916	−	0.857840i	$-0.328194\pi$
$67$	−2.81514	−	2.81514i	−0.343924	−	0.343924i	−0.857840	+	0.513916i	$0.828194\pi$
$68$	8.19026	+	0.959002i	0.993215	+	0.116296i
$69$	−0.263117			−0.0316756
$70$	−6.68053	+	3.46484i	−0.798476	+	0.414128i
$71$	2.46762	+	0.490841i	0.292853	+	0.0582521i	0.339330	−	0.940667i	$-0.389800\pi$
$71$	2.46762	+	0.490841i	0.292853	+	0.0582521i	−0.0464774	+	0.998919i	$0.514800\pi$
$72$	2.35948	+	3.64686i	0.278067	+	0.429786i
$73$	−1.59686	−	0.317635i	−0.186898	−	0.0371764i	0.100754	−	0.994911i	$-0.467875\pi$
$73$	−1.59686	−	0.317635i	−0.186898	−	0.0371764i	−0.287652	+	0.957735i	$0.592875\pi$
$74$	3.00196	−	3.87254i	0.348970	−	0.450173i
$75$	−2.94640	−	5.28455i	−0.340222	−	0.610208i
$76$	−3.26362	+	5.52617i	−0.374363	+	0.633895i
$77$	11.8367	−	4.90291i	1.34891	−	0.558738i
$78$	−4.30480	+	5.55321i	−0.487422	+	0.628777i
$79$	11.3771	−	2.26304i	1.28002	−	0.254612i	0.492180	−	0.870493i	$-0.336200\pi$
$79$	11.3771	−	2.26304i	1.28002	−	0.254612i	0.787839	+	0.615882i	$0.211200\pi$
$80$	2.82831	−	8.48532i	0.316215	−	0.948688i
$81$	1.43868	+	1.43868i	0.159853	+	0.159853i
$82$	−2.14445	+	7.84818i	−0.236815	+	0.866687i
$83$	3.37733	−	8.15361i	0.370711	−	0.894974i	−0.622920	−	0.782286i	$-0.714054\pi$
$83$	3.37733	−	8.15361i	0.370711	−	0.894974i	0.993630	−	0.112689i	$-0.0359463\pi$
$84$	−5.70258	−	0.808048i	−0.622202	−	0.0881653i
$85$	6.41399	+	6.62275i	0.695695	+	0.718338i
$86$	−6.96438	−	8.02079i	−0.750988	−	0.864904i
$87$	9.85163	+	4.08068i	1.05621	+	0.437495i
$88$	−6.03464	+	13.9803i	−0.643294	+	1.49031i
$89$	0.681248	+	0.681248i	0.0722121	+	0.0722121i	0.742290	−	0.670078i	$-0.233739\pi$
$89$	0.681248	+	0.681248i	0.0722121	+	0.0722121i	−0.670078	+	0.742290i	$0.733739\pi$
$90$	−0.535982	+	4.82660i	−0.0564975	+	0.508768i
$91$	1.90622	+	9.58323i	0.199826	+	1.00460i
$92$	−0.0241612	−	0.434201i	−0.00251898	−	0.0452686i
$93$	−2.93983	+	1.21772i	−0.304846	+	0.126272i
$94$	3.03563	+	9.08967i	0.313101	+	0.937528i
$95$	−6.73429	+	2.47719i	−0.690924	+	0.254155i
$96$	5.53181	−	4.03200i	0.564588	−	0.411514i
$97$	−11.6951	−	2.32630i	−1.18746	−	0.236200i	−0.438447	−	0.898757i	$-0.644471\pi$
$97$	−11.6951	−	2.32630i	−1.18746	−	0.236200i	−0.749012	+	0.662557i	$0.769471\pi$
$98$	1.42722	−	1.23924i	0.144171	−	0.125182i
$99$	1.61292	−	8.10868i	0.162104	−	0.814953i
$100$	8.45012	−	5.34748i	0.845012	−	0.534748i
$101$	6.26011			0.622904			0.311452	−	0.950262i	$-0.399185\pi$
$101$	6.26011			0.622904			0.311452	+	0.950262i	$0.399185\pi$
$102$	1.05562	+	6.97655i	0.104522	+	0.690782i
$103$	−4.11894	+	4.11894i	−0.405851	+	0.405851i	−0.880289	−	0.474438i	$-0.842651\pi$
$103$	−4.11894	+	4.11894i	−0.405851	+	0.405851i	0.474438	+	0.880289i	$0.342651\pi$
$104$	−9.55931	−	6.59393i	−0.937367	−	0.646588i
$105$	−4.36658	−	4.73269i	−0.426135	−	0.461863i
$106$	−6.31680	−	0.445317i	−0.613542	−	0.0432531i
$107$	−10.4754	−	2.08369i	−1.01270	−	0.201438i	−0.339268	−	0.940690i	$-0.610179\pi$
$107$	−10.4754	−	2.08369i	−1.01270	−	0.201438i	−0.673429	+	0.739252i	$0.735179\pi$
$108$	−7.31878	+	8.18129i	−0.704250	+	0.787245i
$109$	−6.00168	+	8.98215i	−0.574857	+	0.860334i	−0.998975	−	0.0452732i	$-0.985584\pi$
$109$	−6.00168	+	8.98215i	−0.574857	+	0.860334i	0.424118	+	0.905607i	$0.360584\pi$
$110$	−15.1127	+	7.83819i	−1.44094	+	0.747342i
$111$	3.87345	+	1.60443i	0.367651	+	0.152286i
$112$	0.809808	−	9.48470i	0.0765197	−	0.896220i
$113$	−7.29212	−	4.87244i	−0.685985	−	0.458361i	0.163105	−	0.986609i	$-0.447849\pi$
$113$	−7.29212	−	4.87244i	−0.685985	−	0.458361i	−0.849090	+	0.528248i	$0.822849\pi$
$114$	−5.29737	−	1.44746i	−0.496145	−	0.135567i
$115$	0.286154	−	0.393076i	0.0266840	−	0.0366545i
$116$	−5.82938	+	16.6321i	−0.541244	+	1.54425i
$117$	5.82526	+	2.41290i	0.538545	+	0.223073i
$118$	−1.44571	+	20.5073i	−0.133088	+	1.88785i
$119$	8.28806	+	5.25233i	0.759765	+	0.481480i
$120$	7.64169	+	0.420768i	0.697588	+	0.0384107i
$121$	16.6143	−	6.88188i	1.51039	−	0.625625i
$122$	3.26474	−	11.9482i	0.295575	−	1.08174i
$123$	−6.96156			−0.627703
$124$	−2.27946	−	4.73955i	−0.204701	−	0.425624i
$125$	11.0991	+	1.34553i	0.992732	+	0.120348i
$126$	0.649340	+	5.12748i	0.0578478	+	0.456792i
$127$	−15.2295	+	6.30827i	−1.35140	+	0.559768i	−0.936682	−	0.350182i	$-0.886120\pi$
$127$	−15.2295	+	6.30827i	−1.35140	+	0.559768i	−0.414718	+	0.909950i	$0.636120\pi$
$128$	7.16166	+	8.75846i	0.633007	+	0.774146i
$129$	5.04968	−	7.55738i	0.444600	−	0.665391i
$130$	−3.61436	−	12.4704i	−0.317000	−	1.09373i
$131$	−5.07745	−	7.59894i	−0.443619	−	0.663922i	0.540518	−	0.841332i	$-0.318228\pi$
$131$	−5.07745	−	7.59894i	−0.443619	−	0.663922i	−0.984137	+	0.177410i	$0.943228\pi$
$132$	−12.9004	−	1.82797i	−1.12284	−	0.159105i
$133$	−6.34968	+	4.24272i	−0.550587	+	0.367890i
$134$	5.03730	+	2.51508i	0.435157	+	0.217270i
$135$	−12.1235	+	1.90846i	−1.04343	+	0.164254i
$136$	−11.4159	+	2.38264i	−0.978906	+	0.204310i
$137$	−10.5339	−	10.5339i	−0.899969	−	0.899969i	0.0954638	−	0.995433i	$-0.469567\pi$
$137$	−10.5339	−	10.5339i	−0.899969	−	0.899969i	−0.995433	+	0.0954638i	$0.969567\pi$
$138$	0.352942	−	0.117870i	0.0300444	−	0.0100337i
$139$	−18.6171	−	3.70317i	−1.57908	−	0.314099i	−0.673802	−	0.738912i	$-0.735340\pi$
$139$	−18.6171	−	3.70317i	−1.57908	−	0.314099i	−0.905281	+	0.424813i	$0.860340\pi$
$140$	7.40901	−	7.64040i	0.626176	−	0.645732i
$141$	−6.81801	+	4.55565i	−0.574180	+	0.383655i
$142$	−3.52992	+	0.447026i	−0.296224	+	0.0375136i
$143$	4.31227	+	21.6792i	0.360610	+	1.81291i
$144$	−4.79867	−	3.83486i	−0.399889	−	0.319572i
$145$	−16.8104	+	10.2796i	−1.39603	+	0.853675i
$146$	2.28430	−	0.289282i	0.189050	−	0.0239411i
$147$	1.34476	+	0.898540i	0.110914	+	0.0741103i
$148$	−2.29198	+	6.53937i	−0.188400	+	0.537533i
$149$	−6.81551	−	6.81551i	−0.558348	−	0.558348i	0.370489	−	0.928837i	$-0.379190\pi$
$149$	−6.81551	−	6.81551i	−0.558348	−	0.558348i	−0.928837	+	0.370489i	$0.879190\pi$
$150$	6.31962	+	5.76871i	0.515995	+	0.471014i
$151$	−1.46741	−	3.54264i	−0.119416	−	0.288296i	0.852857	−	0.522145i	$-0.174868\pi$
$151$	−1.46741	−	3.54264i	−0.119416	−	0.288296i	−0.972273	+	0.233849i	$0.924868\pi$
$152$	1.90219	−	8.87475i	0.154288	−	0.719837i
$153$	5.78947	−	2.56393i	0.468051	−	0.207281i
$154$	−13.6812	+	11.8792i	−1.10246	+	0.957256i
$155$	1.37805	−	5.71621i	0.110687	−	0.459137i
$156$	3.28670	−	9.37744i	0.263146	−	0.750796i
$157$		−	5.55597i		−	0.443415i	−0.975113	−	0.221707i	$-0.928837\pi$
$157$		−	5.55597i		−	0.443415i	0.975113	−	0.221707i	$-0.0711630\pi$
$158$	−14.2472	+	8.13225i	−1.13345	+	0.646967i
$159$	−1.05709	−	5.31434i	−0.0838326	−	0.421455i
$160$	0.00735200	+	12.6491i	0.000581227	+	1.00000i
$161$	0.198022	−	0.478066i	0.0156063	−	0.0376769i
$162$	−2.57432	−	1.28533i	−0.202258	−	0.100985i
$163$	−2.41479	−	12.1400i	−0.189141	−	0.950875i	−0.952416	−	0.304802i	$-0.901410\pi$
$163$	−2.41479	−	12.1400i	−0.189141	−	0.950875i	0.763275	−	0.646074i	$-0.223590\pi$
$164$	−0.639258	−	11.4881i	−0.0499176	−	0.897071i
$165$	−9.87811	−	10.7063i	−0.769010	−	0.833486i
$166$	−0.877698	+	12.4501i	−0.0681226	+	0.966315i
$167$	8.73814	−	5.83864i	0.676178	−	0.451807i	−0.169480	−	0.985534i	$-0.554209\pi$
$167$	8.73814	−	5.83864i	0.676178	−	0.451807i	0.845657	+	0.533726i	$0.179209\pi$
$168$	8.01134	−	1.47071i	0.618089	−	0.113468i
$169$	−3.85753			−0.296733
$170$	−11.5705	−	6.01036i	−0.887414	−	0.460973i
$171$			4.92796i			0.376851i
$172$	12.9350	+	7.63912i	0.986288	+	0.582477i
$173$	−5.65262	−	8.45974i	−0.429760	−	0.643182i	0.551880	−	0.833924i	$-0.313911\pi$
$173$	−5.65262	−	8.45974i	−0.429760	−	0.643182i	−0.981640	+	0.190742i	$0.938911\pi$
$174$	−15.0429	−	1.06048i	−1.14040	−	0.0803950i
$175$	11.8192	−	1.37628i	0.893444	−	0.104037i
$176$	1.83195	−	21.4564i	0.138089	−	1.61733i
$177$	−17.2528	+	3.43180i	−1.29680	+	0.257950i
$178$	−1.21900	−	0.608635i	−0.0913678	−	0.0456191i
$179$	11.9459	+	4.94815i	0.892877	+	0.369842i	0.781477	−	0.623934i	$-0.214467\pi$
$179$	11.9459	+	4.94815i	0.892877	+	0.369842i	0.111400	+	0.993776i	$0.464467\pi$
$180$	−1.44324	−	6.71445i	−0.107573	−	0.500465i
$181$	23.8958	−	4.75317i	1.77616	−	0.353301i	0.805286	−	0.592886i	$-0.202012\pi$
$181$	23.8958	−	4.75317i	1.77616	−	0.353301i	0.970875	+	0.239586i	$0.0770115\pi$
$182$	−6.85003	−	12.0009i	−0.507758	−	0.889564i
$183$	10.5984			0.783455
$184$	0.226921	+	0.571607i	0.0167288	+	0.0421395i
$185$	−6.60948	+	4.04172i	−0.485938	+	0.297153i
$186$	3.39794	−	2.95040i	0.249149	−	0.216334i
$187$	18.7493	+	11.8818i	1.37108	+	0.868887i
$188$	−8.14389	−	10.8329i	−0.593955	−	0.790069i
$189$	−12.0675	+	4.99851i	−0.877780	+	0.363588i
$190$	7.92357	−	6.33967i	0.574836	−	0.459928i
$191$	−10.9978	+	10.9978i	−0.795776	+	0.795776i	−0.982426	−	0.186651i	$-0.940237\pi$
$191$	−10.9978	+	10.9978i	−0.795776	+	0.795776i	0.186651	+	0.982426i	$0.440237\pi$
$192$	−5.61407	+	7.88659i	−0.405160	+	0.569165i
$193$	−10.5866	+	15.8440i	−0.762040	+	1.14047i	0.224101	+	0.974566i	$0.428055\pi$
$193$	−10.5866	+	15.8440i	−0.762040	+	1.14047i	−0.986141	+	0.165908i	$0.946945\pi$
$194$	16.7298	−	2.11865i	1.20113	−	0.152110i
$195$	9.47797	−	5.79581i	0.678732	−	0.415047i
$196$	−1.35930	+	2.30166i	−0.0970931	+	0.164404i
$197$	5.15513	−	1.02542i	0.367288	−	0.0730581i	−0.00799587	−	0.999968i	$-0.502545\pi$
$197$	5.15513	−	1.02542i	0.367288	−	0.0730581i	0.375284	+	0.926910i	$0.377545\pi$
$198$	1.46894	+	11.5994i	0.104393	+	0.824335i
$199$	−1.43987	−	2.15492i	−0.102070	−	0.152758i	0.776919	−	0.629600i	$-0.216781\pi$
$199$	−1.43987	−	2.15492i	−0.102070	−	0.152758i	−0.878989	+	0.476842i	$0.841781\pi$
$200$	−8.93934	+	10.9585i	−0.632107	+	0.774881i
$201$	−0.939869	+	4.72504i	−0.0662933	+	0.333279i
$202$	−8.39723	+	2.80437i	−0.590827	+	0.197315i
$203$	−14.8287	+	14.8287i	−1.04077	+	1.04077i
$204$	−4.54132	−	8.88536i	−0.317956	−	0.622100i
$205$	7.57107	−	10.4000i	0.528786	−	0.726369i
$206$	3.67991	−	7.37027i	0.256391	−	0.513511i
$207$	−0.185513	−	0.277639i	−0.0128940	−	0.0192973i
$208$	15.7766	+	4.56267i	1.09391	+	0.316365i
$209$	−14.3643	+	9.59791i	−0.993599	+	0.663901i
$210$	7.97740	+	4.39225i	0.550493	+	0.303094i
$211$	−5.92420	−	3.95842i	−0.407839	−	0.272509i	0.334683	−	0.942331i	$-0.391371\pi$
$211$	−5.92420	−	3.95842i	−0.407839	−	0.272509i	−0.742522	+	0.669821i	$0.766371\pi$
$212$	8.67276	−	2.23243i	0.595648	−	0.153324i
$213$	−1.16509	−	2.81279i	−0.0798310	−	0.192729i
$214$	14.9850	−	1.89769i	1.02436	−	0.129724i
$215$	5.79834	+	15.7629i	0.395444	+	1.07502i
$216$	6.15231	−	14.2529i	0.418611	−	0.969787i
$217$		−	6.25794i		−	0.424817i
$218$	4.02679	−	14.7371i	0.272729	−	0.998125i
$219$	0.753962	+	1.82022i	0.0509480	+	0.122999i
$220$	16.7607	−	17.2842i	1.13001	−	1.16530i
$221$	−11.6772	+	12.2565i	−0.785491	+	0.824462i
$222$	−5.91454	−	0.416959i	−0.396958	−	0.0279845i
$223$	−0.964578	+	2.32870i	−0.0645929	+	0.155941i	−0.952880	−	0.303348i	$-0.901896\pi$
$223$	−0.964578	+	2.32870i	−0.0645929	+	0.155941i	0.888287	+	0.459289i	$0.151896\pi$
$224$	3.16265	+	13.0854i	0.211313	+	0.874307i
$225$	3.49884	−	6.83495i	0.233256	−	0.455663i
$226$	11.9643	+	3.26914i	0.795853	+	0.217460i
$227$	−5.92148	+	8.86211i	−0.393022	+	0.588199i	−0.974230	−	0.225556i	$-0.927580\pi$
$227$	−5.92148	+	8.86211i	−0.393022	+	0.588199i	0.581208	+	0.813755i	$0.302580\pi$
$228$	7.75425	−	0.431487i	0.513538	−	0.0285759i
$229$	−7.09348	+	17.1252i	−0.468750	+	1.13166i	0.495959	+	0.868346i	$0.334817\pi$
$229$	−7.09348	+	17.1252i	−0.468750	+	1.13166i	−0.964709	+	0.263318i	$0.915183\pi$
$230$	−0.207754	+	0.655456i	−0.0136989	+	0.0432195i
$231$	−12.8907	−	8.61331i	−0.848148	−	0.566714i
$232$	0.368691	−	24.9215i	0.0242057	−	1.63617i
$233$	−2.93561	+	14.7583i	−0.192318	+	0.966850i	0.757210	+	0.653171i	$0.226562\pi$
$233$	−2.93561	+	14.7583i	−0.192318	+	0.966850i	−0.949529	+	0.313679i	$0.898438\pi$
$234$	−8.89484	−	0.627062i	−0.581474	−	0.0409923i
$235$	0.609165	−	15.1401i	0.0397375	−	0.987629i
$236$	−7.24749	−	28.1558i	−0.471772	−	1.83279i
$237$	−9.92562	−	9.92562i	−0.644739	−	0.644739i
$238$	−13.4704	−	3.33256i	−0.873157	−	0.216017i
$239$		−	7.19961i		−	0.465704i	−0.972512	−	0.232852i	$-0.925194\pi$
$239$		−	7.19961i		−	0.465704i	0.972512	−	0.232852i	$-0.0748058\pi$
$240$	−10.4390	+	2.85888i	−0.673832	+	0.184540i
$241$	20.0196	+	3.98215i	1.28958	+	0.256513i	0.791794	−	0.610788i	$-0.209147\pi$
$241$	20.0196	+	3.98215i	1.28958	+	0.256513i	0.497784	+	0.867301i	$0.334147\pi$
$242$	−19.2033	+	16.6741i	−1.23444	+	1.07185i
$243$	−2.73199	+	13.7346i	−0.175257	+	0.881076i
$244$	0.973215	+	17.4897i	0.0623037	+	1.11966i
$245$	−2.80484	+	1.03176i	−0.179195	+	0.0659165i
$246$	9.33815	−	3.11861i	0.595379	−	0.198835i
$247$	−5.04198	−	12.1724i	−0.320813	−	0.774512i
$248$	5.18084	+	5.33643i	0.328983	+	0.338864i
$249$	−10.4743	+	2.08347i	−0.663782	+	0.132034i
$250$	−15.4909	+	3.16723i	−0.979732	+	0.200313i
$251$	−17.1369	+	17.1369i	−1.08167	+	1.08167i	−0.0853147	+	0.996354i	$0.527190\pi$
$251$	−17.1369	+	17.1369i	−1.08167	+	1.08167i	−0.996354	+	0.0853147i	$0.972810\pi$
$252$	−3.16800	−	6.58704i	−0.199565	−	0.414945i
$253$	0.447966	−	1.08148i	0.0281634	−	0.0679924i
$254$	17.6027	−	15.2843i	1.10449	−	0.959020i
$255$	2.35143	−	10.9058i	0.147252	−	0.682950i
$256$	−13.5301	−	8.54024i	−0.845633	−	0.533765i
$257$	12.9543	+	5.36584i	0.808066	+	0.334712i	0.748182	−	0.663493i	$-0.230927\pi$
$257$	12.9543	+	5.36584i	0.808066	+	0.334712i	0.0598839	+	0.998205i	$0.480927\pi$
$258$	−3.38806	+	12.3995i	−0.210931	+	0.771960i
$259$	−5.83031	+	5.83031i	−0.362278	+	0.362278i
$260$	10.4347	+	15.1085i	0.647132	+	0.936991i
$261$	2.64006	+	13.2725i	0.163416	+	0.821547i
$262$	10.2150	+	7.91854i	0.631082	+	0.489209i
$263$	−6.29267	−	15.1918i	−0.388023	−	0.936769i	−0.990359	−	0.138527i	$-0.955763\pi$
$263$	−6.29267	−	15.1918i	−0.388023	−	0.936769i	0.602336	−	0.798243i	$-0.294237\pi$
$264$	18.1233	−	3.32704i	1.11541	−	0.204765i
$265$	9.08885	+	4.20042i	0.558324	+	0.258030i
$266$	6.61674	−	8.53563i	0.405698	−	0.523353i
$267$	0.227443	−	1.14343i	0.0139193	−	0.0699770i
$268$	−7.88366	−	1.11711i	−0.481571	−	0.0682381i
$269$	−1.18653	+	5.96508i	−0.0723440	+	0.363698i	−0.999951	−	0.00985882i	$-0.996862\pi$
$269$	−1.18653	+	5.96508i	−0.0723440	+	0.363698i	0.927607	+	0.373556i	$0.121862\pi$
$270$	15.4074	−	7.99102i	0.937666	−	0.486318i
$271$			27.0840i			1.64523i	0.568595	+	0.822617i	$0.307487\pi$
$271$			27.0840i			1.64523i	−0.568595	+	0.822617i	$0.692513\pi$
$272$	14.2458	−	8.31008i	0.863778	−	0.503873i
$273$	8.36065	−	8.36065i	0.506009	−	0.506009i
$274$	18.8489	+	9.41108i	1.13870	+	0.568544i
$275$	26.7374	−	3.11342i	1.61232	−	0.187746i
$276$	−0.420628	+	0.316218i	−0.0253188	+	0.0190341i
$277$	−23.4807	−	4.67059i	−1.41082	−	0.280629i	−0.569864	−	0.821739i	$-0.693004\pi$
$277$	−23.4807	−	4.67059i	−1.41082	−	0.280629i	−0.840952	+	0.541110i	$0.818004\pi$
$278$	26.6317	−	3.37262i	1.59726	−	0.202276i
$279$	−3.35768	−	2.24353i	−0.201019	−	0.134317i
$280$	−6.51564	+	13.5678i	−0.389384	+	0.810831i
$281$	−6.14963	−	2.54726i	−0.366856	−	0.151957i	0.191637	−	0.981466i	$-0.438620\pi$
$281$	−6.14963	−	2.54726i	−0.366856	−	0.151957i	−0.558493	+	0.829509i	$0.688620\pi$
$282$	7.10477	−	9.16518i	0.423083	−	0.545779i
$283$	11.3401	−	16.9716i	0.674097	−	1.00886i	−0.323931	−	0.946081i	$-0.605005\pi$
$283$	11.3401	−	16.9716i	0.674097	−	1.00886i	0.998028	−	0.0627761i	$-0.0199954\pi$
$284$	4.53473	−	2.18095i	0.269087	−	0.129416i
$285$	7.01982	+	5.11033i	0.415818	+	0.302710i
$286$	−15.4962	−	27.1485i	−0.916309	−	1.60532i
$287$	5.23927	−	12.6487i	0.309264	−	0.746630i
$288$	8.15479	+	2.99434i	0.480526	+	0.176443i
$289$	0.822542	+	16.9801i	0.0483848	+	0.998829i
$290$	17.9442	−	21.3196i	1.05372	−	1.25193i
$291$	5.52188	+	13.3310i	0.323698	+	0.781477i
$292$	−2.93454	+	1.41135i	−0.171731	+	0.0825929i
$293$	32.4575			1.89619			0.948094	−	0.317991i	$-0.103008\pi$
$293$	32.4575			1.89619			0.948094	+	0.317991i	$0.103008\pi$
$294$	−2.20637	−	0.602870i	−0.128678	−	0.0351601i
$295$	13.6365	−	29.5066i	0.793949	−	1.71794i
$296$	0.144961	−	9.79858i	0.00842570	−	0.569531i
$297$	−27.2991	+	11.3077i	−1.58406	+	0.656137i
$298$	12.1954	+	6.08906i	0.706461	+	0.352729i
$299$	0.742293	+	0.495984i	0.0429279	+	0.0286835i
$300$	−11.0613	−	4.90705i	−0.638624	−	0.283308i
$301$	9.93089	+	14.8626i	0.572407	+	0.856668i
$302$	3.55538	+	4.09468i	0.204589	+	0.235623i
$303$	−4.20860	−	6.29862i	−0.241778	−	0.361846i
$304$	1.42410	+	12.7566i	0.0816775	+	0.731641i
$305$	−11.5263	+	15.8331i	−0.659994	+	0.906603i
$306$	−6.61734	+	6.03276i	−0.378288	+	0.344870i
$307$	3.31700	−	3.31700i	0.189311	−	0.189311i	−0.606087	−	0.795398i	$-0.707262\pi$
$307$	3.31700	−	3.31700i	0.189311	−	0.189311i	0.795398	+	0.606087i	$0.207262\pi$
$308$	13.0301	−	22.0635i	0.742461	−	1.25718i
$309$	6.91339	+	1.37516i	0.393289	+	0.0782301i
$310$	0.712226	+	8.28498i	0.0404517	+	0.470555i
$311$	10.2723	+	15.3736i	0.582489	+	0.871756i	0.999307	−	0.0372340i	$-0.0118547\pi$
$311$	10.2723	+	15.3736i	0.582489	+	0.871756i	−0.416818	+	0.908990i	$0.636855\pi$
$312$	−0.207874	+	14.0511i	−0.0117685	+	0.795489i
$313$	−5.90432	−	29.6830i	−0.333732	−	1.67778i	−0.675000	−	0.737818i	$-0.735856\pi$
$313$	−5.90432	−	29.6830i	−0.333732	−	1.67778i	0.341268	−	0.939966i	$-0.389144\pi$
$314$	2.48894	+	7.45270i	0.140459	+	0.420580i
$315$	1.91522	−	7.94441i	0.107910	−	0.447617i
$316$	15.4680	−	17.2909i	0.870144	−	0.972689i
$317$	8.86720	+	5.92488i	0.498032	+	0.332774i	0.779085	−	0.626918i	$-0.215684\pi$
$317$	8.86720	+	5.92488i	0.498032	+	0.332774i	−0.281054	+	0.959692i	$0.590684\pi$
$318$	3.79866	+	6.65504i	0.213018	+	0.373196i
$319$	−33.5455	+	33.5455i	−1.87819	+	1.87819i
$320$	−5.67635	−	16.9641i	−0.317317	−	0.948319i
$321$	4.94600	+	11.9407i	0.276059	+	0.666465i
$322$	−0.0514617	+	0.729981i	−0.00286785	+	0.0406802i
$323$	−12.3427	−	4.76595i	−0.686766	−	0.265185i
$324$	4.02896	+	0.570898i	0.223831	+	0.0317166i
$325$	−1.64931	+	20.4626i	−0.0914870	+	1.13506i
$326$	8.67757	+	15.2026i	0.480606	+	0.841995i
$327$	13.0723			0.722898
$328$	6.00388	+	15.1236i	0.331509	+	0.835063i
$329$	−3.14609	−	15.8165i	−0.173449	−	0.871989i
$330$	18.0465	+	9.93618i	0.993429	+	0.546969i
$331$	11.9045	+	4.93102i	0.654333	+	0.271033i	0.685052	−	0.728495i	$-0.259780\pi$
$331$	11.9045	+	4.93102i	0.654333	+	0.271033i	−0.0307189	+	0.999528i	$0.509780\pi$
$332$	−4.40000	−	17.0936i	−0.241481	−	0.938132i
$333$	1.03802	+	5.21846i	0.0568829	+	0.285970i
$334$	−9.10566	+	11.7463i	−0.498240	+	0.642731i
$335$	−6.03668	−	6.54282i	−0.329819	−	0.357473i
$336$	−10.0875	+	5.56167i	−0.550317	+	0.303414i
$337$	26.4206	−	17.6537i	1.43922	−	0.961657i	0.441290	−	0.897364i	$-0.354521\pi$
$337$	26.4206	−	17.6537i	1.43922	−	0.961657i	0.997931	−	0.0642926i	$-0.0204791\pi$
$338$	5.17444	−	1.72808i	0.281452	−	0.0939950i
$339$			10.6127i			0.576401i
$340$	18.2130	+	2.87893i	0.987736	+	0.156132i
$341$		−	14.1568i		−	0.766631i
$342$	−2.20760	−	6.61030i	−0.119374	−	0.357444i
$343$	−16.4958	+	11.0221i	−0.890689	+	0.595139i
$344$	−20.7730	−	4.45243i	−1.12001	−	0.240059i
$345$	−0.587872	−	0.0236532i	−0.0316499	−	0.00127344i
$346$	11.3721	+	8.81555i	0.611368	+	0.473927i
$347$	1.49738	+	7.52782i	0.0803834	+	0.404115i	0.999938	+	0.0111520i	$0.00354988\pi$
$347$	1.49738	+	7.52782i	0.0803834	+	0.404115i	−0.919554	+	0.392963i	$0.871450\pi$
$348$	20.6534	−	5.31632i	1.10714	−	0.284985i
$349$	−19.7104	−	8.16431i	−1.05507	−	0.437026i	−0.213373	−	0.976971i	$-0.568445\pi$
$349$	−19.7104	−	8.16431i	−1.05507	−	0.437026i	−0.841700	+	0.539945i	$0.818445\pi$
$350$	−15.2375	+	7.14080i	−0.814480	+	0.381692i
$351$	−4.39635	−	22.1020i	−0.234660	−	1.17972i
$352$	7.15456	+	29.6019i	0.381339	+	1.57779i
$353$	25.2409			1.34344			0.671719	−	0.740806i	$-0.265556\pi$
$353$	25.2409			1.34344			0.671719	+	0.740806i	$0.265556\pi$
$354$	21.6053	−	12.3322i	1.14831	−	0.655449i
$355$	5.46919	+	1.31850i	0.290274	+	0.0699785i
$356$	1.90780	+	0.270333i	0.101113	+	0.0143276i
$357$	−0.287335	−	11.8701i	−0.0152074	−	0.628233i
$358$	−18.2407	−	1.28592i	−0.964050	−	0.0679630i
$359$	−4.58018	−	11.0575i	−0.241733	−	0.583595i	0.755722	−	0.654892i	$-0.227286\pi$
$359$	−4.58018	−	11.0575i	−0.241733	−	0.583595i	−0.997455	+	0.0712976i	$0.977286\pi$
$360$	4.94384	+	8.36013i	0.260564	+	0.440618i
$361$	−6.15365	+	6.15365i	−0.323876	+	0.323876i
$362$	−29.9242	+	17.0806i	−1.57278	+	0.897735i
$363$	−18.0938	−	12.0899i	−0.949680	−	0.634556i
$364$	14.5646	+	13.0292i	0.763394	+	0.682914i
$365$	−3.53925	−	0.853231i	−0.185253	−	0.0446601i
$366$	−14.2165	+	4.74781i	−0.743110	+	0.248172i
$367$	5.22310	+	26.2583i	0.272644	+	1.37067i	0.837930	+	0.545777i	$0.183765\pi$
$367$	5.22310	+	26.2583i	0.272644	+	1.37067i	−0.565287	+	0.824894i	$0.691235\pi$
$368$	−0.560454	−	0.665092i	−0.0292157	−	0.0346703i
$369$	−4.90831	−	7.34580i	−0.255516	−	0.382407i
$370$	7.05528	−	8.38239i	0.366786	−	0.435780i
$371$	10.4514	+	2.07891i	0.542609	+	0.107932i
$372$	−3.23625	+	5.47983i	−0.167792	+	0.284116i
$373$	−12.4880	+	12.4880i	−0.646602	+	0.646602i	−0.952170	−	0.305568i	$-0.901154\pi$
$373$	−12.4880	+	12.4880i	−0.646602	+	0.646602i	0.305568	+	0.952170i	$0.401154\pi$
$374$	−30.4728	−	7.53893i	−1.57571	−	0.389829i
$375$	−6.10797	−	12.0719i	−0.315414	−	0.623392i
$376$	15.7770	+	10.8828i	0.813635	+	0.561239i
$377$	−20.1007	−	30.0829i	−1.03524	−	1.54935i
$378$	13.9479	−	12.1109i	0.717405	−	0.622916i
$379$	−8.12173	−	12.1550i	−0.417185	−	0.624362i	0.562047	−	0.827106i	$-0.310014\pi$
$379$	−8.12173	−	12.1550i	−0.417185	−	0.624362i	−0.979232	+	0.202744i	$0.935014\pi$
$380$	−7.78855	+	12.0535i	−0.399544	+	0.618332i
$381$	16.5857	+	11.0822i	0.849711	+	0.567759i
$382$	9.82560	−	19.6791i	0.502721	−	1.00687i
$383$	−8.40628	+	3.48200i	−0.429541	+	0.177922i	−0.586970	−	0.809609i	$-0.699679\pi$
$383$	−8.40628	+	3.48200i	−0.429541	+	0.177922i	0.157429	+	0.987530i	$0.449679\pi$
$384$	3.99764	−	13.0939i	0.204004	−	0.668197i
$385$	26.8870	−	9.89031i	1.37029	−	0.504057i
$386$	7.10302	−	25.9954i	0.361534	−	1.32313i
$387$	11.5348			0.586348
$388$	−21.4920	+	10.3365i	−1.09109	+	0.524754i
$389$	−0.177429	−	0.428351i	−0.00899599	−	0.0217182i	0.919318	−	0.393516i	$-0.128741\pi$
$389$	−0.177429	−	0.428351i	−0.00899599	−	0.0217182i	−0.928314	+	0.371798i	$0.878741\pi$
$390$	−10.1172	+	12.0203i	−0.512307	+	0.608673i
$391$	0.874796	−	0.196128i	0.0442403	−	0.00991862i
$392$	0.792265	−	3.69635i	0.0400154	−	0.186694i
$393$	−4.23217	+	10.2174i	−0.213485	+	0.515398i
$394$	−6.45567	+	3.68486i	−0.325232	+	0.185640i
$395$	25.6227	−	4.03346i	1.28922	−	0.202945i
$396$	−7.16667	−	14.9013i	−0.360139	−	0.748816i
$397$	19.5275	−	29.2250i	0.980057	−	1.46676i	0.0982424	−	0.995163i	$-0.468678\pi$
$397$	19.5275	−	29.2250i	0.980057	−	1.46676i	0.881815	−	0.471596i	$-0.156322\pi$
$398$	2.89677	+	2.24555i	0.145202	+	0.112559i
$399$	8.53764	+	3.53640i	0.427416	+	0.177042i
$400$	7.08198	−	18.7042i	0.354099	−	0.935208i
$401$	−22.5699	−	15.0807i	−1.12709	−	0.753095i	−0.155045	−	0.987907i	$-0.549552\pi$
$401$	−22.5699	−	15.0807i	−1.12709	−	0.753095i	−0.972041	+	0.234813i	$0.924552\pi$
$402$	−0.855973	−	6.75915i	−0.0426921	−	0.337116i
$403$	10.5892	+	2.10631i	0.527483	+	0.104923i
$404$	10.0076	−	7.52350i	0.497899	−	0.374308i
$405$	3.08506	+	3.34372i	0.153298	+	0.166151i
$406$	13.2481	−	26.5338i	0.657492	−	1.31685i
$407$	−13.1894	+	13.1894i	−0.653772	+	0.653772i
$408$	10.0721	+	9.88431i	0.498642	+	0.489346i
$409$		−	16.6303i		−	0.822317i	−0.911564	−	0.411158i	$-0.865124\pi$
$409$		−	16.6303i		−	0.822317i	0.911564	−	0.411158i	$-0.134876\pi$
$410$	−5.49678	+	17.3421i	−0.271466	+	0.856466i
$411$	−3.51686	+	17.6805i	−0.173474	+	0.872113i
$412$	−1.63448	+	11.5349i	−0.0805251	+	0.568283i
$413$	6.74910	−	33.9300i	0.332102	−	1.66959i
$414$	0.373220	+	0.289317i	0.0183428	+	0.0142191i
$415$	8.27882	−	17.9137i	0.406391	−	0.879347i
$416$	−23.2065	+	0.947232i	−1.13779	+	0.0464419i
$417$	8.79012	+	21.2212i	0.430454	+	1.03921i
$418$	14.9684	−	19.3094i	0.732130	−	0.944451i
$419$	−0.138692	−	0.697252i	−0.00677555	−	0.0340630i	0.977250	−	0.212092i	$-0.0680278\pi$
$419$	−0.138692	−	0.697252i	−0.00677555	−	0.0340630i	−0.984025	+	0.178029i	$0.943028\pi$
$420$	−12.6684	−	2.31803i	−0.618155	−	0.113108i
$421$	−0.658273	+	0.658273i	−0.0320822	+	0.0320822i	−0.722966	−	0.690884i	$-0.757222\pi$
$421$	−0.658273	+	0.658273i	−0.0320822	+	0.0320822i	0.690884	+	0.722966i	$0.257222\pi$
$422$	9.71992	+	2.65588i	0.473158	+	0.129286i
$423$	−9.61418	−	3.98233i	−0.467458	−	0.193627i
$424$	−10.6335	+	6.87973i	−0.516406	+	0.334109i
$425$	13.7352	+	15.3735i	0.666253	+	0.745726i
$426$	2.82290	+	3.25110i	0.136770	+	0.157516i
$427$	−7.97633	+	19.2566i	−0.386002	+	0.931891i
$428$	−19.2506	+	9.25846i	−0.930513	+	0.447525i
$429$	18.9135	−	18.9135i	0.913153	−	0.913153i
$430$	−14.8392	−	18.5466i	−0.715610	−	0.894397i
$431$	−5.47579	+	1.08920i	−0.263760	+	0.0524651i	−0.325198	−	0.945646i	$-0.605431\pi$
$431$	−5.47579	+	1.08920i	−0.263760	+	0.0524651i	0.0614388	+	0.998111i	$0.480431\pi$
$432$	−1.86767	+	21.8747i	−0.0898585	+	1.05245i
$433$	−10.5504	−	25.4710i	−0.507021	−	1.22406i	−0.945590	−	0.325359i	$-0.894515\pi$
$433$	−10.5504	−	25.4710i	−0.507021	−	1.22406i	0.438570	−	0.898697i	$-0.355485\pi$
$434$	2.80340	+	8.39432i	0.134568	+	0.402940i
$435$	21.6443	+	10.0029i	1.03776	+	0.479604i
$436$	1.20038	+	21.5721i	0.0574879	+	1.03312i
$437$	−0.136123	+	0.684337i	−0.00651165	+	0.0327363i
$438$	−1.82677	−	2.10387i	−0.0872864	−	0.100527i
$439$	2.11470	+	0.420641i	0.100929	+	0.0200761i	0.245297	−	0.969448i	$-0.421115\pi$
$439$	2.11470	+	0.420641i	0.100929	+	0.0200761i	−0.144367	+	0.989524i	$0.546115\pi$
$440$	−14.7397	+	30.6931i	−0.702689	+	1.46324i
$441$			2.05250i			0.0977383i
$442$	10.1730	−	21.6718i	0.483879	−	1.03082i
$443$	−7.40975	−	7.40975i	−0.352048	−	0.352048i	0.508823	−	0.860871i	$-0.330081\pi$
$443$	−7.40975	−	7.40975i	−0.352048	−	0.352048i	−0.860871	+	0.508823i	$0.830081\pi$
$444$	8.12047	−	2.09026i	0.385380	−	0.0991995i
$445$	1.46084	+	1.58333i	0.0692506	+	0.0750569i
$446$	0.250674	−	3.55579i	0.0118697	−	0.168372i
$447$	−2.27544	+	11.4394i	−0.107625	+	0.541066i
$448$	−10.1043	−	16.1358i	−0.477382	−	0.762347i
$449$	19.2284	+	12.8480i	0.907443	+	0.606334i	0.919283	−	0.393596i	$-0.128769\pi$
$449$	19.2284	+	12.8480i	0.907443	+	0.606334i	−0.0118408	+	0.999930i	$0.503769\pi$
$450$	−1.63142	+	10.7357i	−0.0769057	+	0.506086i
$451$	11.8523	−	28.6140i	0.558103	−	1.34738i
$452$	−17.5132	+	0.974526i	−0.823753	+	0.0458379i
$453$	−2.57791	+	3.85811i	−0.121121	+	0.181270i
$454$	3.97298	−	14.5402i	0.186461	−	0.682405i
$455$	3.39750	+	21.5828i	0.159277	+	1.01182i
$456$	−10.2082	+	4.05250i	−0.478041	+	0.189776i
$457$	−9.43005	+	22.7661i	−0.441119	+	1.06496i	0.534438	+	0.845208i	$0.320523\pi$
$457$	−9.43005	+	22.7661i	−0.441119	+	1.06496i	−0.975557	+	0.219748i	$0.929477\pi$
$458$	1.84345	−	26.1492i	0.0861386	−	1.22187i
$459$	−19.1149	−	12.1135i	−0.892207	−	0.565411i
$460$	−0.0149494	−	0.972289i	−0.000697020	−	0.0453332i
$461$	11.0867	+	26.7656i	0.516359	+	1.24660i	0.940125	+	0.340829i	$0.110708\pi$
$461$	11.0867	+	26.7656i	0.516359	+	1.24660i	−0.423767	+	0.905771i	$0.639292\pi$
$462$	21.1500	+	5.77905i	0.983987	+	0.268866i
$463$			29.8326i			1.38644i	0.720727	+	0.693219i	$0.243808\pi$
$463$			29.8326i			1.38644i	−0.720727	+	0.693219i	$0.756192\pi$
$464$	10.6696	+	33.5945i	0.495326	+	1.55958i
$465$	−6.67782	+	2.45642i	−0.309676	+	0.113914i
$466$	−2.67357	−	21.1117i	−0.123851	−	0.977981i
$467$	−0.849324	−	2.05045i	−0.0393020	−	0.0948834i	0.903010	−	0.429620i	$-0.141353\pi$
$467$	−0.849324	−	2.05045i	−0.0393020	−	0.0948834i	−0.942312	+	0.334737i	$0.891353\pi$
$468$	12.2123	−	3.14353i	0.564515	−	0.145310i
$469$	−7.87775	−	5.26375i	−0.363761	−	0.243057i
$470$	5.96525	+	20.5816i	0.275157	+	0.949358i
$471$	−5.59015	+	3.73522i	−0.257580	+	0.172110i
$472$	22.3348	+	34.5211i	1.02804	+	1.58896i
$473$	22.4657	+	33.6223i	1.03298	+	1.54596i
$474$	17.7605	+	8.86767i	0.815768	+	0.407305i
$475$	−15.2688	+	4.92931i	−0.700583	+	0.226172i
$476$	19.5619	−	1.56416i	0.896619	−	0.0716932i
$477$	4.86235	−	4.86235i	0.222632	−	0.222632i
$478$	3.22525	+	9.65747i	0.147519	+	0.441722i
$479$	5.87111	−	29.5161i	0.268258	−	1.34862i	−0.578081	−	0.815979i	$-0.696198\pi$
$479$	5.87111	−	29.5161i	0.268258	−	1.34862i	0.846339	−	0.532645i	$-0.178802\pi$
$480$	12.7220	−	8.51125i	0.580676	−	0.388484i
$481$	−7.90317	−	11.8279i	−0.360354	−	0.539307i
$482$	−28.6380	+	3.62669i	−1.30442	+	0.165191i
$483$	−0.614135	+	0.122159i	−0.0279441	+	0.00555843i
$484$	18.2895	−	30.9690i	0.831342	−	1.40768i
$485$	−25.9208	−	6.24891i	−1.17700	−	0.283748i
$486$	−2.48812	−	19.6473i	−0.112863	−	0.891219i
$487$	−0.813936	+	1.21814i	−0.0368829	+	0.0551992i	−0.849453	−	0.527664i	$-0.823068\pi$
$487$	−0.813936	+	1.21814i	−0.0368829	+	0.0551992i	0.812570	+	0.582864i	$0.198068\pi$
$488$	−9.14039	−	23.0244i	−0.413766	−	1.04227i
$489$	−10.5912	+	10.5912i	−0.478951	+	0.478951i
$490$	3.30018	−	2.64048i	0.149087	−	0.119285i
$491$	−20.3629	+	8.43459i	−0.918964	+	0.380648i	−0.791481	−	0.611193i	$-0.790690\pi$
$491$	−20.3629	+	8.43459i	−0.918964	+	0.380648i	−0.127483	+	0.991841i	$0.540690\pi$
$492$	−11.1290	+	8.36652i	−0.501735	+	0.377192i
$493$	−35.7959	−	6.22378i	−1.61217	−	0.280305i
$494$	12.2162	+	14.0692i	0.549632	+	0.633005i
$495$	4.33261	−	17.9719i	0.194736	−	0.807777i
$496$	−9.34009	−	4.83733i	−0.419383	−	0.217203i
$497$	5.98750			0.268576
$498$	13.1168	−	7.48696i	0.587776	−	0.335499i
$499$	9.86482	−	1.96224i	0.441610	−	0.0878417i	0.0307230	−	0.999528i	$-0.490219\pi$
$499$	9.86482	−	1.96224i	0.441610	−	0.0878417i	0.410887	+	0.911686i	$0.365219\pi$
$500$	19.3605	−	11.1880i	0.865827	−	0.500344i
$501$	−11.7491	−	4.86664i	−0.524911	−	0.217425i
$502$	15.3103	−	30.6640i	0.683331	−	1.36860i
$503$	2.27632	−	0.452788i	0.101496	−	0.0201888i	−0.144081	−	0.989566i	$-0.546023\pi$
$503$	2.27632	−	0.452788i	0.101496	−	0.0201888i	0.245577	+	0.969377i	$0.421023\pi$
$504$	7.20034	+	7.41659i	0.320729	+	0.330361i
$505$	13.9867	+	0.562759i	0.622401	+	0.0250425i
$506$	−0.116417	+	1.65137i	−0.00517536	+	0.0734122i
$507$	2.59337	+	3.88126i	0.115176	+	0.172373i
$508$	−16.7651	+	28.3877i	−0.743830	+	1.25950i
$509$			3.10751i			0.137738i	0.997626	+	0.0688691i	$0.0219391\pi$
$509$			3.10751i			0.137738i	−0.997626	+	0.0688691i	$0.978061\pi$
$510$	1.73136	+	15.6823i	0.0766661	+	0.694425i
$511$	−3.87466			−0.171405
$512$	21.9749	+	5.39461i	0.971165	+	0.238410i
$513$	14.6444	−	9.78506i	0.646565	−	0.432021i
$514$	−19.7805	−	1.39447i	−0.872479	−	0.0615074i
$515$	−9.57306	+	8.83251i	−0.421839	+	0.389207i
$516$	−1.00998	−	18.1503i	−0.0444617	−	0.799022i
$517$	−7.11710	−	35.7801i	−0.313010	−	1.57361i
$518$	5.20886	−	10.4325i	0.228864	−	0.458379i
$519$	−4.71159	+	11.3748i	−0.206816	+	0.499297i
$520$	−20.7652	−	15.5919i	−0.910615	−	0.683750i
$521$	−4.24741	−	21.3532i	−0.186082	−	0.935500i	−0.955103	−	0.296275i	$-0.904255\pi$
$521$	−4.24741	−	21.3532i	−0.186082	−	0.935500i	0.769020	−	0.639225i	$-0.220745\pi$
$522$	−9.48710	−	16.6209i	−0.415239	−	0.727476i
$523$			10.5314i			0.460507i	0.973131	+	0.230254i	$0.0739556\pi$
$523$			10.5314i			0.460507i	−0.973131	+	0.230254i	$0.926044\pi$
$524$	−17.2495	−	6.04578i	−0.753549	−	0.264111i
$525$	−9.33063	−	10.9666i	−0.407222	−	0.478622i
$526$	15.2465	+	17.5592i	0.664778	+	0.765617i
$527$	8.86650	−	6.23996i	0.386231	−	0.271817i
$528$	−22.8199	+	12.5816i	−0.993111	+	0.547546i
$529$	8.78363	+	21.2055i	0.381897	+	0.921980i
$530$	−14.0733	−	1.56281i	−0.611307	−	0.0678842i
$531$	−15.7855	−	15.7855i	−0.685030	−	0.685030i
$532$	−5.05186	+	14.4137i	−0.219026	+	0.624914i
$533$	19.6396	+	13.1228i	0.850687	+	0.568411i
$534$	0.207141	+	1.63568i	0.00896385	+	0.0707826i
$535$	−23.2175	−	5.59721i	−1.00378	−	0.241988i
$536$	11.0755	−	2.03321i	0.478388	−	0.0878215i
$537$	−3.05250	−	15.3459i	−0.131725	−	0.662226i
$538$	−1.08062	−	8.53302i	−0.0465886	−	0.367885i
$539$	−5.98275	+	3.99755i	−0.257695	+	0.172187i
$540$	−17.0875	+	17.6212i	−0.735330	+	0.758295i
$541$	−28.5304	−	5.67506i	−1.22662	−	0.243990i	−0.461068	−	0.887365i	$-0.652534\pi$
$541$	−28.5304	−	5.67506i	−1.22662	−	0.243990i	−0.765551	+	0.643375i	$0.777534\pi$
$542$	−12.1330	−	36.3301i	−0.521155	−	1.56051i
$543$	−20.8473	−	20.8473i	−0.894643	−	0.894643i
$544$	−15.3864	+	17.5288i	−0.659686	+	0.751541i
$545$	−14.2168	+	19.5289i	−0.608980	+	0.836527i
$546$	−7.46950	+	14.9602i	−0.319665	+	0.640238i
$547$	−4.93677	+	3.29865i	−0.211081	+	0.141040i	−0.656617	−	0.754224i	$-0.728013\pi$
$547$	−4.93677	+	3.29865i	−0.211081	+	0.141040i	0.445536	+	0.895264i	$0.353013\pi$
$548$	−29.4996	−	4.18006i	−1.26016	−	0.178563i
$549$	7.47247	+	11.1833i	0.318917	+	0.477294i
$550$	−34.4704	+	16.1540i	−1.46982	+	0.688808i
$551$	15.7101	−	23.5119i	0.669274	−	1.00164i
$552$	0.422567	−	0.612602i	0.0179857	−	0.0260741i
$553$	25.5042	−	10.5642i	1.08455	−	0.449235i
$554$	33.5890	−	4.25368i	1.42706	−	0.180722i
$555$	8.51006	+	3.93293i	0.361232	+	0.166944i
$556$	−34.2125	+	16.4543i	−1.45093	+	0.697818i
$557$	−10.9811			−0.465286			−0.232643	−	0.972562i	$-0.574737\pi$
$557$	−10.9811			−0.465286			−0.232643	+	0.972562i	$0.574737\pi$
$558$	5.50900	+	1.50529i	0.233214	+	0.0637238i
$559$	−28.4918	+	11.8017i	−1.20508	+	0.499159i
$560$	2.66196	−	21.1185i	0.112488	−	0.892419i
$561$	−0.650011	−	26.8527i	−0.0274435	−	1.13372i
$562$	9.39013	+	0.661979i	0.396099	+	0.0279239i
$563$	−34.2405	−	14.1829i	−1.44306	−	0.597736i	−0.482525	−	0.875882i	$-0.660280\pi$
$563$	−34.2405	−	14.1829i	−1.44306	−	0.597736i	−0.960539	+	0.278146i	$0.910280\pi$
$564$	−5.42447	+	15.4768i	−0.228411	+	0.651691i
$565$	−15.8545	−	11.5418i	−0.667003	−	0.485569i
$566$	−7.60855	+	27.8455i	−0.319811	+	1.17044i
$567$	4.02594	+	2.69004i	0.169073	+	0.112971i
$568$	−5.10582	+	4.95695i	−0.214235	+	0.207989i
$569$	39.1164	+	16.2025i	1.63984	+	0.679246i	0.996282	−	0.0861476i	$-0.0274557\pi$
$569$	39.1164	+	16.2025i	1.63984	+	0.679246i	0.643562	+	0.765394i	$0.277456\pi$
$570$	−11.7056	−	3.71022i	−0.490293	−	0.155404i
$571$	−1.41255	+	2.11402i	−0.0591132	+	0.0884691i	−0.859849	−	0.510549i	$-0.829442\pi$
$571$	−1.41255	+	2.11402i	−0.0591132	+	0.0884691i	0.800736	+	0.599018i	$0.204442\pi$
$572$	32.9482	+	29.4747i	1.37763	+	1.23240i
$573$	18.4592	+	3.67177i	0.771145	+	0.153390i
$574$	−1.36158	+	19.3139i	−0.0568311	+	0.806145i
$575$	0.674677	−	0.852510i	0.0281360	−	0.0355521i
$576$	−12.2801	−	0.363426i	−0.511672	−	0.0151428i
$577$	4.86415	−	4.86415i	0.202497	−	0.202497i	−0.598572	−	0.801069i	$-0.704265\pi$
$577$	4.86415	−	4.86415i	0.202497	−	0.202497i	0.801069	+	0.598572i	$0.204265\pi$
$578$	−8.71000	−	22.4084i	−0.362288	−	0.932066i
$579$	23.0587			0.958286
$580$	−14.5195	+	36.6363i	−0.602889	+	1.52124i
$581$	4.09743	−	20.5991i	0.169990	−	0.854597i
$582$	−13.3789	−	15.4084i	−0.554575	−	0.638697i
$583$	23.6432	+	4.70292i	0.979201	+	0.194775i
$584$	3.30410	−	3.20776i	0.136725	−	0.132738i
$585$	12.7982	+	5.91472i	0.529142	+	0.244543i
$586$	−43.5381	+	14.5402i	−1.79854	+	0.600648i
$587$	−17.0587	+	7.06596i	−0.704089	+	0.291643i	−0.705856	−	0.708355i	$-0.749438\pi$
$587$	−17.0587	+	7.06596i	−0.704089	+	0.291643i	0.00176703	+	0.999998i	$0.499438\pi$
$588$	3.22966	−	0.179715i	0.133189	−	0.00741132i
$589$	1.64623	+	8.27616i	0.0678317	+	0.341013i
$590$	−5.07361	+	45.6886i	−0.208877	+	1.88097i
$591$	−4.49747	−	4.49747i	−0.185001	−	0.185001i
$592$	4.19507	+	13.2086i	0.172416	+	0.542871i
$593$	−3.73773	−	1.54822i	−0.153490	−	0.0635776i	0.304616	−	0.952475i	$-0.401472\pi$
$593$	−3.73773	−	1.54822i	−0.153490	−	0.0635776i	−0.458106	+	0.888898i	$0.651472\pi$
$594$	31.5531	−	27.3973i	1.29464	−	1.12412i
$595$	18.0455	+	12.4801i	0.739794	+	0.511635i
$596$	−19.0865	−	2.70454i	−0.781814	−	0.110782i
$597$	−1.20016	+	2.89745i	−0.0491194	+	0.118585i
$598$	−1.21789	−	0.332778i	−0.0498032	−	0.0136083i
$599$	5.51007	+	5.51007i	0.225135	+	0.225135i	0.810657	−	0.585522i	$-0.199110\pi$
$599$	5.51007	+	5.51007i	0.225135	+	0.225135i	−0.585522	+	0.810657i	$0.699110\pi$
$600$	17.0357	+	1.62706i	0.695480	+	0.0664246i
$601$	4.04593	−	0.804786i	0.165037	−	0.0328279i	−0.111880	−	0.993722i	$-0.535687\pi$
$601$	4.04593	−	0.804786i	0.165037	−	0.0328279i	0.276917	+	0.960894i	$0.410687\pi$
$602$	−19.9793	−	15.4877i	−0.814293	−	0.631233i
$603$	−5.64850	+	2.33969i	−0.230025	+	0.0952793i
$604$	−6.60345	−	3.89984i	−0.268691	−	0.158682i
$605$	37.7394	−	13.8823i	1.53432	−	0.564398i
$606$	8.46699	+	6.56353i	0.343948	+	0.266625i
$607$	8.38947	+	1.66877i	0.340518	+	0.0677333i	0.362387	−	0.932028i	$-0.381962\pi$
$607$	8.38947	+	1.66877i	0.340518	+	0.0677333i	−0.0218692	+	0.999761i	$0.506962\pi$
$608$	−7.62490	−	16.4736i	−0.309231	−	0.668092i
$609$	24.8890	+	4.95073i	1.00855	+	0.200614i
$610$	8.36837	−	26.4019i	0.338825	−	1.06898i
$611$	27.8222			1.12556
$612$	6.17389	−	11.0567i	0.249565	−	0.446939i
$613$	1.98628	+	1.98628i	0.0802250	+	0.0802250i	0.746081	−	0.665856i	$-0.231933\pi$
$613$	1.98628	+	1.98628i	0.0802250	+	0.0802250i	−0.665856	+	0.746081i	$0.731933\pi$
$614$	−2.96344	+	5.93530i	−0.119595	+	0.239529i
$615$	−15.5539	−	0.625817i	−0.627196	−	0.0252354i
$616$	−7.59457	+	35.4328i	−0.305994	+	1.42763i
$617$	−2.72027	+	13.6757i	−0.109514	+	0.550563i	0.886604	+	0.462530i	$0.153058\pi$
$617$	−2.72027	+	13.6757i	−0.109514	+	0.550563i	−0.996118	+	0.0880332i	$0.971942\pi$
$618$	−9.88957	+	1.25241i	−0.397817	+	0.0503792i
$619$	−20.9589	+	31.3672i	−0.842409	+	1.26075i	0.120982	+	0.992655i	$0.461396\pi$
$619$	−20.9589	+	31.3672i	−0.842409	+	1.26075i	−0.963391	+	0.268100i	$0.913604\pi$
$620$	−4.66684	−	10.7943i	−0.187425	−	0.433510i
$621$	−0.456701	+	1.10257i	−0.0183268	+	0.0442447i
$622$	−20.6661	−	16.0202i	−0.828636	−	0.642351i
$623$	1.90637	+	1.27380i	0.0763771	+	0.0510336i
$624$	−6.01572	−	18.9411i	−0.240821	−	0.758252i
$625$	24.6773	+	4.00404i	0.987091	+	0.160162i
$626$	21.2172	+	37.1714i	0.848011	+	1.48567i
$627$	19.3139	+	8.00008i	0.771323	+	0.319492i
$628$	−6.67725	−	8.88198i	−0.266451	−	0.354429i
$629$	−14.0742	−	2.44706i	−0.561174	−	0.0975705i
$630$	0.989855	+	11.5145i	0.0394368	+	0.458749i
$631$	−42.8560	+	17.7516i	−1.70607	+	0.706678i	−0.999999	−	0.00146103i	$-0.999535\pi$
$631$	−42.8560	+	17.7516i	−1.70607	+	0.706678i	−0.706073	+	0.708139i	$0.749535\pi$
$632$	−13.0027	+	30.1231i	−0.517220	+	1.19823i
$633$			8.62185i			0.342688i
$634$	−14.5485	−	3.97526i	−0.577797	−	0.157878i
$635$	−34.5938	+	12.7252i	−1.37281	+	0.504986i
$636$	−8.07676	−	7.22528i	−0.320264	−	0.286501i
$637$	−2.09999	−	5.06983i	−0.0832048	−	0.200874i
$638$	29.9699	−	60.0250i	1.18652	−	2.37641i
$639$	2.14658	−	3.21258i	0.0849173	−	0.127088i
$640$	15.2137	+	20.2125i	0.601372	+	0.798969i
$641$	10.3377	−	6.90744i	0.408315	−	0.272827i	−0.334405	−	0.942429i	$-0.608535\pi$
$641$	10.3377	−	6.90744i	0.408315	−	0.272827i	0.742720	+	0.669602i	$0.233535\pi$
$642$	−11.9836	−	13.8014i	−0.472956	−	0.544698i
$643$	−7.37281	+	4.92635i	−0.290755	+	0.194276i	−0.692390	−	0.721524i	$-0.743442\pi$
$643$	−7.37281	+	4.92635i	−0.290755	+	0.194276i	0.401635	+	0.915800i	$0.368442\pi$
$644$	−0.257983	−	1.00224i	−0.0101660	−	0.0394938i
$645$	11.9617	−	16.4312i	0.470991	−	0.646979i
$646$	18.6913	+	0.863762i	0.735401	+	0.0339843i
$647$	20.4757	+	20.4757i	0.804982	+	0.804982i	0.983869	−	0.178888i	$-0.0572499\pi$
$647$	20.4757	+	20.4757i	0.804982	+	0.804982i	−0.178888	+	0.983869i	$0.557250\pi$
$648$	−5.66014	+	1.03908i	−0.222351	+	0.0408188i
$649$	15.2679	−	76.7567i	0.599316	−	3.01297i
$650$	−6.95438	−	28.1871i	−0.272773	−	1.10559i
$651$	−6.29643	+	4.20714i	−0.246777	+	0.164891i
$652$	−18.4504	−	16.5053i	−0.722572	−	0.646396i
$653$	−13.9681	+	2.77843i	−0.546615	+	0.108728i	−0.460670	−	0.887572i	$-0.652391\pi$
$653$	−13.9681	+	2.77843i	−0.546615	+	0.108728i	−0.0859446	+	0.996300i	$0.527391\pi$
$654$	−17.5350	+	5.85605i	−0.685671	+	0.228990i
$655$	−10.6612	−	17.4344i	−0.416568	−	0.681220i
$656$	−14.8285	−	17.5970i	−0.578957	−	0.687049i
$657$	−1.38910	+	2.07894i	−0.0541941	+	0.0811072i
$658$	11.3055	+	19.8066i	0.440734	+	0.772142i
$659$	27.2426	+	27.2426i	1.06122	+	1.06122i	0.998000	+	0.0632204i	$0.0201371\pi$
$659$	27.2426	+	27.2426i	1.06122	+	1.06122i	0.0632204	+	0.998000i	$0.479863\pi$
$660$	−28.6585	−	5.24386i	−1.11553	−	0.204117i
$661$	−13.3373	+	5.52449i	−0.518761	+	0.214878i	−0.626672	−	0.779283i	$-0.715584\pi$
$661$	−13.3373	+	5.52449i	−0.518761	+	0.214878i	0.107912	+	0.994160i	$0.465584\pi$
$662$	−18.1776	−	1.28147i	−0.706491	−	0.0498057i
$663$	20.1823	+	3.50907i	0.783816	+	0.136281i
$664$	13.5596	+	20.9580i	0.526215	+	0.813329i
$665$	−14.5682	+	8.90853i	−0.564932	+	0.345458i
$666$	−3.73012	−	6.53497i	−0.144539	−	0.253225i
$667$			1.91605i			0.0741899i
$668$	6.95214	−	19.8355i	0.268986	−	0.767458i
$669$	2.99150	−	0.595046i	0.115658	−	0.0230058i
$670$	11.0286	+	6.07217i	0.426070	+	0.234588i
$671$	−18.0441	+	43.5623i	−0.696585	+	1.68171i
$672$	11.0397	−	11.9793i	0.425866	−	0.462111i
$673$	−33.2852	+	6.62084i	−1.28305	+	0.255215i	−0.789094	−	0.614272i	$-0.789450\pi$
$673$	−33.2852	+	6.62084i	−1.28305	+	0.255215i	−0.493956	+	0.869487i	$0.664450\pi$
$674$	−27.5318	+	35.5162i	−1.06049	+	1.36803i
$675$	−27.2587	+	3.17413i	−1.04919	+	0.122172i
$676$	−6.16678	+	4.63604i	−0.237184	+	0.178309i
$677$	0.871648	+	1.30451i	0.0335001	+	0.0501365i	0.847842	−	0.530249i	$-0.177902\pi$
$677$	0.871648	+	1.30451i	0.0335001	+	0.0501365i	−0.814342	+	0.580386i	$0.802902\pi$
$678$	−4.75421	−	14.2357i	−0.182584	−	0.546718i
$679$	−28.3773			−1.08902
$680$	−25.7203	+	4.29719i	−0.986329	+	0.164790i
$681$	12.8976			0.494236
$682$	6.34187	+	18.9897i	0.242843	+	0.727152i
$683$	−5.47423	−	8.19277i	−0.209466	−	0.313487i	0.711829	−	0.702353i	$-0.247867\pi$
$683$	−5.47423	−	8.19277i	−0.209466	−	0.313487i	−0.921295	+	0.388865i	$0.872867\pi$
$684$	5.92250	+	7.87802i	0.226452	+	0.301224i
$685$	−22.5885	−	24.4824i	−0.863060	−	0.935423i
$686$	17.1896	−	22.1746i	0.656302	−	0.846632i
$687$	21.9994	−	4.37595i	0.839329	−	0.166953i
$688$	29.8592	−	3.33337i	1.13837	−	0.127083i
$689$	−7.03551	+	16.9852i	−0.268031	+	0.647085i
$690$	0.799159	−	0.231624i	0.0304235	−	0.00881777i
$691$	17.1474	−	3.41084i	0.652319	−	0.129754i	0.142173	−	0.989842i	$-0.454591\pi$
$691$	17.1474	−	3.41084i	0.652319	−	0.129754i	0.510147	+	0.860087i	$0.329591\pi$
$692$	−19.2035	−	6.73064i	−0.730008	−	0.255861i
$693$		−	19.6751i		−	0.747395i
$694$	−5.38084	−	9.42694i	−0.204254	−	0.357842i
$695$	−41.2626	−	9.94746i	−1.56518	−	0.377329i
$696$	−25.3226	+	16.3835i	−0.959852	+	0.621013i
$697$	23.1454	−	5.18917i	0.876695	−	0.196554i
$698$	30.0967	+	2.12173i	1.13918	+	0.0803088i
$699$	16.8227	−	6.96819i	0.636293	−	0.263561i
$700$	17.2405	−	16.4046i	0.651630	−	0.620036i
$701$	27.0539	+	27.0539i	1.02181	+	1.02181i	0.999757	+	0.0220543i	$0.00702068\pi$
$701$	27.0539	+	27.0539i	1.02181	+	1.02181i	0.0220543	+	0.999757i	$0.492979\pi$
$702$	15.7983	+	27.6778i	0.596270	+	1.04463i
$703$	6.17688	−	9.24435i	0.232965	−	0.348657i
$704$	−22.8580	−	36.5026i	−0.861492	−	1.37574i
$705$	−15.6427	+	9.56559i	−0.589140	+	0.360261i
$706$	−33.8578	+	11.3073i	−1.27426	+	0.425556i
$707$	14.6116	−	2.90642i	0.549525	−	0.109307i
$708$	−23.4566	+	26.2209i	−0.881553	+	0.985442i
$709$	33.6322	−	22.4723i	1.26308	−	0.843965i	0.270170	−	0.962813i	$-0.412920\pi$
$709$	33.6322	−	22.4723i	1.26308	−	0.843965i	0.992912	+	0.118848i	$0.0379202\pi$
$710$	−7.92695	+	0.681447i	−0.297493	+	0.0255743i
$711$	3.47532	−	17.4716i	0.130335	−	0.655236i
$712$	−2.68020	+	0.492026i	−0.100445	+	0.0184395i
$713$	−0.404303	−	0.404303i	−0.0151413	−	0.0151413i
$714$	5.70295	+	15.7937i	0.213427	+	0.591064i
$715$	7.68585	+	48.8247i	0.287435	+	1.82594i
$716$	25.0439	−	6.44646i	0.935934	−	0.240916i
$717$	−7.24390	+	4.84022i	−0.270528	+	0.180761i
$718$	11.0973	+	12.7806i	0.414148	+	0.476969i
$719$	8.43475	−	5.63592i	0.314563	−	0.210184i	−0.388258	−	0.921551i	$-0.626923\pi$
$719$	8.43475	−	5.63592i	0.314563	−	0.210184i	0.702822	+	0.711366i	$0.251923\pi$
$720$	−10.3767	−	8.99945i	−0.386718	−	0.335390i
$721$	−7.70159	+	11.5262i	−0.286822	+	0.429260i
$722$	5.49774	−	11.0111i	0.204605	−	0.409791i
$723$	−9.45232	−	22.8199i	−0.351536	−	0.848682i
$724$	32.4883	−	36.3170i	1.20742	−	1.34971i
$725$	−38.4829	+	21.4561i	−1.42922	+	0.796861i
$726$	29.6868	+	8.11166i	1.10178	+	0.301052i
$727$		−	24.7548i		−	0.918106i	−0.888409	−	0.459053i	$-0.848189\pi$
$727$		−	24.7548i		−	0.918106i	0.888409	−	0.459053i	$-0.151811\pi$
$728$	−25.3735	−	10.9526i	−0.940406	−	0.405929i
$729$	21.2950	−	8.82066i	0.788702	−	0.326691i
$730$	5.12972	−	0.440982i	0.189860	−	0.0163215i
$731$	−11.1556	+	28.8904i	−0.412605	+	1.06855i
$732$	16.9430	−	12.7373i	0.626230	−	0.470784i
$733$	24.9772	+	10.3459i	0.922555	+	0.382135i	0.792849	−	0.609418i	$-0.208597\pi$
$733$	24.9772	+	10.3459i	0.922555	+	0.382135i	0.129705	+	0.991553i	$0.458597\pi$
$734$	−18.7693	−	32.8827i	−0.692786	−	1.21372i
$735$	2.92377	+	2.12846i	0.107845	+	0.0785094i
$736$	1.04973	+	0.641076i	0.0386936	+	0.0236304i
$737$	−17.8211	−	11.9077i	−0.656449	−	0.438625i
$738$	9.87467	+	7.65476i	0.363492	+	0.281776i
$739$	11.4978	−	27.7582i	0.422954	−	1.02110i	−0.558517	−	0.829493i	$-0.688630\pi$
$739$	11.4978	−	27.7582i	0.422954	−	1.02110i	0.981471	−	0.191609i	$-0.0613705\pi$
$740$	−5.70875	+	14.4046i	−0.209858	+	0.529524i
$741$	−8.85762	+	13.2564i	−0.325393	+	0.486985i
$742$	−14.9506	+	1.89334i	−0.548855	+	0.0695066i
$743$	−9.22939	+	46.3993i	−0.338593	+	1.70222i	0.318092	+	0.948060i	$0.396958\pi$
$743$	−9.22939	+	46.3993i	−0.338593	+	1.70222i	−0.656686	+	0.754164i	$0.728042\pi$
$744$	1.88624	−	8.80033i	0.0691528	−	0.322636i
$745$	−14.6149	−	15.8403i	−0.535450	−	0.580344i
$746$	11.1569	−	22.3455i	0.408483	−	0.818126i
$747$	−9.58346	−	9.58346i	−0.350640	−	0.350640i
$748$	44.2531	−	3.53845i	1.61805	−	0.129379i
$749$	−25.4178			−0.928747
$750$	13.6011	+	13.4569i	0.496641	+	0.491377i
$751$	10.7779	+	2.14386i	0.393292	+	0.0782306i	0.387775	−	0.921754i	$-0.373244\pi$
$751$	10.7779	+	2.14386i	0.393292	+	0.0782306i	0.00551715	+	0.999985i	$0.498244\pi$
$752$	−26.0383	−	7.53038i	−0.949517	−	0.274605i
$753$	28.7632	+	5.72135i	1.04819	+	0.208498i
$754$	40.4392	+	31.3481i	1.47271	+	1.14163i
$755$	−2.96010	−	8.04709i	−0.107729	−	0.292864i
$756$	−13.2842	+	22.4937i	−0.483142	+	0.818087i
$757$	17.4180	−	7.21479i	0.633069	−	0.262226i	−0.0429873	−	0.999076i	$-0.513688\pi$
$757$	17.4180	−	7.21479i	0.633069	−	0.262226i	0.676057	+	0.736850i	$0.263688\pi$
$758$	16.3395	+	12.6663i	0.593478	+	0.460059i
$759$	−1.38930	+	0.276349i	−0.0504284	+	0.0100308i
$760$	5.04779	−	19.6575i	0.183103	−	0.713052i
$761$	18.2790	+	18.2790i	0.662615	+	0.662615i	0.955996	−	0.293381i	$-0.0947805\pi$
$761$	18.2790	+	18.2790i	0.662615	+	0.662615i	−0.293381	+	0.955996i	$0.594780\pi$
$762$	−27.2124	−	7.43555i	−0.985801	−	0.269361i
$763$	−9.83817	+	23.7515i	−0.356166	+	0.859860i
$764$	−4.36417	+	30.7989i	−0.157890	+	1.11427i
$765$	13.1657	−	5.20803i	0.476006	−	0.188297i
$766$	9.71623	−	8.43651i	0.351062	−	0.304824i
$767$	55.1419	+	22.8405i	1.99106	+	0.824723i
$768$	0.503374	+	19.3549i	0.0181639	+	0.698408i
$769$	37.5873	+	37.5873i	1.35543	+	1.35543i	0.879460	+	0.475972i	$0.157904\pi$
$769$	37.5873	+	37.5873i	1.35543	+	1.35543i	0.475972	+	0.879460i	$0.342096\pi$
$770$	−31.6352	+	25.3114i	−1.14005	+	0.912160i
$771$	−3.31017	−	16.6414i	−0.119213	−	0.599324i
$772$	2.11740	+	38.0519i	0.0762070	+	1.36952i
$773$	4.07131	−	1.68639i	0.146435	−	0.0606553i	−0.308262	−	0.951301i	$-0.599747\pi$
$773$	4.07131	−	1.68639i	0.146435	−	0.0606553i	0.454697	+	0.890646i	$0.349747\pi$
$774$	−15.4727	+	5.16732i	−0.556153	+	0.185735i
$775$	3.59278	−	12.6476i	0.129057	−	0.454316i
$776$	24.1986	−	23.4931i	0.868681	−	0.843353i
$777$	9.78582	+	1.94652i	0.351064	+	0.0698310i
$778$	0.429891	+	0.495100i	0.0154123	+	0.0177502i
$779$	−3.60155	+	18.1062i	−0.129039	+	0.648723i
$780$	8.18633	−	20.6562i	0.293118	−	0.739610i
$781$	13.5450			0.484677
$782$	−1.08558	+	0.654970i	−0.0388202	+	0.0234217i
$783$	34.1996	−	34.1996i	1.22219	−	1.22219i
$784$	0.593138	+	5.31315i	0.0211835	+	0.189755i
$785$	0.499460	−	12.4135i	0.0178265	−	0.443056i
$786$	1.09985	−	15.6013i	0.0392304	−	0.556481i
$787$	33.1728	+	6.59847i	1.18248	+	0.235210i	0.746898	−	0.664938i	$-0.231542\pi$
$787$	33.1728	+	6.59847i	1.18248	+	0.235210i	0.435583	+	0.900148i	$0.356542\pi$
$788$	7.00882	−	7.83480i	0.249679	−	0.279103i
$789$	−11.0548	+	16.5447i	−0.393561	+	0.589006i
$790$	−32.5631	+	16.8888i	−1.15854	+	0.600876i
$791$	−19.2825	−	7.98708i	−0.685608	−	0.283988i
$792$	16.2887	+	16.7779i	0.578793	+	0.596175i
$793$	−29.8996	−	19.9783i	−1.06177	−	0.709450i
$794$	−13.1019	+	47.9498i	−0.464968	+	1.70168i
$795$	−1.88407	−	11.9687i	−0.0668212	−	0.424484i
$796$	−4.89164	−	1.71447i	−0.173380	−	0.0607678i
$797$	13.4584	+	5.57464i	0.476720	+	0.197464i	0.608088	−	0.793870i	$-0.291937\pi$
$797$	13.4584	+	5.57464i	0.476720	+	0.197464i	−0.131368	+	0.991334i	$0.541937\pi$
$798$	−13.0365	−	0.919038i	−0.461487	−	0.0325336i
$799$	19.2723	−	20.2285i	0.681806	−	0.715634i
$800$	−1.12068	+	28.2621i	−0.0396220	+	0.999215i
$801$	1.36690	−	0.566190i	0.0482972	−	0.0200054i
$802$	37.0307	+	10.1183i	1.30760	+	0.357290i
$803$	−8.76529			−0.309320
$804$	4.17612	+	8.68318i	0.147280	+	0.306232i
$805$	0.485408	−	1.05032i	0.0171084	−	0.0370190i
$806$	−15.1477	+	1.91830i	−0.533556	+	0.0675691i
$807$	6.79947	−	2.81643i	0.239353	−	0.0991431i
$808$	−10.0538	+	14.5751i	−0.353691	+	0.512750i
$809$	−30.1168	+	45.0730i	−1.05885	+	1.58468i	−0.277358	+	0.960767i	$0.589459\pi$
$809$	−30.1168	+	45.0730i	−1.05885	+	1.58468i	−0.781493	+	0.623914i	$0.785541\pi$
$810$	−5.63616	−	3.10319i	−0.198034	−	0.109035i
$811$	−26.4696	−	39.6146i	−0.929474	−	1.39106i	−0.920349	−	0.391098i	$-0.872095\pi$
$811$	−26.4696	−	39.6146i	−0.929474	−	1.39106i	−0.00912529	−	0.999958i	$-0.502905\pi$
$812$	−5.88432	+	41.5270i	−0.206499	+	1.45731i
$813$	27.2506	−	18.2083i	0.955720	−	0.638592i
$814$	11.7835	−	23.6005i	0.413012	−	0.827198i
$815$	−4.30393	−	27.3409i	−0.150760	−	0.957711i
$816$	−17.9385	−	8.74664i	−0.627973	−	0.306194i
$817$	−17.0435	−	17.0435i	−0.596275	−	0.596275i
$818$	7.44997	+	22.3077i	0.260482	+	0.779970i
$819$	14.7168	+	2.92736i	0.514248	+	0.102290i
$820$	−0.395532	−	25.7249i	−0.0138126	−	0.898352i
$821$	−4.47788	+	2.99202i	−0.156279	+	0.104422i	−0.631251	−	0.775579i	$-0.717458\pi$
$821$	−4.47788	+	2.99202i	−0.156279	+	0.104422i	0.474972	+	0.880001i	$0.342458\pi$
$822$	−3.20294	−	25.2918i	−0.111715	−	0.882153i
$823$	3.97170	+	19.9671i	0.138445	+	0.696008i	0.986192	+	0.165607i	$0.0529585\pi$
$823$	3.97170	+	19.9671i	0.138445	+	0.696008i	−0.847747	+	0.530401i	$0.822042\pi$
$824$	−2.97487	−	16.2050i	−0.103635	−	0.564526i
$825$	−21.1078	−	24.8087i	−0.734879	−	0.863729i
$826$	6.14665	+	48.5367i	0.213869	+	1.68881i
$827$	−16.9066	−	11.2966i	−0.587899	−	0.392822i	0.225744	−	0.974187i	$-0.427519\pi$
$827$	−16.9066	−	11.2966i	−0.587899	−	0.392822i	−0.813643	+	0.581365i	$0.802519\pi$
$828$	−0.630239	−	0.220892i	−0.0219023	−	0.00767654i
$829$	−35.0136	−	35.0136i	−1.21607	−	1.21607i	−0.968996	−	0.247078i	$-0.920530\pi$
$829$	−35.0136	−	35.0136i	−1.21607	−	1.21607i	−0.247078	−	0.968996i	$-0.579470\pi$
$830$	−3.08022	+	27.7379i	−0.106916	+	0.962795i
$831$	11.0865	+	26.7651i	0.384585	+	0.928470i
$832$	30.7046	−	11.6666i	1.06449	−	0.404465i
$833$	−5.14075	−	1.98503i	−0.178117	−	0.0687771i
$834$	−21.2975	−	24.5281i	−0.737473	−	0.849340i
$835$	20.0481	−	12.2595i	0.693795	−	0.424258i
$836$	−11.4284	+	32.6068i	−0.395258	+	1.12773i
$837$			14.4328i			0.498870i
$838$	0.498391	+	0.873154i	0.0172166	+	0.0301626i
$839$	4.76340	+	23.9472i	0.164451	+	0.826750i	0.971641	+	0.236459i	$0.0759869\pi$
$839$	4.76340	+	23.9472i	0.164451	+	0.826750i	−0.807191	+	0.590291i	$0.799013\pi$
$840$	18.0316	−	2.56575i	0.622151	−	0.0885269i
$841$	18.6183	−	44.9485i	0.642010	−	1.54995i
$842$	0.588108	−	1.17789i	0.0202675	−	0.0405927i
$843$	1.57140	+	7.89995i	0.0541218	+	0.272089i
$844$	−14.2279	+	0.791716i	−0.489746	+	0.0272520i
$845$	−8.61872	−	0.346776i	−0.296493	−	0.0119295i
$846$	14.6803	+	1.03492i	0.504720	+	0.0355814i
$847$	35.5840	−	23.7765i	1.22268	−	0.816969i
$848$	11.1816	−	13.9919i	0.383979	−	0.480484i
$849$	−24.6998			−0.847695
$850$	−25.3111	−	14.4688i	−0.868164	−	0.496277i
$851$			0.753351i			0.0258245i
$852$	−5.24302	−	3.09640i	−0.179623	−	0.106081i
$853$	−17.3262	−	25.9305i	−0.593239	−	0.887845i	0.406427	−	0.913683i	$-0.366775\pi$
$853$	−17.3262	−	25.9305i	−0.593239	−	0.887845i	−0.999666	+	0.0258382i	$0.991775\pi$
$854$	2.07288	−	29.4037i	0.0709325	−	1.00617i
$855$	−0.443004	+	11.0103i	−0.0151504	+	0.376546i
$856$	21.6749	−	21.0430i	0.740834	−	0.719234i
$857$	5.53545	−	1.10107i	0.189087	−	0.0376118i	−0.0996381	−	0.995024i	$-0.531768\pi$
$857$	5.53545	−	1.10107i	0.189087	−	0.0376118i	0.288726	+	0.957412i	$0.406768\pi$
$858$	−16.8975	+	33.8431i	−0.576873	+	1.15538i
$859$	22.6594	+	9.38584i	0.773130	+	0.320241i	0.734139	−	0.678999i	$-0.237586\pi$
$859$	22.6594	+	9.38584i	0.773130	+	0.320241i	0.0389904	+	0.999240i	$0.487586\pi$
$860$	28.2135	+	18.2306i	0.962073	+	0.621658i
$861$	−16.2488	+	3.23209i	−0.553758	+	0.110149i
$862$	6.85722	−	3.91406i	0.233558	−	0.133313i
$863$	−30.6653			−1.04386			−0.521929	−	0.852989i	$-0.674787\pi$
$863$	−30.6653			−1.04386			−0.521929	+	0.852989i	$0.674787\pi$
$864$	−7.29406	−	30.1791i	−0.248149	−	1.02672i
$865$	−11.8689	−	19.4094i	−0.403555	−	0.659939i
$866$	25.5626	+	29.4401i	0.868651	+	1.00042i
$867$	16.5316	−	12.2431i	0.561441	−	0.415798i
$868$	−7.52089	−	10.0042i	−0.255276	−	0.339564i
$869$	57.6959	−	23.8984i	1.95720	−	0.810698i
$870$	−33.5144	−	3.72169i	−1.13624	−	0.126177i
$871$	11.5584	−	11.5584i	0.391641	−	0.391641i
$872$	−11.2739	−	28.3988i	−0.381784	−	0.961704i
$873$	−10.1735	+	15.2258i	−0.344322	+	0.515315i
$874$	−0.123972	−	0.978941i	−0.00419343	−	0.0331132i
$875$	26.5308	−	2.01246i	0.896904	−	0.0680336i
$876$	3.39289	+	2.00375i	0.114635	+	0.0677006i
$877$	38.3389	−	7.62608i	1.29461	−	0.257514i	0.500739	−	0.865598i	$-0.333061\pi$
$877$	38.3389	−	7.62608i	1.29461	−	0.257514i	0.793873	+	0.608084i	$0.208061\pi$
$878$	−3.02507	+	0.383093i	−0.102091	+	0.0129288i
$879$	−21.8208	−	32.6572i	−0.735998	−	1.10150i
$880$	6.02190	−	47.7744i	0.202998	−	1.61047i
$881$	−4.71704	+	23.7141i	−0.158921	+	0.798950i	0.816285	+	0.577650i	$0.196030\pi$
$881$	−4.71704	+	23.7141i	−0.158921	+	0.798950i	−0.975206	+	0.221300i	$0.928970\pi$
$882$	−0.919471	−	2.75320i	−0.0309602	−	0.0927052i
$883$	14.4381	−	14.4381i	0.485881	−	0.485881i	−0.421123	−	0.907004i	$-0.638364\pi$
$883$	14.4381	−	14.4381i	0.485881	−	0.485881i	0.907004	+	0.421123i	$0.138364\pi$
$884$	−3.93746	+	33.6275i	−0.132431	+	1.13101i
$885$	−38.8558	+	6.11657i	−1.30612	+	0.205606i
$886$	13.2587	+	6.61996i	0.445435	+	0.222402i
$887$	−20.7345	−	31.0313i	−0.696195	−	1.04193i	−0.996123	−	0.0879676i	$-0.971963\pi$
$887$	−20.7345	−	31.0313i	−0.696195	−	1.04193i	0.299928	−	0.953962i	$-0.403037\pi$
$888$	−9.95630	+	6.44162i	−0.334112	+	0.216167i
$889$	−32.6180	+	21.7947i	−1.09397	+	0.730970i
$890$	−2.66885	−	1.46943i	−0.0894599	−	0.0492554i
$891$	9.10750	+	6.08544i	0.305113	+	0.203870i
$892$	1.25666	+	4.88199i	0.0420759	+	0.163461i
$893$	8.32144	+	20.0897i	0.278466	+	0.672277i
$894$	−2.07233	−	16.3640i	−0.0693090	−	0.547295i
$895$	26.2454	+	12.1293i	0.877286	+	0.405439i
$896$	20.7822	+	17.1179i	0.694284	+	0.571870i
$897$		−	1.08030i		−	0.0360703i
$898$	−31.5482	−	8.62028i	−1.05278	−	0.287663i
$899$	8.86760	+	21.4083i	0.295751	+	0.714006i
$900$	−2.62097	−	15.1316i	−0.0873656	−	0.504385i
$901$	7.47587	+	16.8809i	0.249057	+	0.562383i
$902$	−3.08017	+	43.6920i	−0.102558	+	1.45478i
$903$	8.27763	−	19.9840i	0.275462	−	0.665024i
$904$	23.0555	−	9.15271i	0.766813	−	0.304415i
$905$	53.8168	−	8.47168i	1.78893	−	0.281608i
$906$	1.72963	−	6.33006i	0.0574632	−	0.210302i
$907$	−1.54129	+	2.30670i	−0.0511776	+	0.0765928i	−0.856176	−	0.516684i	$-0.827166\pi$
$907$	−1.54129	+	2.30670i	−0.0511776	+	0.0765928i	0.804998	+	0.593277i	$0.202166\pi$
$908$	1.18434	+	21.2838i	0.0393038	+	0.706328i
$909$	3.67895	−	8.88178i	0.122023	−	0.294590i
$910$	−14.2259	−	27.4289i	−0.471585	−	0.909258i
$911$	29.0881	+	19.4360i	0.963731	+	0.643944i	0.934626	−	0.355632i	$-0.115734\pi$
$911$	29.0881	+	19.4360i	0.963731	+	0.643944i	0.0291045	+	0.999576i	$0.490734\pi$
$912$	11.8777	−	10.0090i	0.393309	−	0.331430i
$913$	9.26922	−	46.5995i	0.306767	−	1.54222i
$914$	2.45067	−	34.7626i	0.0810610	−	1.14985i
$915$	23.6795	+	0.952752i	0.782821	+	0.0314970i
$916$	9.24141	+	35.9020i	0.305345	+	1.18624i
$917$	−15.3792	−	15.3792i	−0.507864	−	0.507864i
$918$	31.0670	+	7.68593i	1.02536	+	0.253673i
$919$		−	24.3629i		−	0.803658i	−0.915715	−	0.401829i	$-0.868375\pi$
$919$		−	24.3629i		−	0.803658i	0.915715	−	0.401829i	$-0.131625\pi$
$920$	0.455614	+	1.29752i	0.0150212	+	0.0427779i
$921$	−5.56738	−	1.10742i	−0.183451	−	0.0364907i
$922$	−26.8619	−	30.9365i	−0.884649	−	1.01884i
$923$	−2.01529	+	10.1315i	−0.0663341	+	0.333484i
$924$	−30.9592	+	1.72273i	−1.01848	+	0.0566737i
$925$	−15.1306	+	8.43609i	−0.497492	+	0.277377i
$926$	−13.3643	−	40.0170i	−0.439177	−	1.31504i
$927$	3.42328	+	8.26454i	0.112435	+	0.271443i
$928$	−29.3616	−	40.2835i	−0.963842	−	1.32237i
$929$	12.9525	−	2.57640i	0.424956	−	0.0845290i	0.0220209	−	0.999758i	$-0.492990\pi$
$929$	12.9525	−	2.57640i	0.424956	−	0.0845290i	0.402935	+	0.915228i	$0.367990\pi$
$930$	7.85712	−	6.28651i	0.257645	−	0.206143i
$931$	3.03271	−	3.03271i	0.0993930	−	0.0993930i
$932$	13.0438	+	27.1213i	0.427264	+	0.888387i
$933$	8.56220	−	20.6710i	0.280314	−	0.676737i
$934$	2.05782	+	2.36997i	0.0673340	+	0.0775477i
$935$	40.8227	+	28.2326i	1.33504	+	0.923306i
$936$	−14.9732	+	9.68752i	−0.489415	+	0.316646i
$937$	22.3474	+	9.25661i	0.730059	+	0.302400i	0.716576	−	0.697509i	$-0.245708\pi$
$937$	22.3474	+	9.25661i	0.730059	+	0.302400i	0.0134827	+	0.999909i	$0.495708\pi$
$938$	12.9251	+	3.53168i	0.422021	+	0.115313i
$939$	−25.8962	+	25.8962i	−0.845091	+	0.845091i
$940$	−17.2217	−	24.9356i	−0.561711	−	0.813309i
$941$	−0.107935	−	0.542625i	−0.00351858	−	0.0176891i	0.978986	−	0.203927i	$-0.0653705\pi$
$941$	−0.107935	−	0.542625i	−0.00351858	−	0.0176891i	−0.982505	+	0.186238i	$0.940370\pi$
$942$	5.82526	−	7.51462i	0.189797	−	0.244839i
$943$	−0.478698	−	1.15568i	−0.0155885	−	0.0376341i
$944$	−45.4242	−	36.3008i	−1.47843	−	1.18149i
$945$	−27.4112	+	10.0832i	−0.891687	+	0.328005i
$946$	−45.1972	−	35.0365i	−1.46949	−	1.13913i
$947$	6.65000	−	33.4318i	0.216096	−	1.08639i	−0.708580	−	0.705631i	$-0.750664\pi$
$947$	6.65000	−	33.4318i	0.216096	−	1.08639i	0.924675	−	0.380756i	$-0.124336\pi$
$948$	−27.7962	−	3.93869i	−0.902780	−	0.127923i
$949$	1.30414	−	6.55637i	0.0423343	−	0.212829i
$950$	18.2732	−	13.4522i	0.592862	−	0.436446i
$951$		−	12.9050i		−	0.418472i
$952$	−25.5394	+	10.8614i	−0.827737	+	0.352020i
$953$	20.4911	−	20.4911i	0.663772	−	0.663772i	−0.292495	−	0.956267i	$-0.594486\pi$
$953$	20.4911	−	20.4911i	0.663772	−	0.663772i	0.956267	+	0.292495i	$0.0944855\pi$
$954$	−4.34408	+	8.70051i	−0.140645	+	0.281689i
$955$	−25.5607	+	23.5834i	−0.827125	+	0.763140i
$956$	−8.65261	−	11.5096i	−0.279845	−	0.372246i
$957$	56.3041	+	11.1996i	1.82005	+	0.362031i
$958$	5.34704	+	42.2226i	0.172755	+	1.36415i
$959$	−29.4775	−	19.6962i	−0.951877	−	0.636024i
$960$	−13.2523	+	17.1160i	−0.427715	+	0.552417i
$961$	22.2518	+	9.21700i	0.717800	+	0.297323i
$962$	15.8998	+	12.3254i	0.512631	+	0.397387i
$963$	−9.11254	+	13.6379i	−0.293647	+	0.439474i
$964$	36.7899	−	17.6939i	1.18492	−	0.569882i
$965$	−25.0775	+	34.4478i	−0.807274	+	1.10892i
$966$	0.769068	−	0.438980i	0.0247444	−	0.0141239i
$967$	−16.2453	+	39.2196i	−0.522414	+	1.26122i	0.413986	+	0.910283i	$0.364136\pi$
$967$	−16.2453	+	39.2196i	−0.522414	+	1.26122i	−0.936400	+	0.350935i	$0.885864\pi$
$968$	−10.6600	+	49.7346i	−0.342625	+	1.59853i
$969$	3.50259	+	15.6227i	0.112519	+	0.501874i
$970$	37.5692	−	3.22967i	1.20627	−	0.103698i
$971$	−21.0527	−	50.8258i	−0.675614	−	1.63108i	−0.771916	−	0.635725i	$-0.780701\pi$
$971$	−21.0527	−	50.8258i	−0.675614	−	1.63108i	0.0963016	−	0.995352i	$-0.469299\pi$
$972$	12.1390	+	25.2400i	0.389359	+	0.809573i
$973$	−45.1730			−1.44818
$974$	0.546106	−	1.99862i	0.0174984	−	0.0640399i
$975$	21.6973	−	12.0973i	0.694869	−	0.387424i
$976$	22.5752	+	26.7900i	0.722613	+	0.857526i
$977$	−42.6246	+	17.6557i	−1.36368	+	0.564856i	−0.940068	−	0.340986i	$-0.889239\pi$
$977$	−42.6246	+	17.6557i	−1.36368	+	0.564856i	−0.423615	+	0.905842i	$0.639239\pi$
$978$	9.46230	−	18.9515i	0.302571	−	0.606002i
$979$	4.31261	+	2.88159i	0.137831	+	0.0920960i
$980$	−3.24395	+	5.02031i	−0.103624	+	0.160368i
$981$	9.21670	+	13.7938i	0.294267	+	0.440401i
$982$	23.5360	−	20.4361i	0.751065	−	0.652142i
$983$	13.8770	+	20.7684i	0.442607	+	0.662409i	0.983960	−	0.178387i	$-0.0570878\pi$
$983$	13.8770	+	20.7684i	0.442607	+	0.662409i	−0.541353	+	0.840795i	$0.682088\pi$
$984$	11.1803	−	16.2083i	0.356415	−	0.516700i
$985$	11.6101	−	1.82763i	0.369928	−	0.0582331i
$986$	50.8043	−	7.68717i	1.61794	−	0.244809i
$987$	−13.7987	+	13.7987i	−0.439216	+	0.439216i
$988$	−22.6893	−	13.3997i	−0.721842	−	0.426302i
$989$	1.60182	+	0.318622i	0.0509349	+	0.0101316i
$990$	2.23926	+	26.0482i	0.0711682	+	0.827865i
$991$	−17.0005	−	25.4430i	−0.540037	−	0.808223i	0.456642	−	0.889651i	$-0.349052\pi$
$991$	−17.0005	−	25.4430i	−0.540037	−	0.808223i	−0.996679	+	0.0814276i	$0.974052\pi$
$992$	14.6957	+	2.30460i	0.466588	+	0.0731712i
$993$	−3.04193	−	15.2928i	−0.0965329	−	0.485304i
$994$	−8.03156	+	2.68225i	−0.254746	+	0.0850759i
$995$	−3.02332	−	4.94408i	−0.0958458	−	0.156738i
$996$	−14.2407	+	15.9189i	−0.451233	+	0.504409i
$997$	−31.2211	−	20.8613i	−0.988781	−	0.660683i	−0.0476996	−	0.998862i	$-0.515189\pi$
$997$	−31.2211	−	20.8613i	−0.988781	−	0.660683i	−0.941082	+	0.338179i	$0.890189\pi$
$998$	−12.3535	+	7.05131i	−0.391043	+	0.223205i
$999$	13.4465	−	13.4465i	0.425430	−	0.425430i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	680.2.cf.a.37.12	✓	832
5.3	odd	4		680.2.ct.a.173.64	yes	832
8.5	even	2	inner	680.2.cf.a.37.38	yes	832
17.6	odd	16		680.2.ct.a.397.16	yes	832
40.13	odd	4		680.2.ct.a.173.16	yes	832
85.23	even	16	inner	680.2.cf.a.533.38	yes	832
136.125	odd	16		680.2.ct.a.397.64	yes	832
680.533	even	16	inner	680.2.cf.a.533.12	yes	832

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
680.2.cf.a.37.12	✓	832	1.1	even	1	trivial
680.2.cf.a.37.38	yes	832	8.5	even	2	inner
680.2.cf.a.533.12	yes	832	680.533	even	16	inner
680.2.cf.a.533.38	yes	832	85.23	even	16	inner
680.2.ct.a.173.16	yes	832	40.13	odd	4
680.2.ct.a.173.64	yes	832	5.3	odd	4
680.2.ct.a.397.16	yes	832	17.6	odd	16
680.2.ct.a.397.64	yes	832	136.125	odd	16

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 680 = 2^{3} \cdot 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	680.cf (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.34139 + 0.447975i) q^{2} +(-0.672289 - 1.00615i) q^{3} +(1.59864 - 1.20182i) q^{4} +(2.23426 + 0.0898960i) q^{5} +(1.35253 + 1.04847i) q^{6} +(2.33408 - 0.464277i) q^{7} +(-1.60601 + 2.32825i) q^{8} +(0.587682 - 1.41879i) q^{9} +(-3.03728 + 0.880308i) q^{10} +(5.28016 - 1.05029i) q^{11} +(-2.28395 - 0.800503i) q^{12} +4.10579i q^{13} +(-2.92291 + 1.66838i) q^{14} +(-1.41162 - 2.30844i) q^{15} +(1.11128 - 3.84253i) q^{16} +(2.98518 + 2.84407i) q^{17} +(-0.152726 + 2.16641i) q^{18} +(-2.96469 + 1.22802i) q^{19} +(3.67981 - 2.54146i) q^{20} +(-2.03631 - 2.03631i) q^{21} +(-6.61224 + 3.77423i) q^{22} +(0.120801 - 0.180792i) q^{23} +(3.42227 + 0.0506294i) q^{24} +(4.98384 + 0.401702i) q^{25} +(-1.83929 - 5.50745i) q^{26} +(-5.38312 + 1.07077i) q^{27} +(3.17336 - 3.54734i) q^{28} +(-7.32694 + 4.89570i) q^{29} +(2.92765 + 2.46414i) q^{30} +(0.513010 - 2.57908i) q^{31} +(0.230706 + 5.65215i) q^{32} +(-4.60654 - 4.60654i) q^{33} +(-5.27835 - 2.47771i) q^{34} +(5.25667 - 0.827490i) q^{35} +(-0.765634 - 2.97442i) q^{36} +(-2.88079 + 1.92488i) q^{37} +(3.42668 - 2.97535i) q^{38} +(4.13105 - 2.76028i) q^{39} +(-3.79754 + 5.05754i) q^{40} +(3.19616 - 4.78340i) q^{41} +(3.64369 + 1.81926i) q^{42} +(2.87440 + 6.93943i) q^{43} +(7.17881 - 8.02481i) q^{44} +(1.44058 - 3.11712i) q^{45} +(-0.0810508 + 0.296627i) q^{46} -6.77633i q^{47} +(-4.61327 + 1.46518i) q^{48} +(-1.23480 + 0.511471i) q^{49} +(-6.86521 + 1.69380i) q^{50} +(0.854664 - 4.91557i) q^{51} +(4.93441 + 6.56367i) q^{52} +(4.13689 + 1.71356i) q^{53} +(6.74117 - 3.84782i) q^{54} +(11.8917 - 1.87195i) q^{55} +(-2.66759 + 6.17994i) q^{56} +(3.22870 + 2.15735i) q^{57} +(7.63510 - 9.84932i) q^{58} +(5.56300 - 13.4303i) q^{59} +(-5.03099 - 1.99385i) q^{60} +(-4.86588 + 7.28231i) q^{61} +(0.467217 + 3.68936i) q^{62} +(0.712984 - 3.58441i) q^{63} +(-2.84149 - 7.47837i) q^{64} +(-0.369094 + 9.17341i) q^{65} +(8.24277 + 4.11554i) q^{66} +(-2.81514 - 2.81514i) q^{67} +(8.19026 + 0.959002i) q^{68} -0.263117 q^{69} +(-6.68053 + 3.46484i) q^{70} +(2.46762 + 0.490841i) q^{71} +(2.35948 + 3.64686i) q^{72} +(-1.59686 - 0.317635i) q^{73} +(3.00196 - 3.87254i) q^{74} +(-2.94640 - 5.28455i) q^{75} +(-3.26362 + 5.52617i) q^{76} +(11.8367 - 4.90291i) q^{77} +(-4.30480 + 5.55321i) q^{78} +(11.3771 - 2.26304i) q^{79} +(2.82831 - 8.48532i) q^{80} +(1.43868 + 1.43868i) q^{81} +(-2.14445 + 7.84818i) q^{82} +(3.37733 - 8.15361i) q^{83} +(-5.70258 - 0.808048i) q^{84} +(6.41399 + 6.62275i) q^{85} +(-6.96438 - 8.02079i) q^{86} +(9.85163 + 4.08068i) q^{87} +(-6.03464 + 13.9803i) q^{88} +(0.681248 + 0.681248i) q^{89} +(-0.535982 + 4.82660i) q^{90} +(1.90622 + 9.58323i) q^{91} +(-0.0241612 - 0.434201i) q^{92} +(-2.93983 + 1.21772i) q^{93} +(3.03563 + 9.08967i) q^{94} +(-6.73429 + 2.47719i) q^{95} +(5.53181 - 4.03200i) q^{96} +(-11.6951 - 2.32630i) q^{97} +(1.42722 - 1.23924i) q^{98} +(1.61292 - 8.10868i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 832 q - 8 q^{2} - 16 q^{6} - 16 q^{7} - 8 q^{8} - 8 q^{10} - 32 q^{12} - 32 q^{14} - 16 q^{15} - 16 q^{17} - 16 q^{18} - 8 q^{20} - 8 q^{22} - 16 q^{23} - 16 q^{25} - 48 q^{26} - 40 q^{28} - 72 q^{30} - 32 q^{31}+ \cdots - 16 q^{98}+O(q^{100}) \) 832 * q - 8 * q^2 - 16 * q^6 - 16 * q^7 - 8 * q^8 - 8 * q^10 - 32 * q^12 - 32 * q^14 - 16 * q^15 - 16 * q^17 - 16 * q^18 - 8 * q^20 - 8 * q^22 - 16 * q^23 - 16 * q^25 - 48 * q^26 - 40 * q^28 - 72 * q^30 - 32 * q^31 - 8 * q^32 + 48 * q^36 + 96 * q^39 + 48 * q^40 - 32 * q^41 + 8 * q^42 - 32 * q^46 + 72 * q^48 - 16 * q^52 - 64 * q^54 - 16 * q^55 - 16 * q^56 - 16 * q^57 - 64 * q^58 - 8 * q^60 - 8 * q^62 - 64 * q^63 + 64 * q^65 - 16 * q^66 - 128 * q^68 - 72 * q^70 - 32 * q^71 - 16 * q^72 - 96 * q^73 - 16 * q^76 - 64 * q^78 - 136 * q^80 - 32 * q^81 - 8 * q^82 - 96 * q^84 - 32 * q^86 - 16 * q^87 + 80 * q^88 + 136 * q^90 + 104 * q^92 + 48 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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