LMFDB - Embedded newform 196.2.j.a.111.19

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [196,2,Mod(27,196)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("196.27"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(196, base_ring=CyclotomicField(14)) chi = DirichletCharacter(H, H._module([7, 1])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 196 = 2^{2} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	196.j (of order $14$, degree $6$, 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:	$1.56506787962$
Analytic rank:	$0$
Dimension:	$156$
Relative dimension:	$26$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			111.19
Character	$\chi$	$=$	196.111
Dual form			196.2.j.a.83.19

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.846372 - 1.13298i) q^{2} +(0.635719 + 0.797166i) q^{3} +(-0.567307 - 1.91785i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(1.44123 - 0.0455600i) q^{6} +(2.60326 - 0.472259i) q^{7} +(-2.65305 - 0.980468i) q^{8} +(0.436227 - 1.91124i) q^{9} +(0.0415101 + 1.31312i) q^{10} +(5.04868 - 1.15233i) q^{11} +(1.16820 - 1.67145i) q^{12} +(-2.71007 + 0.618555i) q^{13} +(1.66827 - 3.34916i) q^{14} +(-0.923453 - 0.210772i) q^{15} +(-3.35632 + 2.17602i) q^{16} +(-2.67586 + 5.55648i) q^{17} +(-1.79619 - 2.11186i) q^{18} -5.31475 q^{19} +(1.52288 + 1.06436i) q^{20} +(2.03141 + 1.77501i) q^{21} +(2.96750 - 6.69538i) q^{22} +(2.67158 + 5.54759i) q^{23} +(-0.904999 - 2.73823i) q^{24} +(-0.920568 + 4.03327i) q^{25} +(-1.59291 + 3.59399i) q^{26} +(4.55681 - 2.19445i) q^{27} +(-2.38257 - 4.72476i) q^{28} +(-6.99898 - 3.37053i) q^{29} +(-1.02039 + 0.867866i) q^{30} -2.80797 q^{31} +(-0.375299 + 5.64439i) q^{32} +(4.12814 + 3.29208i) q^{33} +(4.03063 + 7.73455i) q^{34} +(-1.61723 + 1.85084i) q^{35} +(-3.91295 + 0.247638i) q^{36} +(-5.03268 - 2.42361i) q^{37} +(-4.49826 + 6.02153i) q^{38} +(-2.21593 - 1.76715i) q^{39} +(2.49482 - 0.824553i) q^{40} +(8.64941 - 6.89767i) q^{41} +(3.73039 - 0.799240i) q^{42} +(-1.76174 - 1.40494i) q^{43} +(-5.07415 - 9.02891i) q^{44} +(0.790172 + 1.64081i) q^{45} +(8.54648 + 1.66847i) q^{46} +(1.31376 + 5.75595i) q^{47} +(-3.86833 - 1.29221i) q^{48} +(6.55394 - 2.45883i) q^{49} +(3.79049 + 4.45664i) q^{50} +(-6.13053 + 1.39925i) q^{51} +(2.72374 + 4.84660i) q^{52} +(3.53549 - 1.70260i) q^{53} +(1.37049 - 7.02012i) q^{54} +(-2.99945 + 3.76119i) q^{55} +(-7.36962 - 1.29949i) q^{56} +(-3.37869 - 4.23674i) q^{57} +(-9.74251 + 5.07701i) q^{58} +(3.63089 - 4.55299i) q^{59} +(0.119651 + 1.89062i) q^{60} +(-2.83755 + 5.89224i) q^{61} +(-2.37659 + 3.18138i) q^{62} +(0.233014 - 5.18146i) q^{63} +(6.07736 + 5.20247i) q^{64} +(1.61006 - 2.01896i) q^{65} +(7.22383 - 1.89079i) q^{66} +7.05842i q^{67} +(12.1745 + 1.97967i) q^{68} +(-2.72398 + 5.65640i) q^{69} +(0.728195 + 3.39879i) q^{70} +(0.607747 + 1.26200i) q^{71} +(-3.03124 + 4.64290i) q^{72} +(-4.23286 - 0.966123i) q^{73} +(-7.00543 + 3.65067i) q^{74} +(-3.80041 + 1.83018i) q^{75} +(3.01510 + 10.1929i) q^{76} +(12.5988 - 5.38410i) q^{77} +(-3.87766 + 1.01495i) q^{78} -1.47889i q^{79} +(1.17734 - 3.52447i) q^{80} +(-0.652553 - 0.314253i) q^{81} +(-0.494335 - 15.6376i) q^{82} +(2.36598 - 10.3660i) q^{83} +(2.25177 - 4.90293i) q^{84} +(-1.27487 - 5.58558i) q^{85} +(-3.08286 + 0.806921i) q^{86} +(-1.76251 - 7.72207i) q^{87} +(-14.5242 - 1.89289i) q^{88} +(8.05318 + 1.83809i) q^{89} +(2.52779 + 0.493483i) q^{90} +(-6.76290 + 2.89012i) q^{91} +(9.12386 - 8.27088i) q^{92} +(-1.78508 - 2.23842i) q^{93} +(7.63333 + 3.38321i) q^{94} +(3.86013 - 3.07835i) q^{95} +(-4.73810 + 3.28907i) q^{96} -11.4703i q^{97} +(2.76126 - 9.50660i) q^{98} -10.1519i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) $ 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/196\mathbb{Z}\right)^\times$.

$n$	$99$	$101$
$\chi(n)$	$-1$	$e\left(\frac{11}{14}\right)$

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 $

$2$	0.846372	−	1.13298i	0.598476	−	0.801141i
$2$	0.846372	−	1.13298i	0.598476	−	0.801141i
$3$	0.635719	+	0.797166i	0.367033	+	0.460244i	0.930714	−	0.365748i	$-0.119187\pi$
$3$	0.635719	+	0.797166i	0.367033	+	0.460244i	−0.563681	+	0.825992i	$0.690615\pi$
$4$	−0.567307	−	1.91785i	−0.283654	−	0.958927i
$5$	−0.726306	+	0.579209i	−0.324814	+	0.259030i	−0.772297	−	0.635262i	$-0.780892\pi$
$5$	−0.726306	+	0.579209i	−0.324814	+	0.259030i	0.447483	+	0.894293i	$0.352321\pi$
$6$	1.44123	−	0.0455600i	0.588381	−	0.0185998i
$7$	2.60326	−	0.472259i	0.983940	−	0.178497i
$7$	2.60326	−	0.472259i	0.983940	−	0.178497i
$8$	−2.65305	−	0.980468i	−0.937995	−	0.346648i
$9$	0.436227	−	1.91124i	0.145409	−	0.637079i
$10$	0.0415101	+	1.31312i	0.0131267	+	0.415245i
$11$	5.04868	−	1.15233i	1.52224	−	0.347440i	0.622061	−	0.782969i	$-0.286296\pi$
$11$	5.04868	−	1.15233i	1.52224	−	0.347440i	0.900175	+	0.435529i	$0.143439\pi$
$12$	1.16820	−	1.67145i	0.337230	−	0.482507i
$13$	−2.71007	+	0.618555i	−0.751638	+	0.171556i	−0.581142	−	0.813802i	$-0.697394\pi$
$13$	−2.71007	+	0.618555i	−0.751638	+	0.171556i	−0.170495	+	0.985358i	$0.554537\pi$
$14$	1.66827	−	3.34916i	0.445863	−	0.895101i
$15$	−0.923453	−	0.210772i	−0.238434	−	0.0544211i
$16$	−3.35632	+	2.17602i	−0.839081	+	0.544006i
$17$	−2.67586	+	5.55648i	−0.648991	+	1.34764i	0.273593	+	0.961846i	$0.411788\pi$
$17$	−2.67586	+	5.55648i	−0.648991	+	1.34764i	−0.922583	+	0.385798i	$0.873926\pi$
$18$	−1.79619	−	2.11186i	−0.423366	−	0.497769i
$19$	−5.31475			−1.21929			−0.609644	−	0.792675i	$-0.708688\pi$
$19$	−5.31475			−1.21929			−0.609644	+	0.792675i	$0.708688\pi$
$20$	1.52288	+	1.06436i	0.340526	+	0.237998i
$21$	2.03141	+	1.77501i	0.443290	+	0.387339i
$22$	2.96750	−	6.69538i	0.632672	−	1.42746i
$23$	2.67158	+	5.54759i	0.557062	+	1.15675i	0.969347	+	0.245697i	$0.0790167\pi$
$23$	2.67158	+	5.54759i	0.557062	+	1.15675i	−0.412284	+	0.911055i	$0.635269\pi$
$24$	−0.904999	−	2.73823i	−0.184732	−	0.558938i
$25$	−0.920568	+	4.03327i	−0.184114	+	0.806655i
$26$	−1.59291	+	3.59399i	−0.312396	+	0.704840i
$27$	4.55681	−	2.19445i	0.876959	−	0.422321i
$28$	−2.38257	−	4.72476i	−0.450264	−	0.892895i
$29$	−6.99898	−	3.37053i	−1.29968	−	0.625892i	−0.349307	−	0.937008i	$-0.613583\pi$
$29$	−6.99898	−	3.37053i	−1.29968	−	0.625892i	−0.950372	+	0.311116i	$0.899297\pi$
$30$	−1.02039	+	0.867866i	−0.186296	+	0.158450i
$31$	−2.80797			−0.504326			−0.252163	−	0.967685i	$-0.581142\pi$
$31$	−2.80797			−0.504326			−0.252163	+	0.967685i	$0.581142\pi$
$32$	−0.375299	+	5.64439i	−0.0663442	+	0.997797i
$33$	4.12814	+	3.29208i	0.718617	+	0.573078i
$34$	4.03063	+	7.73455i	0.691247	+	1.32646i
$35$	−1.61723	+	1.85084i	−0.273361	+	0.312849i
$36$	−3.91295	+	0.247638i	−0.652158	+	0.0412730i
$37$	−5.03268	−	2.42361i	−0.827367	−	0.398439i	−0.0282401	−	0.999601i	$-0.508990\pi$
$37$	−5.03268	−	2.42361i	−0.827367	−	0.398439i	−0.799127	+	0.601162i	$0.794705\pi$
$38$	−4.49826	+	6.02153i	−0.729714	+	0.976821i
$39$	−2.21593	−	1.76715i	−0.354833	−	0.282970i
$40$	2.49482	−	0.824553i	0.394466	−	0.130373i
$41$	8.64941	−	6.89767i	1.35081	−	1.07724i	0.361351	−	0.932430i	$-0.382316\pi$
$41$	8.64941	−	6.89767i	1.35081	−	1.07724i	0.989460	−	0.144805i	$-0.0462556\pi$
$42$	3.73039	−	0.799240i	0.575611	−	0.123325i
$43$	−1.76174	−	1.40494i	−0.268663	−	0.214252i	0.479886	−	0.877331i	$-0.340678\pi$
$43$	−1.76174	−	1.40494i	−0.268663	−	0.214252i	−0.748549	+	0.663079i	$0.769249\pi$
$44$	−5.07415	−	9.02891i	−0.764957	−	1.36116i
$45$	0.790172	+	1.64081i	0.117792	+	0.244597i
$46$	8.54648	+	1.66847i	1.26011	+	0.246002i
$47$	1.31376	+	5.75595i	0.191631	+	0.839592i	0.975734	+	0.218960i	$0.0702665\pi$
$47$	1.31376	+	5.75595i	0.191631	+	0.839592i	−0.784102	+	0.620631i	$0.786876\pi$
$48$	−3.86833	−	1.29221i	−0.558346	−	0.186514i
$49$	6.55394	−	2.45883i	0.936277	−	0.351261i
$50$	3.79049	+	4.45664i	0.536057	+	0.630264i
$51$	−6.13053	+	1.39925i	−0.858446	+	0.195935i
$52$	2.72374	+	4.84660i	0.377715	+	0.672103i
$53$	3.53549	−	1.70260i	0.485636	−	0.233870i	−0.175011	−	0.984566i	$-0.555996\pi$
$53$	3.53549	−	1.70260i	0.485636	−	0.233870i	0.660647	+	0.750696i	$0.270282\pi$
$54$	1.37049	−	7.02012i	0.186500	−	0.955317i
$55$	−2.99945	+	3.76119i	−0.404445	+	0.507159i
$56$	−7.36962	−	1.29949i	−0.984807	−	0.173651i
$57$	−3.37869	−	4.23674i	−0.447518	−	0.561170i
$58$	−9.74251	+	5.07701i	−1.27925	+	0.666644i
$59$	3.63089	−	4.55299i	0.472701	−	0.592749i	−0.487129	−	0.873330i	$-0.661956\pi$
$59$	3.63089	−	4.55299i	0.472701	−	0.592749i	0.959830	+	0.280581i	$0.0905273\pi$
$60$	0.119651	+	1.89062i	0.0154469	+	0.244078i
$61$	−2.83755	+	5.89224i	−0.363311	+	0.754424i	−0.999859	−	0.0168139i	$-0.994648\pi$
$61$	−2.83755	+	5.89224i	−0.363311	+	0.754424i	0.636547	+	0.771238i	$0.280362\pi$
$62$	−2.37659	+	3.18138i	−0.301827	+	0.404036i
$63$	0.233014	−	5.18146i	0.0293570	−	0.652803i
$64$	6.07736	+	5.20247i	0.759670	+	0.650308i
$65$	1.61006	−	2.01896i	0.199704	−	0.250421i
$66$	7.22383	−	1.89079i	0.889191	−	0.232740i
$67$			7.05842i			0.862324i	0.902275	+	0.431162i	$0.141896\pi$
$67$			7.05842i			0.862324i	−0.902275	+	0.431162i	$0.858104\pi$
$68$	12.1745	+	1.97967i	1.47638	+	0.240071i
$69$	−2.72398	+	5.65640i	−0.327928	+	0.680950i
$70$	0.728195	+	3.39879i	0.0870359	+	0.406233i
$71$	0.607747	+	1.26200i	0.0721264	+	0.149772i	0.933914	−	0.357496i	$-0.116370\pi$
$71$	0.607747	+	1.26200i	0.0721264	+	0.149772i	−0.861788	+	0.507268i	$0.830655\pi$
$72$	−3.03124	+	4.64290i	−0.357235	+	0.547171i
$73$	−4.23286	−	0.966123i	−0.495419	−	0.113076i	−0.0324911	−	0.999472i	$-0.510344\pi$
$73$	−4.23286	−	0.966123i	−0.495419	−	0.113076i	−0.462928	+	0.886396i	$0.653201\pi$
$74$	−7.00543	+	3.65067i	−0.814365	+	0.424382i
$75$	−3.80041	+	1.83018i	−0.438834	+	0.211331i
$76$	3.01510	+	10.1929i	0.345855	+	1.16921i
$77$	12.5988	−	5.38410i	1.43577	−	0.613575i
$78$	−3.87766	+	1.01495i	−0.439058	+	0.114921i
$79$		−	1.47889i		−	0.166388i	−0.996533	−	0.0831942i	$-0.973488\pi$
$79$		−	1.47889i		−	0.166388i	0.996533	−	0.0831942i	$-0.0265122\pi$
$80$	1.17734	−	3.52447i	0.131631	−	0.394048i
$81$	−0.652553	−	0.314253i	−0.0725058	−	0.0349170i
$82$	−0.494335	−	15.6376i	−0.0545901	−	1.72689i
$83$	2.36598	−	10.3660i	0.259700	−	1.13782i	−0.661873	−	0.749616i	$-0.730238\pi$
$83$	2.36598	−	10.3660i	0.259700	−	1.13782i	0.921573	−	0.388205i	$-0.126905\pi$
$84$	2.25177	−	4.90293i	0.245688	−	0.534953i
$85$	−1.27487	−	5.58558i	−0.138279	−	0.605841i
$86$	−3.08286	+	0.806921i	−0.332434	+	0.0870125i
$87$	−1.76251	−	7.72207i	−0.188961	−	0.827892i
$88$	−14.5242	−	1.89289i	−1.54829	−	0.201782i
$89$	8.05318	+	1.83809i	0.853636	+	0.194837i	0.626881	−	0.779115i	$-0.284331\pi$
$89$	8.05318	+	1.83809i	0.853636	+	0.194837i	0.226755	+	0.973952i	$0.427188\pi$
$90$	2.52779	+	0.493483i	0.266452	+	0.0520177i
$91$	−6.76290	+	2.89012i	−0.708944	+	0.302967i
$92$	9.12386	−	8.27088i	0.951228	−	0.862299i
$93$	−1.78508	−	2.23842i	−0.185104	−	0.232113i
$94$	7.63333	+	3.38321i	0.787318	+	0.348952i
$95$	3.86013	−	3.07835i	0.396041	−	0.315833i
$96$	−4.73810	+	3.28907i	−0.483581	+	0.335689i
$97$		−	11.4703i		−	1.16463i	−0.812963	−	0.582316i	$-0.802147\pi$
$97$		−	11.4703i		−	1.16463i	0.812963	−	0.582316i	$-0.197853\pi$
$98$	2.76126	−	9.50660i	0.278929	−	0.960312i
$99$		−	10.1519i		−	1.02030i
$100$	8.25747	−	0.522590i	0.825747	−	0.0522590i
$101$	−11.8837	+	9.47693i	−1.18247	+	0.942989i	−0.999197	−	0.0400725i	$-0.987241\pi$
$101$	−11.8837	+	9.47693i	−1.18247	+	0.942989i	−0.183274	+	0.983062i	$0.558670\pi$
$102$	−3.60338	+	8.13008i	−0.356788	+	0.804998i
$103$	−6.06708	−	7.60788i	−0.597808	−	0.749627i	0.387227	−	0.921984i	$-0.373433\pi$
$103$	−6.06708	−	7.60788i	−0.597808	−	0.749627i	−0.985034	+	0.172357i	$0.944862\pi$
$104$	7.79642	+	1.01608i	0.764502	+	0.0996345i
$105$	−2.50353	−	0.112586i	−0.244319	−	0.0109872i
$106$	1.06332	−	5.44668i	0.103279	−	0.529029i
$107$	4.09741	+	0.935207i	0.396111	+	0.0904098i	0.415937	−	0.909394i	$-0.363454\pi$
$107$	4.09741	+	0.935207i	0.396111	+	0.0904098i	−0.0198252	+	0.999803i	$0.506311\pi$
$108$	−6.79374	−	7.49438i	−0.653728	−	0.721147i
$109$	−1.62349	−	7.11295i	−0.155502	−	0.681297i	−0.991229	−	0.132153i	$-0.957811\pi$
$109$	−1.62349	−	7.11295i	−0.155502	−	0.681297i	0.835728	−	0.549144i	$-0.185046\pi$
$110$	1.72272	+	6.58169i	0.164255	+	0.627540i
$111$	−1.26735	−	5.55262i	−0.120291	−	0.527031i
$112$	−7.70974	+	7.24982i	−0.728502	+	0.685043i
$113$	−1.59142	+	6.97247i	−0.149708	+	0.655915i	0.843257	+	0.537510i	$0.180635\pi$
$113$	−1.59142	+	6.97247i	−0.149708	+	0.655915i	−0.992965	+	0.118404i	$0.962222\pi$
$114$	−7.65979	+	0.242140i	−0.717405	+	0.0226785i
$115$	−5.15360	−	2.48184i	−0.480575	−	0.231433i
$116$	−2.49361	+	15.3352i	−0.231526	+	1.42383i
$117$			5.44941i			0.503798i
$118$	−2.08538	−	7.96726i	−0.191975	−	0.733446i
$119$	−4.34186	+	15.7287i	−0.398018	+	1.44184i
$120$	2.24331	+	1.46461i	0.204785	+	0.133700i
$121$	14.2507	−	6.86277i	1.29552	−	0.623888i
$122$	4.27419	+	8.20193i	0.386967	+	0.742568i
$123$	10.9972	+	2.51004i	0.991583	+	0.226322i
$124$	1.59298	+	5.38527i	0.143054	+	0.483611i
$125$	−3.68284	−	7.64750i	−0.329403	−	0.684013i
$126$	−5.67330	−	4.64945i	−0.505417	−	0.414206i
$127$	2.83208	−	5.88087i	0.251306	−	0.521843i	−0.736707	−	0.676212i	$-0.763620\pi$
$127$	2.83208	−	5.88087i	0.251306	−	0.521843i	0.988013	+	0.154369i	$0.0493346\pi$
$128$	11.0380	−	2.48233i	0.975633	−	0.219409i
$129$		−	2.29755i		−	0.202288i
$130$	−0.924732	−	3.53297i	−0.0811044	−	0.309862i
$131$	9.72960	−	12.2005i	0.850080	−	1.06597i	−0.146965	−	0.989142i	$-0.546951\pi$
$131$	9.72960	−	12.2005i	0.850080	−	1.06597i	0.997045	−	0.0768243i	$-0.0244781\pi$
$132$	3.97181	−	9.78480i	0.345702	−	0.851657i
$133$	−13.8357	+	2.50994i	−1.19971	+	0.217640i
$134$	7.99709	+	5.97406i	0.690843	+	0.516080i
$135$	−2.03860	+	4.23319i	−0.175454	+	0.364335i
$136$	12.5471	−	12.1180i	1.07591	−	1.03911i
$137$	1.56347	−	1.96053i	0.133576	−	0.167500i	−0.710545	−	0.703652i	$-0.751551\pi$
$137$	1.56347	−	1.96053i	0.133576	−	0.167500i	0.844121	+	0.536153i	$0.180123\pi$
$138$	4.10311	+	7.87364i	0.349280	+	0.670249i
$139$	2.50048	+	3.13550i	0.212088	+	0.265950i	0.876484	−	0.481431i	$-0.159883\pi$
$139$	2.50048	+	3.13550i	0.212088	+	0.265950i	−0.664396	+	0.747380i	$0.731311\pi$
$140$	4.46710	+	2.05161i	0.377539	+	0.173393i
$141$	−3.75327	+	4.70645i	−0.316082	+	0.396355i
$142$	1.94421	+	0.379554i	0.163154	+	0.0318515i
$143$	−12.9695	+	6.24578i	−1.08456	+	0.522298i
$144$	2.69478	+	7.36397i	0.224565	+	0.613664i
$145$	7.03565	−	1.60584i	0.584279	−	0.133358i
$146$	−4.67718	+	3.97807i	−0.387086	+	0.329227i
$147$	6.12656	+	3.66146i	0.505310	+	0.301992i
$148$	−1.79305	+	11.0269i	−0.147388	+	0.906403i
$149$	0.452330	+	1.98179i	0.0370563	+	0.162354i	0.990071	−	0.140571i	$-0.0448938\pi$
$149$	0.452330	+	1.98179i	0.0370563	+	0.162354i	−0.953014	+	0.302925i	$0.902037\pi$
$150$	−1.14300	+	5.85482i	−0.0933253	+	0.478044i
$151$	−1.45269	−	3.01654i	−0.118218	−	0.245483i	0.833460	−	0.552580i	$-0.186357\pi$
$151$	−1.45269	−	3.01654i	−0.118218	−	0.245483i	−0.951678	+	0.307097i	$0.900642\pi$
$152$	14.1003	+	5.21095i	1.14369	+	0.422664i
$153$	9.45246	+	7.53808i	0.764186	+	0.609418i
$154$	4.56321	−	18.8313i	0.367714	−	1.51747i
$155$	2.03944	−	1.62640i	0.163812	−	0.130636i
$156$	−2.13202	+	5.25235i	−0.170698	+	0.420525i
$157$	−0.749519	−	0.597722i	−0.0598181	−	0.0477034i	0.593124	−	0.805111i	$-0.297894\pi$
$157$	−0.749519	−	0.597722i	−0.0598181	−	0.0477034i	−0.652942	+	0.757407i	$0.726466\pi$
$158$	−1.67556	−	1.25169i	−0.133301	−	0.0995794i
$159$	3.60483	+	1.73600i	0.285882	+	0.137673i
$160$	−2.99670	−	4.31693i	−0.236910	−	0.341283i
$161$	9.57472	+	13.1801i	0.754593	+	1.03874i
$162$	−0.908346	+	0.473357i	−0.0713664	+	0.0371904i
$163$	8.79053	+	7.01022i	0.688528	+	0.549082i	0.904055	−	0.427415i	$-0.140576\pi$
$163$	8.79053	+	7.01022i	0.688528	+	0.549082i	−0.215528	+	0.976498i	$0.569147\pi$
$164$	−18.1356	−	12.6752i	−1.41615	−	0.989767i
$165$	−4.90510			−0.381861
$166$	−9.74207	−	11.4542i	−0.756131	−	0.889015i
$167$	−2.46446	−	1.18682i	−0.190706	−	0.0918390i	0.336094	−	0.941828i	$-0.390894\pi$
$167$	−2.46446	−	1.18682i	−0.190706	−	0.0918390i	−0.526800	+	0.849989i	$0.676608\pi$
$168$	−3.64910	−	6.70092i	−0.281534	−	0.516988i
$169$	−4.75074	+	2.28784i	−0.365441	+	0.175987i
$170$	−7.40739	−	3.28307i	−0.568121	−	0.251800i
$171$	−2.31844	+	10.1577i	−0.177295	+	0.776782i
$172$	−1.69502	+	4.17579i	−0.129244	+	0.318401i
$173$	5.47431	+	11.3675i	0.416204	+	0.864257i	0.998678	+	0.0514072i	$0.0163706\pi$
$173$	5.47431	+	11.3675i	0.416204	+	0.864257i	−0.582474	+	0.812850i	$0.697915\pi$
$174$	−10.2407	−	4.53885i	−0.776347	−	0.344089i
$175$	−0.491729	+	10.9344i	−0.0371712	+	0.826564i
$176$	−14.4375	+	14.8537i	−1.08827	+	1.11964i
$177$	5.93771			0.446306
$178$	8.89852	−	7.56842i	0.666972	−	0.567277i
$179$	−4.51082	+	9.36681i	−0.337154	+	0.700108i	−0.998762	−	0.0497418i	$-0.984160\pi$
$179$	−4.51082	+	9.36681i	−0.337154	+	0.700108i	0.661608	+	0.749850i	$0.269874\pi$
$180$	2.69856	−	2.44628i	0.201139	−	0.182335i
$181$	−8.90161	−	2.03174i	−0.661652	−	0.151018i	−0.121508	−	0.992590i	$-0.538773\pi$
$181$	−8.90161	−	2.03174i	−0.661652	−	0.151018i	−0.540144	+	0.841573i	$0.681630\pi$
$182$	−2.44947	+	10.1084i	−0.181567	+	0.749282i
$183$	−6.50098	+	1.48381i	−0.480566	+	0.109686i
$184$	−1.64860	−	17.3374i	−0.121536	−	1.27813i
$185$	5.05904	−	1.15469i	0.371948	−	0.0848947i
$186$	−4.04693	+	0.127931i	−0.296735	+	0.00938035i
$187$	−7.10667	+	31.1364i	−0.519691	+	2.27692i
$188$	10.2938	−	5.78499i	0.750750	−	0.421914i
$189$	10.8262	−	7.86471i	0.787492	−	0.572074i
$190$	−0.220616	−	6.97891i	−0.0160052	−	0.506303i
$191$	13.2051	−	10.5307i	0.955486	−	0.761975i	−0.0158035	−	0.999875i	$-0.505031\pi$
$191$	13.2051	−	10.5307i	0.955486	−	0.761975i	0.971290	+	0.237900i	$0.0764592\pi$
$192$	−0.283735	+	8.15198i	−0.0204768	+	0.588318i
$193$	−6.54666	−	8.20926i	−0.471239	−	0.590915i	0.488235	−	0.872712i	$-0.337641\pi$
$193$	−6.54666	−	8.20926i	−0.471239	−	0.590915i	−0.959474	+	0.281797i	$0.909070\pi$
$194$	−12.9957	−	9.70813i	−0.933034	−	0.697003i
$195$	2.63299			0.188553
$196$	−8.43377	−	11.1746i	−0.602412	−	0.798185i
$197$	−11.8054			−0.841099			−0.420550	−	0.907269i	$-0.638163\pi$
$197$	−11.8054			−0.841099			−0.420550	+	0.907269i	$0.638163\pi$
$198$	−11.5019	−	8.59229i	−0.817408	−	0.610628i
$199$	0.317945	+	0.398690i	0.0225385	+	0.0282624i	0.792973	−	0.609257i	$-0.208532\pi$
$199$	0.317945	+	0.398690i	0.0225385	+	0.0282624i	−0.770435	+	0.637519i	$0.779961\pi$
$200$	6.39681	−	9.79789i	0.452323	−	0.692816i
$201$	−5.62674	+	4.48717i	−0.396880	+	0.316501i
$202$	0.679181	+	21.4850i	0.0477870	+	1.51168i
$203$	−19.8120	−	5.46904i	−1.39053	−	0.383852i
$204$	6.16146	+	10.9637i	0.431388	+	0.767609i
$205$	−2.28692	+	10.0196i	−0.159725	+	0.699802i
$206$	−13.7546	+	0.434809i	−0.958330	+	0.0302946i
$207$	11.7682	−	2.68601i	0.817944	−	0.186690i
$208$	7.74988	−	7.97325i	0.537357	−	0.552845i
$209$	−26.8325	+	6.12434i	−1.85604	+	0.423630i
$210$	−2.24647	+	2.74117i	−0.155021	+	0.189159i
$211$	−0.438590	−	0.100105i	−0.0301938	−	0.00689154i	0.207397	−	0.978257i	$-0.433501\pi$
$211$	−0.438590	−	0.100105i	−0.0301938	−	0.00689154i	−0.237591	+	0.971365i	$0.576358\pi$
$212$	−5.27104	−	5.81465i	−0.362017	−	0.399352i
$213$	−0.619668	+	1.28675i	−0.0424589	+	0.0881669i
$214$	4.52751	−	3.85077i	0.309494	−	0.263233i
$215$	2.09332			0.142763
$216$	−14.2410	+	1.35417i	−0.968980	+	0.0921393i
$217$	−7.30987	+	1.32609i	−0.496226	+	0.0900208i
$218$	−9.43294	−	4.18082i	−0.638879	−	0.283161i
$219$	−1.92075	−	3.98848i	−0.129792	−	0.269516i
$220$	8.91502	+	3.61875i	0.601050	+	0.243976i
$221$	3.81477	−	16.7136i	0.256609	−	1.12428i
$222$	−7.36368	−	3.26370i	−0.494218	−	0.219045i
$223$	19.5719	−	9.42534i	1.31063	−	0.631167i	0.357555	−	0.933892i	$-0.383611\pi$
$223$	19.5719	−	9.42534i	1.31063	−	0.631167i	0.953078	+	0.302725i	$0.0978963\pi$
$224$	1.68861	+	14.8711i	0.112825	+	0.993615i
$225$	7.30696	+	3.51885i	0.487131	+	0.234590i
$226$	6.55276	+	7.70436i	0.435883	+	0.512486i
$227$	−1.22521			−0.0813200			−0.0406600	−	0.999173i	$-0.512946\pi$
$227$	−1.22521			−0.0813200			−0.0406600	+	0.999173i	$0.512946\pi$
$228$	−6.20870	+	8.88337i	−0.411181	+	0.588315i
$229$	−15.2692	−	12.1768i	−1.00902	−	0.804667i	−0.0282040	−	0.999602i	$-0.508979\pi$
$229$	−15.2692	−	12.1768i	−1.00902	−	0.804667i	−0.980816	+	0.194936i	$0.937550\pi$
$230$	−7.17375	+	3.73838i	−0.473023	+	0.246502i
$231$	12.3014	+	6.62060i	0.809370	+	0.435604i
$232$	15.2640	+	15.8045i	1.00213	+	1.03761i
$233$	20.5149	+	9.87944i	1.34397	+	0.647224i	0.961003	−	0.276537i	$-0.0891868\pi$
$233$	20.5149	+	9.87944i	1.34397	+	0.647224i	0.382970	+	0.923761i	$0.374901\pi$
$234$	6.17410	+	4.61223i	0.403613	+	0.301511i
$235$	−4.28809	−	3.41964i	−0.279724	−	0.223073i
$236$	−10.7918	−	4.38057i	−0.702486	−	0.285151i
$237$	1.17892	−	0.940160i	0.0765793	−	0.0610700i
$238$	14.1455	+	18.2316i	0.916916	+	1.18178i
$239$	3.76316	+	3.00102i	0.243419	+	0.194120i	0.737598	−	0.675240i	$-0.235960\pi$
$239$	3.76316	+	3.00102i	0.243419	+	0.194120i	−0.494179	+	0.869360i	$0.664531\pi$
$240$	3.55805	−	1.30204i	0.229671	−	0.0840461i
$241$	3.87499	+	8.04649i	0.249610	+	0.518320i	0.987696	−	0.156386i	$-0.0499845\pi$
$241$	3.87499	+	8.04649i	0.249610	+	0.518320i	−0.738086	+	0.674707i	$0.764270\pi$
$242$	4.28598	−	21.9543i	0.275513	−	1.41127i
$243$	−3.54065	−	15.5126i	−0.227133	−	0.995133i
$244$	12.9102	+	2.09930i	0.826492	+	0.134394i
$245$	−3.33599	+	5.58197i	−0.213128	+	0.356619i
$246$	12.1515	−	10.3352i	0.774754	−	0.658949i
$247$	14.4033	−	3.28747i	0.916463	−	0.209177i
$248$	7.44968	+	2.75312i	0.473055	+	0.174823i
$249$	9.76756	−	4.70381i	0.618994	−	0.298092i
$250$	−11.7816	−	2.30003i	−0.745131	−	0.145467i
$251$	−3.20226	+	4.01551i	−0.202125	+	0.253457i	−0.872555	−	0.488516i	$-0.837538\pi$
$251$	−3.20226	+	4.01551i	−0.202125	+	0.253457i	0.670430	+	0.741973i	$0.266110\pi$
$252$	−10.0695	+	2.49259i	−0.634317	+	0.157019i
$253$	19.8806	+	24.9295i	1.24988	+	1.56730i
$254$	−4.26594	−	8.18611i	−0.267669	−	0.513642i
$255$	3.64218	−	4.56715i	0.228082	−	0.286006i
$256$	6.52984	−	14.6069i	0.408115	−	0.912931i
$257$	−4.89436	+	10.1632i	−0.305302	+	0.633966i	−0.996017	−	0.0891610i	$-0.971581\pi$
$257$	−4.89436	+	10.1632i	−0.305302	+	0.633966i	0.690715	+	0.723127i	$0.257296\pi$
$258$	−2.60309	−	1.94458i	−0.162061	−	0.121064i
$259$	−14.2459	−	3.93256i	−0.885200	−	0.244357i
$260$	−4.78547	−	1.94250i	−0.296782	−	0.120469i
$261$	−9.49503	+	11.9064i	−0.587728	+	0.736987i
$262$	−5.58815	−	21.3497i	−0.345237	−	1.31899i
$263$			8.81724i			0.543695i	0.962340	+	0.271847i	$0.0876346\pi$
$263$			8.81724i			0.543695i	−0.962340	+	0.271847i	$0.912365\pi$
$264$	−7.72439	−	12.7816i	−0.475403	−	0.786652i
$265$	−1.58168	+	3.28439i	−0.0971619	+	0.201759i
$266$	−8.86642	+	17.8000i	−0.543635	+	1.09139i
$267$	3.65430	+	7.58823i	0.223640	+	0.464392i
$268$	13.5370	−	4.00430i	0.826905	−	0.244601i
$269$	−7.18151	−	1.63913i	−0.437865	−	0.0999397i	−0.00209460	−	0.999998i	$-0.500667\pi$
$269$	−7.18151	−	1.63913i	−0.437865	−	0.0999397i	−0.435770	+	0.900058i	$0.643524\pi$
$270$	3.07072	+	5.89255i	0.186878	+	0.358609i
$271$	−3.66069	+	1.76290i	−0.222371	+	0.107088i	−0.541753	−	0.840538i	$-0.682239\pi$
$271$	−3.66069	+	1.76290i	−0.222371	+	0.107088i	0.319382	+	0.947626i	$0.396525\pi$
$272$	−3.10998	−	24.4721i	−0.188570	−	1.48384i
$273$	−6.60321	−	3.55385i	−0.399644	−	0.215089i
$274$	−0.897972	−	3.43073i	−0.0542485	−	0.207258i
$275$			21.4235i			1.29189i
$276$	12.3935	+	2.01528i	0.746000	+	0.121305i
$277$	7.24493	+	3.48897i	0.435305	+	0.209632i	0.638686	−	0.769468i	$-0.279478\pi$
$277$	7.24493	+	3.48897i	0.435305	+	0.209632i	−0.203380	+	0.979100i	$0.565193\pi$
$278$	5.66881	−	0.179201i	0.339992	−	0.0107478i
$279$	−1.22491	+	5.36669i	−0.0733335	+	0.321295i
$280$	6.10527	−	3.32473i	0.364860	−	0.198691i
$281$	−4.29563	−	18.8204i	−0.256256	−	1.12273i	−0.925219	−	0.379434i	$-0.876119\pi$
$281$	−4.29563	−	18.8204i	−0.256256	−	1.12273i	0.668963	−	0.743295i	$-0.266738\pi$
$282$	2.15567	+	8.23581i	0.128368	+	0.490435i
$283$	−6.17237	−	27.0429i	−0.366909	−	1.60753i	−0.735218	−	0.677831i	$-0.762920\pi$
$283$	−6.17237	−	27.0429i	−0.366909	−	1.60753i	0.368309	−	0.929704i	$-0.379937\pi$
$284$	2.07555	−	1.88151i	0.123161	−	0.111647i
$285$	4.90792	+	1.12020i	0.290720	+	0.0663550i
$286$	−3.90065	+	19.9805i	−0.230650	+	1.18147i
$287$	19.2592	−	22.0412i	1.13683	−	1.30105i
$288$	10.6240	+	3.17952i	0.626028	+	0.187355i
$289$	−13.1149	−	16.4455i	−0.771464	−	0.967385i
$290$	4.13539	−	9.33042i	0.242838	−	0.547901i
$291$	9.14373	−	7.29188i	0.536015	−	0.427458i
$292$	0.548451	+	8.66610i	0.0320957	+	0.507145i
$293$		−	0.497423i		−	0.0290598i	−0.999894	−	0.0145299i	$-0.995375\pi$
$293$		−	0.497423i		−	0.0290598i	0.999894	−	0.0145299i	$-0.00462517\pi$
$294$	9.33373	−	3.84234i	0.544354	−	0.224090i
$295$			5.40990i			0.314977i
$296$	10.9757	+	11.3643i	0.637948	+	0.660539i
$297$	20.4772	−	16.3300i	1.18821	−	0.947563i
$298$	2.62817	+	1.16485i	0.152246	+	0.0674778i
$299$	−10.6716	−	13.3818i	−0.617157	−	0.773891i
$300$	5.66602	+	6.25036i	0.327128	+	0.360865i
$301$	−5.24977	−	2.82543i	−0.302592	−	0.162855i
$302$	−4.64721	−	0.907243i	−0.267417	−	0.0522060i
$303$	−15.1094	−	3.44862i	−0.868011	−	0.198118i
$304$	17.8380	−	11.5650i	1.02308	−	0.663300i
$305$	−1.35191	−	5.92310i	−0.0774101	−	0.339156i
$306$	16.5408	−	4.32946i	0.945576	−	0.247499i
$307$	5.29958	+	23.2190i	0.302463	+	1.32518i	0.866397	+	0.499357i	$0.166430\pi$
$307$	5.29958	+	23.2190i	0.302463	+	1.32518i	−0.563934	+	0.825820i	$0.690713\pi$
$308$	−17.4733	−	21.1083i	−0.995636	−	1.20276i
$309$	2.20779	−	9.67295i	0.125597	−	0.550275i
$310$	−0.116559	−	3.68720i	−0.00662011	−	0.209419i
$311$	21.9549	+	10.5729i	1.24495	+	0.599534i	0.936152	−	0.351595i	$-0.114361\pi$
$311$	21.9549	+	10.5729i	1.24495	+	0.599534i	0.308793	+	0.951129i	$0.400075\pi$
$312$	4.14635	+	6.86099i	0.234741	+	0.388427i
$313$		−	23.6603i		−	1.33736i	−0.743550	−	0.668680i	$-0.766859\pi$
$313$		−	23.6603i		−	1.33736i	0.743550	−	0.668680i	$-0.233141\pi$
$314$	−1.31158	+	0.343298i	−0.0740168	+	0.0193734i
$315$	2.83191	+	3.89829i	0.159560	+	0.219644i
$316$	−2.83630	+	0.838987i	−0.159554	+	0.0471967i
$317$	13.4108	−	6.45831i	0.753227	−	0.362735i	−0.0175451	−	0.999846i	$-0.505585\pi$
$317$	13.4108	−	6.45831i	0.753227	−	0.362735i	0.770772	+	0.637111i	$0.219871\pi$
$318$	5.01789	−	2.61492i	0.281389	−	0.146637i
$319$	−39.2196	−	8.95162i	−2.19588	−	0.501195i
$320$	−7.42734	−	0.258514i	−0.415201	−	0.0144514i
$321$	1.85928	+	3.86084i	0.103775	+	0.215491i
$322$	23.0367	+	0.307308i	1.28378	+	0.0171256i
$323$	14.2215	−	29.5313i	0.791307	−	1.64317i
$324$	−0.232493	+	1.42978i	−0.0129163	+	0.0794321i
$325$		−	11.4999i		−	0.637898i
$326$	15.3825	−	4.02628i	0.851960	−	0.222995i
$327$	4.63813	−	5.81603i	0.256489	−	0.321627i
$328$	−29.7103	+	9.81941i	−1.64048	+	0.542186i
$329$	6.13836	+	14.3638i	0.338419	+	0.791903i
$330$	−4.15154	+	5.55740i	−0.228535	+	0.305925i
$331$	−0.975324	+	2.02528i	−0.0536087	+	0.111320i	−0.926052	−	0.377395i	$-0.876820\pi$
$331$	−0.975324	+	2.02528i	−0.0536087	+	0.111320i	0.872444	+	0.488715i	$0.162534\pi$
$332$	−21.2228	+	1.34313i	−1.16475	+	0.0737136i
$333$	−6.82748	+	8.56139i	−0.374144	+	0.469161i
$334$	−3.43050	+	1.78770i	−0.187709	+	0.0978187i
$335$	−4.08831	−	5.12657i	−0.223368	−	0.280095i
$336$	−10.6805	−	1.53710i	−0.582671	−	0.0838558i
$337$	−8.07365	+	10.1240i	−0.439800	+	0.551491i	−0.951490	−	0.307678i	$-0.900448\pi$
$337$	−8.07365	+	10.1240i	−0.439800	+	0.551491i	0.511691	+	0.859170i	$0.329019\pi$
$338$	−1.42881	+	7.31887i	−0.0777172	+	0.398094i
$339$	−6.56991	+	3.16390i	−0.356829	+	0.171840i
$340$	−9.98908	+	5.61376i	−0.541734	+	0.304449i
$341$	−14.1765	+	3.23570i	−0.767702	+	0.175223i
$342$	9.54630	+	11.2240i	0.516205	+	0.606924i
$343$	15.9004	−	9.49614i	0.858542	−	0.512743i
$344$	3.29649	+	5.45471i	0.177735	+	0.294098i
$345$	−1.29780	−	5.68603i	−0.0698711	−	0.306125i
$346$	17.5125	+	3.41885i	0.941479	+	0.183799i
$347$	−0.157351	−	0.326743i	−0.00844706	−	0.0175405i	0.896703	−	0.442633i	$-0.145956\pi$
$347$	−0.157351	−	0.326743i	−0.00844706	−	0.0175405i	−0.905150	+	0.425093i	$0.860241\pi$
$348$	−13.8099	+	7.76102i	−0.740289	+	0.416034i
$349$	−19.8892	−	15.8611i	−1.06464	−	0.849026i	−0.0756735	−	0.997133i	$-0.524111\pi$
$349$	−19.8892	−	15.8611i	−1.06464	−	0.849026i	−0.988971	+	0.148107i	$0.952682\pi$
$350$	11.9723	+	9.81171i	0.639948	+	0.524458i
$351$	−10.9919	+	8.76574i	−0.586703	+	0.467880i
$352$	4.60943	+	28.9292i	0.245683	+	1.54193i
$353$	16.5145	+	13.1699i	0.878981	+	0.700964i	0.955147	−	0.296131i	$-0.0956966\pi$
$353$	16.5145	+	13.1699i	0.878981	+	0.700964i	−0.0761665	+	0.997095i	$0.524268\pi$
$354$	5.02552	−	6.72734i	0.267103	−	0.357554i
$355$	−1.17237	−	0.564585i	−0.0622231	−	0.0299651i
$356$	−1.04345	−	16.4876i	−0.0553026	−	0.873840i
$357$	−15.2986	+	6.53782i	−0.809686	+	0.346018i
$358$	6.79462	+	13.0385i	0.359107	+	0.689106i
$359$	−29.2037	−	23.2892i	−1.54131	−	1.22916i	−0.875695	−	0.482864i	$-0.839596\pi$
$359$	−29.2037	−	23.2892i	−1.54131	−	1.22916i	−0.665618	−	0.746292i	$-0.731832\pi$
$360$	−0.487606	−	5.12789i	−0.0256991	−	0.270263i
$361$	9.24659			0.486663
$362$	−9.83601	+	8.36579i	−0.516969	+	0.439696i
$363$	14.5302	+	6.99738i	0.762638	+	0.367267i
$364$	9.37946	+	11.3307i	0.491617	+	0.593888i
$365$	3.63394	−	1.75001i	0.190209	−	0.0915999i
$366$	−3.82112	+	8.62136i	−0.199733	+	0.450646i
$367$	−7.26281	+	31.8205i	−0.379116	+	1.66102i	0.321071	+	0.947055i	$0.395957\pi$
$367$	−7.26281	+	31.8205i	−0.379116	+	1.66102i	−0.700187	+	0.713960i	$0.746900\pi$
$368$	−21.0384	−	12.8061i	−1.09670	−	0.667564i
$369$	−9.40997	−	19.5400i	−0.489864	−	1.01721i
$370$	2.97358	−	6.70911i	0.154589	−	0.348790i
$371$	8.39973	−	6.10198i	0.436092	−	0.316799i
$372$	−3.28027	+	4.69339i	−0.170074	+	0.243341i
$373$	17.4750			0.904820			0.452410	−	0.891810i	$-0.350564\pi$
$373$	17.4750			0.904820			0.452410	+	0.891810i	$0.350564\pi$
$374$	29.2621	+	34.4047i	1.51311	+	1.77903i
$375$	3.75508	−	7.79750i	0.193911	−	0.402661i
$376$	2.15806	−	16.5589i	0.111293	−	0.853962i
$377$	21.0526	+	4.80511i	1.08426	+	0.247476i
$378$	0.252425	−	18.9224i	0.0129833	−	0.973264i
$379$	−1.61455	+	0.368510i	−0.0829337	+	0.0189291i	−0.263786	−	0.964581i	$-0.584971\pi$
$379$	−1.61455	+	0.368510i	−0.0829337	+	0.0189291i	0.180853	+	0.983510i	$0.442114\pi$
$380$	−8.09372	−	5.65680i	−0.415199	−	0.290188i
$381$	6.48844	−	1.48094i	0.332413	−	0.0758710i
$382$	−0.754702	−	23.8740i	−0.0386139	−	1.22150i
$383$	−0.707587	+	3.10014i	−0.0361560	+	0.158410i	−0.989783	−	0.142580i	$-0.954460\pi$
$383$	−0.707587	+	3.10014i	−0.0361560	+	0.158410i	0.953627	+	0.300990i	$0.0973172\pi$
$384$	8.99592	+	7.22108i	0.459071	+	0.368499i
$385$	−6.03209	+	11.2079i	−0.307424	+	0.571206i
$386$	−14.8419	+	0.469179i	−0.755432	+	0.0238806i
$387$	−3.45369	+	2.75423i	−0.175561	+	0.140005i
$388$	−21.9983	+	6.50718i	−1.11680	+	0.330352i
$389$	9.34855	+	11.7227i	0.473990	+	0.594365i	0.960143	−	0.279509i	$-0.0901717\pi$
$389$	9.34855	+	11.7227i	0.473990	+	0.594365i	−0.486153	+	0.873874i	$0.661600\pi$
$390$	2.22849	−	2.98314i	0.112844	−	0.151057i
$391$	−37.9738			−1.92042
$392$	−19.7987	+	0.0974691i	−0.999988	+	0.00492293i
$393$	15.9112			0.802612
$394$	−9.99176	+	13.3753i	−0.503378	+	0.673839i
$395$	0.856589	+	1.07413i	0.0430997	+	0.0540453i
$396$	−19.4699	+	5.75925i	−0.978398	+	0.289413i
$397$	21.8016	−	17.3862i	1.09419	−	0.872587i	0.101688	−	0.994816i	$-0.467576\pi$
$397$	21.8016	−	17.3862i	1.09419	−	0.872587i	0.992502	+	0.122229i	$0.0390043\pi$
$398$	0.720810	−	0.0227861i	0.0361309	−	0.00114216i
$399$	−10.7965	−	9.43373i	−0.540499	−	0.472277i
$400$	−5.68678	−	15.5402i	−0.284339	−	0.777008i
$401$	−0.731013	+	3.20278i	−0.0365051	+	0.159939i	−0.989895	−	0.141802i	$-0.954711\pi$
$401$	−0.731013	+	3.20278i	−0.0365051	+	0.159939i	0.953390	+	0.301741i	$0.0975677\pi$
$402$	0.321582	+	10.1728i	0.0160390	+	0.507375i
$403$	7.60978	−	1.73688i	0.379070	−	0.0865203i
$404$	24.9171	+	17.4148i	1.23967	+	0.866421i
$405$	0.655971	−	0.149721i	0.0325955	−	0.00743970i
$406$	−22.9646	+	17.8178i	−1.13972	+	0.884282i
$407$	−28.2012	−	6.43674i	−1.39788	−	0.319057i
$408$	17.6365	+	2.29850i	0.873139	+	0.113793i
$409$	−12.4942	+	25.9445i	−0.617800	+	1.28288i	0.323795	+	0.946127i	$0.395041\pi$
$409$	−12.4942	+	25.9445i	−0.617800	+	1.28288i	−0.941595	+	0.336748i	$0.890673\pi$
$410$	9.41651	+	11.0714i	0.465048	+	0.546777i
$411$	2.55680			0.126118
$412$	−11.1489	+	15.9518i	−0.549267	+	0.785888i
$413$	7.30196	−	13.5673i	0.359306	−	0.667605i
$414$	6.91705	−	15.6065i	0.339954	−	0.767018i
$415$	4.28569	+	8.89932i	0.210376	+	0.436850i
$416$	−2.47428	−	15.5288i	−0.121312	−	0.761363i
$417$	−0.909914	+	3.98659i	−0.0445587	+	0.195224i
$418$	−15.7715	+	35.5843i	−0.771410	+	1.74048i
$419$	−17.7821	+	8.56341i	−0.868713	+	0.418350i	−0.814489	−	0.580179i	$-0.802983\pi$
$419$	−17.7821	+	8.56341i	−0.868713	+	0.418350i	−0.0542237	+	0.998529i	$0.517268\pi$
$420$	1.20435	+	4.86527i	0.0587661	+	0.237401i
$421$	32.0152	+	15.4177i	1.56032	+	0.751412i	0.997187	−	0.0749514i	$-0.0238802\pi$
$421$	32.0152	+	15.4177i	1.56032	+	0.751412i	0.563137	+	0.826364i	$0.309594\pi$
$422$	−0.484629	+	0.412190i	−0.0235913	+	0.0200651i
$423$	11.5741			0.562751
$424$	−11.0492	+	1.05065i	−0.536595	+	0.0510243i
$425$	−19.9475	−	15.9076i	−0.967595	−	0.771631i
$426$	0.933402	+	1.79115i	0.0452235	+	0.0867814i
$427$	−4.60423	+	16.6791i	−0.222814	+	0.807158i
$428$	−0.530900	−	8.38878i	−0.0256620	−	0.405487i
$429$	−13.2239	−	6.36829i	−0.638455	−	0.307464i
$430$	1.77173	−	2.37170i	0.0854402	−	0.114373i
$431$	−18.4581	−	14.7199i	−0.889097	−	0.709031i	0.0683439	−	0.997662i	$-0.478228\pi$
$431$	−18.4581	−	14.7199i	−0.889097	−	0.709031i	−0.957440	+	0.288631i	$0.906800\pi$
$432$	−10.5190	+	17.2810i	−0.506095	+	0.831433i
$433$	−4.61587	+	3.68104i	−0.221825	+	0.176899i	−0.728096	−	0.685475i	$-0.759595\pi$
$433$	−4.61587	+	3.68104i	−0.221825	+	0.176899i	0.506272	+	0.862374i	$0.331023\pi$
$434$	−4.68444	+	9.40433i	−0.224860	+	0.451422i
$435$	5.75282	+	4.58772i	0.275826	+	0.219964i
$436$	−12.7206	+	7.14884i	−0.609206	+	0.342367i
$437$	−14.1988	−	29.4841i	−0.679219	−	1.41041i
$438$	−6.14456	−	1.19956i	−0.293598	−	0.0573171i
$439$	4.87444	+	21.3563i	0.232644	+	1.01928i	0.947436	+	0.319944i	$0.103664\pi$
$439$	4.87444	+	21.3563i	0.232644	+	1.01928i	−0.714792	+	0.699337i	$0.753479\pi$
$440$	11.6454	−	7.03776i	0.555173	−	0.335512i
$441$	−1.84040	−	13.5987i	−0.0876379	−	0.647559i
$442$	−15.7075	−	18.4680i	−0.747131	−	0.878433i
$443$	−20.9084	+	4.77220i	−0.993387	+	0.226734i	−0.688170	−	0.725549i	$-0.741586\pi$
$443$	−20.9084	+	4.77220i	−0.993387	+	0.226734i	−0.305216	+	0.952283i	$0.598729\pi$
$444$	−9.93013	+	5.58063i	−0.471263	+	0.264845i
$445$	−6.91371	+	3.32947i	−0.327741	+	0.157832i
$446$	5.88637	−	30.1520i	0.278728	−	1.42774i
$447$	−1.29226	+	1.62044i	−0.0611218	+	0.0766443i
$448$	18.2779	+	10.6733i	0.863549	+	0.504265i
$449$	−11.6549	−	14.6148i	−0.550029	−	0.689714i	0.426651	−	0.904416i	$-0.359693\pi$
$449$	−11.6549	−	14.6148i	−0.550029	−	0.689714i	−0.976680	+	0.214702i	$0.931122\pi$
$450$	10.1712	−	5.30042i	0.479475	−	0.249864i
$451$	35.7197	−	44.7911i	1.68198	−	2.10913i
$452$	14.2750	−	0.903420i	0.671439	−	0.0424933i
$453$	1.48118	−	3.07571i	0.0695921	−	0.144509i
$454$	−1.03698	+	1.38814i	−0.0486680	+	0.0651488i
$455$	3.23795	−	6.01624i	0.151797	−	0.282046i
$456$	4.80984	+	14.5530i	0.225242	+	0.681506i
$457$	−13.2680	+	16.6376i	−0.620652	+	0.778273i	−0.988436	−	0.151638i	$-0.951545\pi$
$457$	−13.2680	+	16.6376i	−0.620652	+	0.778273i	0.367784	+	0.929911i	$0.380117\pi$
$458$	−26.7196	+	6.99369i	−1.24853	+	0.326794i
$459$			31.1918i			1.45591i
$460$	−1.83614	+	11.2918i	−0.0856103	+	0.526483i
$461$	−1.12831	+	2.34296i	−0.0525506	+	0.109122i	−0.925591	−	0.378526i	$-0.876431\pi$
$461$	−1.12831	+	2.34296i	−0.0525506	+	0.109122i	0.873040	+	0.487649i	$0.162145\pi$
$462$	17.9126	−	8.33375i	0.833368	−	0.387721i
$463$	16.5778	+	34.4242i	0.770436	+	1.59983i	0.799806	+	0.600258i	$0.204936\pi$
$463$	16.5778	+	34.4242i	0.770436	+	1.59983i	−0.0293703	+	0.999569i	$0.509350\pi$
$464$	30.8252	−	3.91736i	1.43103	−	0.181859i
$465$	2.59302	+	0.591841i	0.120249	+	0.0274460i
$466$	28.5565	−	14.8813i	1.32285	−	0.689365i
$467$	−19.5231	+	9.40182i	−0.903421	+	0.435064i	−0.827123	−	0.562021i	$-0.810024\pi$
$467$	−19.5231	+	9.40182i	−0.903421	+	0.435064i	−0.0762975	+	0.997085i	$0.524310\pi$
$468$	10.4512	−	3.09149i	0.483106	−	0.142904i
$469$	3.33341	+	18.3749i	0.153922	+	0.848475i
$470$	−7.50372	+	1.96405i	−0.346121	+	0.0905950i
$471$		−	0.977474i		−	0.0450396i
$472$	−14.0970	+	8.51934i	−0.648867	+	0.392134i
$473$	−10.5134	−	5.06300i	−0.483408	−	0.232797i
$474$	−0.0673783	−	2.13143i	−0.00309479	−	0.0978997i
$475$	4.89259	−	21.4358i	0.224488	−	0.983544i
$476$	32.6284	−	0.595931i	1.49552	−	0.0273144i
$477$	−1.71180	−	7.49987i	−0.0783778	−	0.343395i
$478$	6.58515	−	1.72362i	0.301198	−	0.0788367i
$479$	3.29653	+	14.4430i	0.150622	+	0.659919i	0.992705	+	0.120571i	$0.0384724\pi$
$479$	3.29653	+	14.4430i	0.150622	+	0.659919i	−0.842082	+	0.539349i	$0.818670\pi$
$480$	1.53625	−	5.13323i	0.0701199	−	0.234299i
$481$	15.1380	+	3.45516i	0.690235	+	0.157542i
$482$	12.3962	+	2.42003i	0.564633	+	0.110229i
$483$	−4.41994	+	16.0115i	−0.201114	+	0.728549i
$484$	−21.2463	−	23.4374i	−0.965741	−	1.06534i
$485$	6.64370	+	8.33093i	0.301675	+	0.378288i
$486$	−20.5722	−	9.11793i	−0.933175	−	0.413598i
$487$	15.1969	−	12.1192i	0.688639	−	0.549172i	−0.215450	−	0.976515i	$-0.569122\pi$
$487$	15.1969	−	12.1192i	0.688639	−	0.549172i	0.904089	+	0.427343i	$0.140550\pi$
$488$	13.3053	−	12.8503i	0.602304	−	0.581705i
$489$			11.4640i			0.518422i
$490$	3.50079	+	8.50405i	0.158150	+	0.384174i
$491$		−	10.0146i		−	0.451952i	−0.974133	−	0.225976i	$-0.927443\pi$
$491$		−	10.0146i		−	0.451952i	0.974133	−	0.225976i	$-0.0725571\pi$
$492$	−1.42490	−	22.5150i	−0.0642395	−	1.01505i
$493$	37.4566	−	29.8706i	1.68696	−	1.34530i
$494$	8.46594	−	19.1012i	0.380901	−	0.859403i
$495$	5.88008	+	7.37339i	0.264290	+	0.331409i
$496$	9.42445	−	6.11020i	0.423170	−	0.274356i
$497$	2.17812	+	2.99830i	0.0977019	+	0.134492i
$498$	2.93765	−	15.0477i	0.131639	−	0.674302i
$499$	12.4803	+	2.84855i	0.558696	+	0.127519i	0.492539	−	0.870291i	$-0.336069\pi$
$499$	12.4803	+	2.84855i	0.558696	+	0.127519i	0.0661570	+	0.997809i	$0.478926\pi$
$500$	−12.5775	+	11.4016i	−0.562482	+	0.509897i
$501$	−0.620610	−	2.71907i	−0.0277268	−	0.121479i
$502$	1.83920	+	7.02672i	0.0820876	+	0.313618i
$503$	−2.26568	−	9.92658i	−0.101022	−	0.442605i	−0.999989	−	0.00458995i	$-0.998539\pi$
$503$	−2.26568	−	9.92658i	−0.101022	−	0.442605i	0.898968	−	0.438015i	$-0.144318\pi$
$504$	−5.69846	+	13.5182i	−0.253829	+	0.602149i
$505$	3.14207	−	13.7663i	0.139820	−	0.612592i
$506$	45.0711	−	1.42478i	2.00365	−	0.0633392i
$507$	−4.84392	−	2.33271i	−0.215126	−	0.103599i
$508$	−12.8853	−	2.09525i	−0.571693	−	0.0929617i
$509$			9.97627i			0.442190i	0.975252	+	0.221095i	$0.0709631\pi$
$509$			9.97627i			0.442190i	−0.975252	+	0.221095i	$0.929037\pi$
$510$	−2.09187	−	7.99204i	−0.0926294	−	0.353893i
$511$	−11.4755	−	0.516063i	−0.507647	−	0.0228293i
$512$	−11.0227	−	19.7611i	−0.487139	−	0.873324i
$513$	−24.2183	+	11.6629i	−1.06927	+	0.514931i
$514$	7.37234	+	14.1471i	0.325180	+	0.624003i
$515$	8.81312	+	2.01154i	0.388352	+	0.0886389i
$516$	−4.40636	+	1.30342i	−0.193979	+	0.0573797i
$517$	13.2655	+	27.5461i	0.583416	+	1.21148i
$518$	−16.5129	+	12.8120i	−0.725536	+	0.562928i
$519$	−5.58168	+	11.5905i	−0.245009	+	0.508766i
$520$	−6.25111	+	3.77778i	−0.274129	+	0.165667i
$521$		−	16.0983i		−	0.705280i	−0.935759	−	0.352640i	$-0.885284\pi$
$521$		−	16.0983i		−	0.705280i	0.935759	−	0.352640i	$-0.114716\pi$
$522$	5.45342	+	20.8350i	0.238690	+	0.911922i
$523$	18.6524	−	23.3893i	0.815612	−	1.02274i	−0.183598	−	0.983001i	$-0.558774\pi$
$523$	18.6524	−	23.3893i	0.815612	−	1.02274i	0.999210	−	0.0397435i	$-0.0126541\pi$
$524$	−28.9185	−	11.7385i	−1.26331	−	0.512799i
$525$	−9.02915	+	6.55922i	−0.394064	+	0.286268i
$526$	9.98980	+	7.46267i	0.435576	+	0.325388i
$527$	7.51372	−	15.6024i	0.327303	−	0.679651i
$528$	−21.0190	−	2.06636i	−0.914736	−	0.0899270i
$529$	−9.29814	+	11.6595i	−0.404267	+	0.506935i
$530$	2.38248	+	4.57184i	0.103488	+	0.198588i
$531$	−7.11794	−	8.92562i	−0.308892	−	0.387339i
$532$	12.6628	+	25.1109i	0.549002	+	1.08870i
$533$	−19.1739	+	24.0433i	−0.830513	+	1.04143i
$534$	11.6902	+	2.28221i	0.505887	+	0.0987607i
$535$	−3.51765	+	1.69401i	−0.152081	+	0.0732385i
$536$	6.92056	−	18.7264i	0.298923	−	0.808856i
$537$	−10.3345	+	2.35879i	−0.445967	+	0.101789i
$538$	−7.93535	+	6.74922i	−0.342117	+	0.290980i
$539$	30.2554	−	19.9662i	1.30319	−	0.860003i
$540$	9.27514	+	1.50821i	0.399139	+	0.0649030i
$541$	−2.64693	−	11.5970i	−0.113801	−	0.498593i	−0.999416	−	0.0341733i	$-0.989120\pi$
$541$	−2.64693	−	11.5970i	−0.113801	−	0.498593i	0.885615	−	0.464419i	$-0.153737\pi$
$542$	−1.10098	+	5.63958i	−0.0472910	+	0.242241i
$543$	−4.03929	−	8.38768i	−0.173343	−	0.359950i
$544$	−30.3587	−	17.1889i	−1.30162	−	0.736969i
$545$	5.29904	+	4.22584i	0.226986	+	0.181015i
$546$	−9.61523	+	4.47345i	−0.411494	+	0.191446i
$547$	0.697519	−	0.556253i	0.0298237	−	0.0237836i	−0.608465	−	0.793581i	$-0.708214\pi$
$547$	0.697519	−	0.556253i	0.0298237	−	0.0237836i	0.638288	+	0.769797i	$0.279643\pi$
$548$	−4.64698	−	1.88629i	−0.198509	−	0.0805782i
$549$	10.0236	+	7.99359i	0.427799	+	0.341158i
$550$	24.2725	+	18.1323i	1.03498	+	0.773163i
$551$	37.1979	+	17.9135i	1.58468	+	0.763143i
$552$	12.7728	−	12.3359i	0.543645	−	0.525053i
$553$	−0.698421	−	3.84994i	−0.0296999	−	0.163716i
$554$	10.0849	−	5.25542i	0.428464	−	0.223281i
$555$	4.13661	+	3.29884i	0.175589	+	0.140028i
$556$	4.59489	−	6.57434i	0.194867	−	0.278814i
$557$	5.08127			0.215300			0.107650	−	0.994189i	$-0.465667\pi$
$557$	5.08127			0.215300			0.107650	+	0.994189i	$0.465667\pi$
$558$	5.04364	+	5.93002i	0.213514	+	0.251038i
$559$	5.64347	+	2.71775i	0.238693	+	0.114949i
$560$	1.40047	−	9.73114i	0.0591806	−	0.411216i
$561$	−29.3387	+	14.1288i	−1.23868	+	0.596517i
$562$	−24.9589	−	11.0622i	−1.05283	−	0.466629i
$563$	−2.45358	+	10.7498i	−0.103406	+	0.453052i	0.896543	+	0.442957i	$0.146071\pi$
$563$	−2.45358	+	10.7498i	−0.103406	+	0.453052i	−0.999949	+	0.0100951i	$0.996787\pi$
$564$	11.1555	+	4.52822i	0.469733	+	0.190672i
$565$	−2.88266	−	5.98591i	−0.121275	−	0.251829i
$566$	−35.8633	−	15.8952i	−1.50745	−	0.668124i
$567$	−1.84717	−	0.509908i	−0.0775740	−	0.0214141i
$568$	−0.375034	−	3.94403i	−0.0157361	−	0.165488i
$569$	−29.8693			−1.25219			−0.626093	−	0.779748i	$-0.715347\pi$
$569$	−29.8693			−1.25219			−0.626093	+	0.779748i	$0.715347\pi$
$570$	5.42310	−	4.61249i	0.227149	−	0.193196i
$571$	−12.1074	+	25.1413i	−0.506680	+	1.05213i	0.478097	+	0.878307i	$0.341327\pi$
$571$	−12.1074	+	25.1413i	−0.506680	+	1.05213i	−0.984777	+	0.173825i	$0.944387\pi$
$572$	19.3362	+	21.3303i	0.808486	+	0.891865i
$573$	16.7894	+	3.83208i	0.701389	+	0.160087i
$574$	−8.67191	−	40.4754i	−0.361958	−	1.68941i
$575$	−24.8343	+	5.66827i	−1.03566	+	0.236383i
$576$	12.5943	−	9.34582i	0.524760	−	0.389409i
$577$	−21.1227	+	4.82112i	−0.879349	+	0.200706i	−0.638282	−	0.769803i	$-0.720355\pi$
$577$	−21.1227	+	4.82112i	−0.879349	+	0.200706i	−0.241067	+	0.970508i	$0.577497\pi$
$578$	−29.7326	+	0.939903i	−1.23671	+	0.0390948i
$579$	2.38231	−	10.4376i	0.0990052	−	0.433770i
$580$	−7.07114	−	12.5823i	−0.293613	−	0.522453i
$581$	1.26381	−	28.1029i	0.0524316	−	1.16590i
$582$	−0.522586	−	16.5313i	−0.0216619	−	0.685246i
$583$	15.8876	−	12.6699i	0.657997	−	0.524735i
$584$	10.2828	+	6.71336i	0.425503	+	0.277801i
$585$	−3.15635	−	3.95794i	−0.130499	−	0.163641i
$586$	−0.563573	−	0.421005i	−0.0232810	−	0.0173916i
$587$	22.0575			0.910410			0.455205	−	0.890387i	$-0.349566\pi$
$587$	22.0575			0.910410			0.455205	+	0.890387i	$0.349566\pi$
$588$	3.54650	−	13.8270i	0.146255	−	0.570217i
$589$	14.9236			0.614918
$590$	6.12934	+	4.57879i	0.252341	+	0.188506i
$591$	−7.50491	−	9.41086i	−0.308711	−	0.387111i
$592$	22.1651	−	2.81681i	0.910982	−	0.115770i
$593$	−29.3534	+	23.4085i	−1.20540	+	0.961274i	−0.999849	−	0.0173730i	$-0.994470\pi$
$593$	−29.3534	+	23.4085i	−1.20540	+	0.961274i	−0.205550	+	0.978647i	$0.565898\pi$
$594$	−1.17032	−	37.0216i	−0.0480188	−	1.51901i
$595$	−5.95667	−	13.9387i	−0.244200	−	0.571429i
$596$	3.54417	−	1.99179i	0.145175	−	0.0815867i
$597$	−0.115699	+	0.506910i	−0.00473524	+	0.0207465i
$598$	−24.1936	+	0.764803i	−0.989349	+	0.0312751i
$599$	18.4439	−	4.20970i	0.753597	−	0.172004i	0.171569	−	0.985172i	$-0.445116\pi$
$599$	18.4439	−	4.20970i	0.753597	−	0.172004i	0.582028	+	0.813168i	$0.302259\pi$
$600$	11.8771	−	1.12938i	0.484882	−	0.0461069i
$601$	38.9502	−	8.89012i	1.58881	−	0.362636i	0.665411	−	0.746477i	$-0.268256\pi$
$601$	38.9502	−	8.89012i	1.58881	−	0.362636i	0.923399	+	0.383842i	$0.125399\pi$
$602$	−7.64443	+	3.55654i	−0.311564	+	0.144954i
$603$	13.4903	+	3.07908i	0.549368	+	0.125390i
$604$	−4.96117	+	4.49735i	−0.201867	+	0.182995i
$605$	−6.37538	+	13.2386i	−0.259196	+	0.538226i
$606$	−16.6954	+	14.1999i	−0.678204	+	0.576830i
$607$	19.3766			0.786472			0.393236	−	0.919438i	$-0.371356\pi$
$607$	19.3766			0.786472			0.393236	+	0.919438i	$0.371356\pi$
$608$	1.99462	−	29.9985i	0.0808927	−	1.21660i
$609$	−8.23510	−	19.2702i	−0.333703	−	0.780868i
$610$	−7.85500	−	3.48146i	−0.318040	−	0.140960i
$611$	−7.12075	−	14.7864i	−0.288075	−	0.598193i
$612$	9.09449	−	22.4048i	0.367623	−	0.905662i
$613$	−10.5186	+	46.0851i	−0.424843	+	1.86136i	0.0779593	+	0.996957i	$0.475160\pi$
$613$	−10.5186	+	46.0851i	−0.424843	+	1.86136i	−0.502802	+	0.864402i	$0.667698\pi$
$614$	30.7921	+	13.6476i	1.24267	+	0.550771i
$615$	−9.44116	+	4.54662i	−0.380704	+	0.183337i
$616$	−38.7043	+	1.93153i	−1.55944	+	0.0778236i
$617$	23.7284	+	11.4270i	0.955268	+	0.460033i	0.845530	−	0.533928i	$-0.179285\pi$
$617$	23.7284	+	11.4270i	0.955268	+	0.460033i	0.109738	+	0.993961i	$0.464999\pi$
$618$	−9.09069	−	10.6883i	−0.365681	−	0.429947i
$619$	−12.4492			−0.500376			−0.250188	−	0.968197i	$-0.580492\pi$
$619$	−12.4492			−0.500376			−0.250188	+	0.968197i	$0.580492\pi$
$620$	−4.27619	−	2.98868i	−0.171736	−	0.120028i
$621$	24.3478	+	19.4167i	0.977042	+	0.779165i
$622$	30.5609	−	15.9259i	1.22538	−	0.638570i
$623$	21.8326	+	0.981828i	0.874704	+	0.0393361i
$624$	11.2827	+	1.10920i	0.451671	+	0.0444034i
$625$	−11.5322	−	5.55359i	−0.461286	−	0.222144i
$626$	−26.8068	−	20.0255i	−1.07141	−	0.800378i
$627$	−21.9401	−	17.4966i	−0.876201	−	0.698747i
$628$	−0.721135	+	1.77656i	−0.0287764	+	0.0708925i
$629$	26.9335	−	21.4787i	1.07391	−	0.856413i
$630$	6.81355	+	0.0908925i	0.271458	+	0.00362125i
$631$	31.6136	+	25.2110i	1.25852	+	1.00363i	0.999285	+	0.0378184i	$0.0120408\pi$
$631$	31.6136	+	25.2110i	1.25852	+	1.00363i	0.259232	+	0.965815i	$0.416531\pi$
$632$	−1.45001	+	3.92358i	−0.0576782	+	0.156072i
$633$	−0.199020	−	0.413268i	−0.00791032	−	0.0164259i
$634$	4.03338	−	20.6604i	0.160186	−	0.820529i
$635$	1.34930	+	5.91168i	0.0535454	+	0.234598i
$636$	1.28434	−	7.89838i	0.0509273	−	0.313191i
$637$	−16.2407	+	10.7176i	−0.643480	+	0.424646i
$638$	−43.3365	+	36.8588i	−1.71571	+	1.45925i
$639$	2.67710	−	0.611030i	0.105904	−	0.0241720i
$640$	−6.57919	+	8.19626i	−0.260065	+	0.323986i
$641$	−41.3677	+	19.9216i	−1.63393	+	0.786857i	−0.634017	+	0.773319i	$0.718595\pi$
$641$	−41.3677	+	19.9216i	−1.63393	+	0.786857i	−0.999908	+	0.0135385i	$0.995690\pi$
$642$	5.94792	+	1.16117i	0.234746	+	0.0458278i
$643$	−8.61176	+	10.7988i	−0.339614	+	0.425863i	−0.922084	−	0.386989i	$-0.873515\pi$
$643$	−8.61176	+	10.7988i	−0.339614	+	0.425863i	0.582470	+	0.812852i	$0.302086\pi$
$644$	19.8458	−	25.8401i	0.782033	−	1.01824i
$645$	1.33076	+	1.66872i	0.0523987	+	0.0657059i
$646$	−21.4218	−	41.1072i	−0.842829	−	1.61734i
$647$	−10.1662	+	12.7480i	−0.399673	+	0.501174i	−0.940422	−	0.340010i	$-0.889570\pi$
$647$	−10.1662	+	12.7480i	−0.399673	+	0.501174i	0.540749	+	0.841184i	$0.318141\pi$
$648$	1.42314	+	1.47354i	0.0559062	+	0.0578860i
$649$	13.0847	−	27.1706i	0.513618	−	1.06654i
$650$	−13.0292	−	9.73317i	−0.511046	−	0.381766i
$651$	−5.70414	−	4.98416i	−0.223563	−	0.195345i
$652$	8.45763	−	20.8359i	0.331227	−	0.815997i
$653$	7.90068	−	9.90714i	0.309177	−	0.387696i	−0.602830	−	0.797870i	$-0.705960\pi$
$653$	7.90068	−	9.90714i	0.309177	−	0.387696i	0.912008	+	0.410173i	$0.134532\pi$
$654$	−2.66388	−	10.1775i	−0.104166	−	0.397970i
$655$			14.4968i			0.566437i
$656$	−14.0207	+	41.9722i	−0.547417	+	1.63874i
$657$	−3.69298	+	7.66855i	−0.144077	+	0.299179i
$658$	21.4693	+	5.20247i	0.836961	+	0.202813i
$659$	20.1815	+	41.9073i	0.786159	+	1.63248i	0.774525	+	0.632543i	$0.217989\pi$
$659$	20.1815	+	41.9073i	0.786159	+	1.63248i	0.0116331	+	0.999932i	$0.496297\pi$
$660$	2.78270	+	9.40726i	0.108316	+	0.366177i
$661$	−15.1941	−	3.46795i	−0.590981	−	0.134887i	−0.0834363	−	0.996513i	$-0.526590\pi$
$661$	−15.1941	−	3.46795i	−0.590981	−	0.134887i	−0.507544	+	0.861626i	$0.669447\pi$
$662$	1.46912	+	2.81917i	0.0570992	+	0.109570i
$663$	15.7486	−	7.58414i	0.611626	−	0.294544i
$664$	−16.4407	+	25.1819i	−0.638021	+	0.977247i
$665$	8.59516	−	9.83675i	0.333306	−	0.381453i
$666$	3.92133	+	14.9816i	0.151948	+	0.580523i
$667$		−	47.8321i		−	1.85207i
$668$	−0.878043	+	5.39976i	−0.0339725	+	0.208923i
$669$	19.9558	+	9.61021i	0.771536	+	0.371552i
$670$	−9.26856	+	0.292996i	−0.358076	+	0.0113194i
$671$	−7.53611	+	33.0178i	−0.290928	+	1.27464i
$672$	−10.7812	+	10.7999i	−0.415895	+	0.416616i
$673$	−6.37705	−	27.9397i	−0.245817	−	1.07700i	−0.935623	−	0.353001i	$-0.885161\pi$
$673$	−6.37705	−	27.9397i	−0.245817	−	1.07700i	0.689805	−	0.723995i	$-0.257696\pi$
$674$	4.63706	+	17.7160i	0.178613	+	0.682396i
$675$	4.65594	+	20.3990i	0.179207	+	0.785158i
$676$	7.08286	+	7.81332i	0.272418	+	0.300512i
$677$	0.0287922	+	0.00657164i	0.00110658	+	0.000252569i	0.223074	−	0.974801i	$-0.428391\pi$
$677$	0.0287922	+	0.00657164i	0.00110658	+	0.000252569i	−0.221968	+	0.975054i	$0.571248\pi$
$678$	−1.97594	+	10.1215i	−0.0758856	+	0.388712i
$679$	−5.41695	−	29.8602i	−0.207883	−	1.14593i
$680$	−2.09418	+	16.0688i	−0.0803083	+	0.616211i
$681$	−0.778889	−	0.976695i	−0.0298471	−	0.0374270i
$682$	−8.33263	+	18.8004i	−0.319073	+	0.719905i
$683$	−9.04267	+	7.21129i	−0.346008	+	0.275932i	−0.781038	−	0.624484i	$-0.785309\pi$
$683$	−9.04267	+	7.21129i	−0.346008	+	0.275932i	0.435030	+	0.900416i	$0.356738\pi$
$684$	20.7963	−	1.31614i	0.795168	−	0.0503237i
$685$			2.32952i			0.0890065i
$686$	2.69870	−	26.0522i	0.103037	−	0.994678i
$687$		−	19.9132i		−	0.759734i
$688$	8.97016	+	0.881849i	0.341984	+	0.0336202i
$689$	−8.52825	+	6.80105i	−0.324901	+	0.259100i
$690$	−7.54060	−	3.34211i	−0.287066	−	0.127232i
$691$	−15.6042	−	19.5671i	−0.593613	−	0.744368i	0.390754	−	0.920495i	$-0.372214\pi$
$691$	−15.6042	−	19.5671i	−0.593613	−	0.744368i	−0.984367	+	0.176128i	$0.943643\pi$
$692$	18.6956	−	16.9478i	0.710701	−	0.644259i
$693$	−4.79433	−	26.4281i	−0.182122	−	1.00392i
$694$	−0.503373	−	0.0982700i	−0.0191078	−	0.00373028i
$695$	−3.63222	−	0.829031i	−0.137778	−	0.0314469i
$696$	−2.89521	+	22.2151i	−0.109743	+	0.842062i
$697$	15.1822	+	66.5174i	0.575066	+	2.51953i
$698$	−34.8041	+	9.10975i	−1.31735	+	0.344809i
$699$	5.16613	+	22.6343i	0.195401	+	0.856108i
$700$	21.2496	−	5.26011i	0.803158	−	0.198813i
$701$	9.79183	−	42.9008i	0.369832	−	1.62034i	−0.357402	−	0.933951i	$-0.616337\pi$
$701$	9.79183	−	42.9008i	0.369832	−	1.62034i	0.727234	−	0.686390i	$-0.240806\pi$
$702$	0.628213	+	19.8727i	0.0237104	+	0.750047i
$703$	26.7474	+	12.8809i	1.00880	+	0.485812i
$704$	36.6776	+	19.2625i	1.38234	+	0.725982i
$705$		−	5.59225i		−	0.210616i
$706$	28.8988	−	7.56407i	1.08762	−	0.284678i
$707$	−26.4608	+	30.2831i	−0.995160	+	1.13891i
$708$	−3.36851	−	11.3877i	−0.126596	−	0.427975i
$709$	−28.0827	+	13.5239i	−1.05467	+	0.507900i	−0.879135	−	0.476573i	$-0.841879\pi$
$709$	−28.0827	+	13.5239i	−1.05467	+	0.507900i	−0.175531	+	0.984474i	$0.556164\pi$
$710$	−1.63193	+	0.850431i	−0.0612453	+	0.0319161i
$711$	−2.82651	−	0.645133i	−0.106003	−	0.0241944i
$712$	−19.5633	−	12.7724i	−0.733167	−	0.478667i
$713$	−7.50170	−	15.5774i	−0.280941	−	0.583380i
$714$	−5.54103	+	22.8665i	−0.207368	+	0.855756i
$715$	5.80220	−	12.0484i	0.216990	−	0.450585i
$716$	20.5232	+	3.33723i	0.766988	+	0.124718i
$717$			4.90767i			0.183280i
$718$	−51.1035	+	13.3760i	−1.90717	+	0.499189i
$719$	11.6224	−	14.5740i	0.433441	−	0.543518i	−0.516360	−	0.856371i	$-0.672713\pi$
$719$	11.6224	−	14.5740i	0.433441	−	0.543518i	0.949801	+	0.312854i	$0.101285\pi$
$720$	−6.22251	−	3.78765i	−0.231899	−	0.141158i
$721$	−19.3871	−	16.9401i	−0.722013	−	0.630881i
$722$	7.82606	−	10.4762i	0.291256	−	0.389885i
$723$	−3.95099	+	8.20432i	−0.146939	+	0.305122i
$724$	1.15338	+	18.2246i	0.0428650	+	0.677312i
$725$	20.0373	−	25.1260i	0.744167	−	0.933157i
$726$	20.2259	−	10.5401i	0.750653	−	0.391180i
$727$	−18.2390	−	22.8710i	−0.676447	−	0.848237i	0.318575	−	0.947898i	$-0.396796\pi$
$727$	−18.2390	−	22.8710i	−0.676447	−	0.848237i	−0.995022	+	0.0996604i	$0.968224\pi$
$728$	20.7760	−	1.03682i	0.770009	−	0.0384271i
$729$	8.76052	−	10.9853i	0.324464	−	0.406865i
$730$	1.09293	−	5.59836i	0.0404511	−	0.207205i
$731$	12.5207	−	6.02965i	0.463094	−	0.223014i
$732$	6.53378	+	11.6262i	0.241495	+	0.429715i
$733$	27.4010	−	6.25409i	1.01208	−	0.231000i	0.315841	−	0.948812i	$-0.397713\pi$
$733$	27.4010	−	6.25409i	1.01208	−	0.231000i	0.696237	+	0.717812i	$0.254856\pi$
$734$	29.9050	+	35.1606i	1.10382	+	1.29780i
$735$	−6.57051	+	0.889225i	−0.242357	+	0.0327996i
$736$	−32.3154	+	12.9974i	−1.19116	+	0.479091i
$737$	8.13363	+	35.6358i	0.299606	+	1.31266i
$738$	−30.1029	−	5.87678i	−1.10810	−	0.216327i
$739$	10.2252	+	21.2329i	0.376142	+	0.781066i	1.00000		0.000471178i	$-0.000149981\pi$
$739$	10.2252	+	21.2329i	0.376142	+	0.781066i	−0.623858	+	0.781538i	$0.714436\pi$
$740$	−5.08456	−	9.04743i	−0.186912	−	0.332590i
$741$	11.7771	+	9.39195i	0.432644	+	0.345022i
$742$	0.195848	−	14.6813i	0.00718981	−	0.538968i
$743$	2.49935	−	1.99316i	0.0916922	−	0.0731221i	−0.576571	−	0.817047i	$-0.695610\pi$
$743$	2.49935	−	1.99316i	0.0916922	−	0.0731221i	0.668263	+	0.743925i	$0.267038\pi$
$744$	2.54121	+	7.68885i	0.0931651	+	0.281887i
$745$	−1.47640	−	1.17739i	−0.0540911	−	0.0431362i
$746$	14.7903	−	19.7989i	0.541513	−	0.724888i
$747$	−18.7799	−	9.04390i	−0.687119	−	0.330899i
$748$	63.7466	−	4.03433i	2.33081	−	0.147510i
$749$	11.1083	+	0.499548i	0.405888	+	0.0182531i
$750$	−5.65625	−	10.8540i	−0.206537	−	0.396333i
$751$	2.87328	+	2.29137i	0.104848	+	0.0836132i	0.674510	−	0.738265i	$-0.264355\pi$
$751$	2.87328	+	2.29137i	0.104848	+	0.0836132i	−0.569663	+	0.821879i	$0.692926\pi$
$752$	−16.9345	−	16.4601i	−0.617537	−	0.600237i
$753$	−5.23676			−0.190838
$754$	23.2624	−	19.7853i	0.847168	−	0.720539i
$755$	2.80231	+	1.34952i	0.101986	+	0.0491141i
$756$	−21.2252	−	16.3014i	−0.771952	−	0.592877i
$757$	17.6860	−	8.51712i	0.642808	−	0.309560i	−0.0839331	−	0.996471i	$-0.526748\pi$
$757$	17.6860	−	8.51712i	0.642808	−	0.309560i	0.726741	+	0.686911i	$0.241034\pi$
$758$	−0.948992	+	2.14115i	−0.0344689	+	0.0777701i
$759$	−7.23447	+	31.6963i	−0.262595	+	1.15050i
$760$	−13.2594	+	4.38229i	−0.480968	+	0.158963i
$761$	7.92651	+	16.4596i	0.287336	+	0.596659i	0.993812	−	0.111078i	$-0.0354304\pi$
$761$	7.92651	+	16.4596i	0.287336	+	0.596659i	−0.706476	+	0.707737i	$0.749716\pi$
$762$	3.81375	−	8.60473i	0.138158	−	0.311716i
$763$	−7.58552	−	17.7502i	−0.274614	−	0.642599i
$764$	−27.6877	−	19.3513i	−1.00170	−	0.700104i
$765$	−11.2315			−0.406076
$766$	2.91353	+	3.42556i	0.105270	+	0.123771i
$767$	−7.02367	+	14.5848i	−0.253610	+	0.526627i
$768$	15.7953	−	4.08051i	0.569962	−	0.147243i
$769$	1.71462	+	0.391351i	0.0618308	+	0.0141125i	0.253324	−	0.967381i	$-0.418476\pi$
$769$	1.71462	+	0.391351i	0.0618308	+	0.0141125i	−0.191494	+	0.981494i	$0.561333\pi$
$770$	7.59295	+	16.3203i	0.273631	+	0.588143i
$771$	−11.2132	+	2.55935i	−0.403835	+	0.0921727i
$772$	−12.0302	+	17.2127i	−0.432976	+	0.619499i
$773$	5.14873	−	1.17516i	0.185187	−	0.0422677i	−0.128922	−	0.991655i	$-0.541152\pi$
$773$	5.14873	−	1.17516i	0.185187	−	0.0422677i	0.314109	+	0.949387i	$0.398294\pi$
$774$	0.197387	+	6.24408i	0.00709493	+	0.224439i
$775$	2.58492	−	11.3253i	0.0928532	−	0.406817i
$776$	−11.2463	+	30.4313i	−0.403717	+	1.09242i
$777$	−5.92152	−	13.8564i	−0.212433	−	0.497095i
$778$	21.1940	−	0.669981i	0.759841	−	0.0240200i
$779$	−45.9695	+	36.6594i	−1.64703	+	1.31346i
$780$	−1.49372	−	5.04970i	−0.0534836	−	0.180808i
$781$	4.52257	+	5.67112i	0.161830	+	0.202929i
$782$	−32.1400	+	43.0237i	−1.14932	+	1.53853i
$783$	−39.2895			−1.40409
$784$	−16.6467	+	22.5142i	−0.594525	+	0.804077i
$785$	0.890586			0.0317864
$786$	13.4668	−	18.0271i	0.480344	−	0.643005i
$787$	−10.6684	−	13.3778i	−0.380288	−	0.476867i	0.554443	−	0.832222i	$-0.312931\pi$
$787$	−10.6684	−	13.3778i	−0.380288	−	0.476867i	−0.934731	+	0.355355i	$0.884360\pi$
$788$	6.69729	+	22.6410i	0.238581	+	0.806553i
$789$	−7.02881	+	5.60529i	−0.250232	+	0.199554i
$790$	1.94196	−	0.0613890i	0.0690920	−	0.00218412i
$791$	−0.850070	+	18.9027i	−0.0302250	+	0.672103i
$792$	−9.95362	+	26.9335i	−0.353687	+	0.957041i
$793$	4.04528	−	17.7235i	0.143652	−	0.629382i
$794$	−1.24601	−	39.4160i	−0.0442193	−	1.39882i
$795$	−3.62371	+	0.827089i	−0.128520	+	0.0293338i
$796$	0.584257	−	0.835952i	0.0207085	−	0.0296295i
$797$	9.81409	−	2.24000i	0.347633	−	0.0793450i	−0.0451393	−	0.998981i	$-0.514373\pi$
$797$	9.81409	−	2.24000i	0.347633	−	0.0793450i	0.392772	+	0.919636i	$0.371516\pi$
$798$	−19.8261	+	4.24776i	−0.701836	+	0.150369i
$799$	−35.4982	−	8.10224i	−1.25584	−	0.286637i
$800$	−22.4199	−	6.70973i	−0.792663	−	0.237225i
$801$	7.02603	−	14.5897i	0.248253	−	0.515502i
$802$	3.00999	+	3.53897i	0.106286	+	0.124965i
$803$	−22.4837			−0.793432
$804$	11.7978	+	8.24566i	0.416078	+	0.290802i
$805$	−14.5882	−	4.02705i	−0.514168	−	0.141935i
$806$	4.47285	−	10.0918i	0.157549	−	0.355469i
$807$	−3.25876	−	6.76689i	−0.114714	−	0.238206i
$808$	40.8199	−	13.4912i	1.43604	−	0.474618i
$809$	7.79090	−	34.1342i	0.273913	−	1.20009i	−0.631437	−	0.775427i	$-0.717535\pi$
$809$	7.79090	−	34.1342i	0.273913	−	1.20009i	0.905350	−	0.424666i	$-0.139608\pi$
$810$	0.385564	−	0.869924i	0.0135473	−	0.0305660i
$811$	46.9910	−	22.6297i	1.65008	−	0.794636i	0.650701	−	0.759334i	$-0.274475\pi$
$811$	46.9910	−	22.6297i	1.65008	−	0.794636i	0.999377	−	0.0353014i	$-0.0112391\pi$
$812$	0.750640	+	41.0990i	0.0263423	+	1.44229i
$813$	−3.73250	−	1.79748i	−0.130904	−	0.0630402i
$814$	−31.1614	+	26.5036i	−1.09221	+	0.928952i
$815$	−10.4450			−0.365872
$816$	17.5312	−	18.0365i	0.613716	−	0.631405i
$817$	9.36321	+	7.46691i	0.327577	+	0.261234i
$818$	18.8200	+	36.1145i	0.658025	+	1.26271i
$819$	2.57354	+	14.1862i	0.0899266	+	0.495707i
$820$	20.5136	−	1.29824i	0.716365	−	0.0453365i
$821$	−12.1018	−	5.82792i	−0.422355	−	0.203396i	0.210619	−	0.977568i	$-0.432452\pi$
$821$	−12.1018	−	5.82792i	−0.422355	−	0.203396i	−0.632975	+	0.774173i	$0.718166\pi$
$822$	2.16400	−	2.89681i	0.0754783	−	0.101038i
$823$	−23.0688	−	18.3968i	−0.804129	−	0.641271i	0.132662	−	0.991161i	$-0.457647\pi$
$823$	−23.0688	−	18.3968i	−0.804129	−	0.641271i	−0.936791	+	0.349890i	$0.886219\pi$
$824$	8.63700	+	26.1327i	0.300884	+	0.910375i
$825$	−17.0781	+	13.6193i	−0.594584	+	0.474165i
$826$	−9.19141	−	19.7560i	−0.319810	−	0.687400i
$827$	3.69263	+	2.94477i	0.128405	+	0.102400i	0.685587	−	0.727991i	$-0.259546\pi$
$827$	3.69263	+	2.94477i	0.128405	+	0.102400i	−0.557181	+	0.830391i	$0.688117\pi$
$828$	−11.8275	−	21.0458i	−0.411035	−	0.731393i
$829$	2.39154	+	4.96608i	0.0830616	+	0.172479i	0.938363	−	0.345652i	$-0.112342\pi$
$829$	2.39154	+	4.96608i	0.0830616	+	0.172479i	−0.855301	+	0.518131i	$0.826628\pi$
$830$	13.7101	+	2.67652i	0.475884	+	0.0929035i
$831$	1.82445	+	7.99342i	0.0632893	+	0.277289i
$832$	−19.6881	−	10.3398i	−0.682561	−	0.358470i
$833$	−3.87499	+	42.9963i	−0.134260	+	1.48973i
$834$	3.74662	+	4.40506i	0.129735	+	0.152535i
$835$	2.47737	−	0.565443i	0.0857329	−	0.0195680i
$836$	26.9679	+	47.9864i	0.932703	+	1.65965i
$837$	−12.7954	+	6.16193i	−0.442273	+	0.212987i
$838$	−5.34807	+	27.3947i	−0.184746	+	0.946334i
$839$	−21.5481	+	27.0205i	−0.743924	+	0.932851i	−0.999423	−	0.0339584i	$-0.989189\pi$
$839$	−21.5481	+	27.0205i	−0.743924	+	0.932851i	0.255500	+	0.966809i	$0.417760\pi$
$840$	6.53160	+	2.75332i	0.225362	+	0.0949987i
$841$	19.5441	+	24.5075i	0.673934	+	0.845086i
$842$	44.5648	−	23.2236i	1.53580	−	0.800337i
$843$	12.2722	−	15.3888i	0.422675	−	0.530018i
$844$	0.0568280	+	0.897942i	0.00195610	+	0.0309085i
$845$	2.12535	−	4.41334i	0.0731144	−	0.151824i
$846$	9.79598	−	13.1132i	0.336793	−	0.450843i
$847$	33.8573	−	24.5956i	1.16335	−	0.845115i
$848$	−8.16134	+	13.4078i	−0.280262	+	0.460425i
$849$	17.6338	−	22.1121i	0.605191	−	0.758885i
$850$	−34.9060	+	9.13644i	−1.19727	+	0.313377i
$851$		−	34.3941i		−	1.17901i
$852$	2.81935	+	0.458448i	0.0965892	+	0.0157062i
$853$	−7.75662	+	16.1068i	−0.265582	+	0.551486i	−0.990527	−	0.137321i	$-0.956151\pi$
$853$	−7.75662	+	16.1068i	−0.265582	+	0.551486i	0.724945	+	0.688807i	$0.241865\pi$
$854$	15.0003	+	19.3332i	0.513299	+	0.661570i
$855$	−4.19957	−	8.72049i	−0.143622	−	0.298234i
$856$	−9.95369	−	6.49853i	−0.340210	−	0.222115i
$857$	−47.5813	−	10.8601i	−1.62535	−	0.370975i	−0.689750	−	0.724047i	$-0.742280\pi$
$857$	−47.5813	−	10.8601i	−1.62535	−	0.370975i	−0.935596	+	0.353072i	$0.885137\pi$
$858$	−18.4075	+	9.59251i	−0.628422	+	0.327483i
$859$	8.65929	−	4.17009i	0.295451	−	0.142282i	−0.280286	−	0.959916i	$-0.590429\pi$
$859$	8.65929	−	4.17009i	0.295451	−	0.142282i	0.575737	+	0.817635i	$0.304715\pi$
$860$	−1.18755	−	4.01468i	−0.0404953	−	0.136899i
$861$	29.8139	+	1.34076i	1.01606	+	0.0456928i
$862$	−32.2998	+	8.45428i	−1.10014	+	0.287954i
$863$		−	16.3319i		−	0.555945i	−0.960589	−	0.277972i	$-0.910338\pi$
$863$		−	16.3319i		−	0.555945i	0.960589	−	0.277972i	$-0.0896624\pi$
$864$	10.6761	+	26.5440i	0.363210	+	0.903045i
$865$	−10.5602	−	5.08552i	−0.359058	−	0.172913i
$866$	0.263808	+	8.34524i	0.00896457	+	0.283583i
$867$	4.77245	−	20.9095i	0.162081	−	0.710123i
$868$	6.69019	+	13.2670i	0.227080	+	0.450310i
$869$	−1.70417	−	7.46646i	−0.0578101	−	0.253282i
$870$	10.0668	−	2.63493i	0.341298	−	0.0893326i
$871$	−4.36603	−	19.1288i	−0.147937	−	0.648155i
$872$	−2.66684	+	20.4628i	−0.0903104	+	0.692958i
$873$	−21.9224	−	5.00365i	−0.741962	−	0.169348i
$874$	−45.4224	−	8.86751i	−1.53644	−	0.299948i
$875$	−13.1990	−	18.1692i	−0.446208	−	0.614231i
$876$	−6.55966	+	5.94641i	−0.221631	+	0.200911i
$877$	1.47907	+	1.85469i	0.0499446	+	0.0626285i	0.806176	−	0.591675i	$-0.201533\pi$
$877$	1.47907	+	1.85469i	0.0499446	+	0.0626285i	−0.756232	+	0.654304i	$0.772962\pi$
$878$	28.3220	+	12.5527i	0.955820	+	0.423634i
$879$	0.396529	−	0.316221i	0.0133746	−	0.0106659i
$880$	1.88268	−	19.1506i	0.0634652	−	0.645568i
$881$		−	0.561898i		−	0.0189308i	−0.999955	−	0.00946541i	$-0.996987\pi$
$881$		−	0.561898i		−	0.0189308i	0.999955	−	0.00946541i	$-0.00301298\pi$
$882$	−16.9648	−	9.42446i	−0.571235	−	0.317338i
$883$			22.3407i			0.751824i	0.926655	+	0.375912i	$0.122670\pi$
$883$			22.3407i			0.751824i	−0.926655	+	0.375912i	$0.877330\pi$
$884$	−34.2184	+	2.16557i	−1.15089	+	0.0728362i
$885$	−4.31259	+	3.43918i	−0.144966	+	0.115607i
$886$	−12.2894	+	27.7279i	−0.412872	+	0.931538i
$887$	−17.4106	−	21.8322i	−0.584590	−	0.733053i	0.398298	−	0.917256i	$-0.369601\pi$
$887$	−17.4106	−	21.8322i	−0.584590	−	0.733053i	−0.982888	+	0.184203i	$0.941030\pi$
$888$	−2.08182	+	15.9740i	−0.0698614	+	0.536051i
$889$	4.59534	−	16.6469i	0.154123	−	0.558320i
$890$	−2.07934	+	10.6511i	−0.0696996	+	0.357025i
$891$	−3.65665	−	0.834608i	−0.122503	−	0.0279604i
$892$	−29.1797	−	32.1890i	−0.977009	−	1.07777i
$893$	−6.98230	−	30.5915i	−0.233654	−	1.02370i
$894$	0.742203	+	2.83561i	0.0248230	+	0.0948369i
$895$	−2.14911	−	9.41588i	−0.0718369	−	0.314738i
$896$	27.5626	−	11.6750i	0.920801	−	0.390034i
$897$	3.88337	−	17.0142i	0.129662	−	0.568086i
$898$	−26.4227	+	0.835270i	−0.881737	+	0.0278733i
$899$	19.6529	+	9.46434i	0.655461	+	0.315653i
$900$	2.60334	−	16.0099i	0.0867780	−	0.533665i
$901$			24.2008i			0.806244i
$902$	−20.5155	−	78.3799i	−0.683090	−	2.60977i
$903$	−1.08504	−	5.98112i	−0.0361078	−	0.199039i
$904$	11.0584	−	16.9380i	0.367797	−	0.563349i
$905$	7.64209	−	3.68024i	0.254032	−	0.122335i
$906$	−2.23110	−	4.28135i	−0.0741233	−	0.142238i
$907$	−2.55072	−	0.582186i	−0.0846954	−	0.0193312i	0.179963	−	0.983673i	$-0.442402\pi$
$907$	−2.55072	−	0.582186i	−0.0846954	−	0.0193312i	−0.264659	+	0.964342i	$0.585259\pi$
$908$	0.695070	+	2.34977i	0.0230667	+	0.0779799i
$909$	12.9287	+	26.8466i	0.428816	+	0.890446i
$910$	−4.07580	−	8.76053i	−0.135111	−	0.290409i
$911$	13.5494	−	28.1357i	0.448912	−	0.932176i	−0.546586	−	0.837403i	$-0.684073\pi$
$911$	13.5494	−	28.1357i	0.448912	−	0.932176i	0.995499	−	0.0947736i	$-0.0302127\pi$
$912$	20.5592	+	6.86777i	0.680784	+	0.227415i
$913$		−	55.0613i		−	1.82226i
$914$	7.62043	+	29.1141i	0.252061	+	0.963008i
$915$	3.86226	−	4.84313i	0.127683	−	0.160109i
$916$	−14.6910	+	36.1922i	−0.485404	+	1.19582i
$917$	19.5669	−	36.3561i	0.646156	−	1.20058i
$918$	35.3399	+	26.3999i	1.16639	+	0.871327i
$919$	−0.443066	+	0.920037i	−0.0146154	+	0.0303492i	−0.908149	−	0.418648i	$-0.862504\pi$
$919$	−0.443066	+	0.920037i	−0.0146154	+	0.0303492i	0.893533	+	0.448997i	$0.148219\pi$
$920$	11.2394	+	11.6374i	0.370552	+	0.383673i
$921$	−15.1403	+	18.9854i	−0.498891	+	0.625590i
$922$	1.69956	+	3.26137i	0.0559722	+	0.107408i
$923$	−2.42765	−	3.04418i	−0.0799072	−	0.100200i
$924$	5.71870	−	27.3481i	0.188131	−	0.899687i
$925$	14.4080	−	18.0671i	0.473732	−	0.594042i
$926$	53.0330	+	10.3533i	1.74277	+	0.340230i
$927$	−17.1871	+	8.27686i	−0.564498	+	0.271848i
$928$	21.6513	−	38.2400i	0.710739	−	1.25529i
$929$	30.5491	−	6.97263i	1.00228	−	0.228764i	0.310269	−	0.950649i	$-0.399581\pi$
$929$	30.5491	−	6.97263i	1.00228	−	0.228764i	0.692014	+	0.721884i	$0.256724\pi$
$930$	2.86521	−	2.43694i	0.0939539	−	0.0799103i
$931$	−34.8326	+	13.0681i	−1.14159	+	0.428289i
$932$	7.30909	−	44.9492i	0.239417	−	1.47236i
$933$	5.52876	+	24.2231i	0.181003	+	0.793028i
$934$	−5.87168	+	30.0768i	−0.192127	+	0.984143i
$935$	−12.8729	−	26.7308i	−0.420987	−	0.874190i
$936$	5.34297	−	14.4576i	0.174641	−	0.472560i
$937$	−31.6509	−	25.2407i	−1.03399	−	0.824579i	−0.0492802	−	0.998785i	$-0.515693\pi$
$937$	−31.6509	−	25.2407i	−1.03399	−	0.824579i	−0.984709	+	0.174206i	$0.944264\pi$
$938$	23.6398	+	11.7753i	0.771867	+	0.384478i
$939$	18.8612	−	15.0413i	0.615513	−	0.490855i
$940$	−4.12570	+	10.1639i	−0.134566	+	0.331510i
$941$	29.3559	+	23.4105i	0.956974	+	0.763162i	0.971575	−	0.236732i	$-0.0760763\pi$
$941$	29.3559	+	23.4105i	0.956974	+	0.763162i	−0.0146007	+	0.999893i	$0.504648\pi$
$942$	−1.10746	−	0.827307i	−0.0360831	−	0.0269551i
$943$	61.3730	+	29.5557i	1.99858	+	0.962465i
$944$	−2.27902	+	23.1822i	−0.0741759	+	0.754517i
$945$	−3.30783	+	11.9828i	−0.107604	+	0.389802i
$946$	−14.6346	+	7.62636i	−0.475811	+	0.247954i
$947$	31.4611	+	25.0894i	1.02235	+	0.815295i	0.982940	−	0.183928i	$-0.0588813\pi$
$947$	31.4611	+	25.0894i	1.02235	+	0.815295i	0.0394081	+	0.999223i	$0.487453\pi$
$948$	−2.47190	−	1.72764i	−0.0802836	−	0.0561112i
$949$	12.0689			0.391775
$950$	−20.1455	−	23.6859i	−0.653607	−	0.768473i
$951$	13.6739	+	6.58499i	0.443405	+	0.213533i
$952$	26.9406	−	37.4719i	0.873151	−	1.21447i
$953$	−41.4340	+	19.9536i	−1.34218	+	0.646359i	−0.960589	−	0.277973i	$-0.910338\pi$
$953$	−41.4340	+	19.9536i	−1.34218	+	0.646359i	−0.381590	+	0.924332i	$0.624623\pi$
$954$	−9.94605	−	4.40824i	−0.322015	−	0.142722i
$955$	−3.49144	+	15.2970i	−0.112980	+	0.495000i
$956$	3.62065	−	8.91970i	0.117100	−	0.288484i
$957$	−17.7967	−	36.9553i	−0.575286	−	1.19459i
$958$	19.1538	+	8.48927i	0.618832	+	0.274276i
$959$	3.14425	−	5.84214i	0.101533	−	0.188653i
$960$	−4.51562	−	6.08517i	−0.145741	−	0.196398i
$961$	−23.1153			−0.745656
$962$	16.7271	−	14.2268i	0.539302	−	0.458691i
$963$	3.57480	−	7.42315i	0.115196	−	0.239208i
$964$	13.2337	−	11.9965i	0.426228	−	0.386381i
$965$	9.50976	+	2.17054i	0.306130	+	0.0698722i
$966$	14.3999	+	18.5594i	0.463308	+	0.597140i
$967$	−49.6052	+	11.3221i	−1.59519	+	0.364093i	−0.925561	−	0.378599i	$-0.876406\pi$
$967$	−49.6052	+	11.3221i	−1.59519	+	0.364093i	−0.669633	+	0.742692i	$0.733549\pi$
$968$	−44.5365	+	4.23493i	−1.43146	+	0.136116i
$969$	32.5822	−	7.43669i	1.04669	−	0.238901i
$970$	15.0619	−	0.476133i	0.483607	−	0.0152877i
$971$	−3.03033	+	13.2767i	−0.0972478	+	0.426070i	−0.999992	−	0.00410823i	$-0.998692\pi$
$971$	−3.03033	+	13.2767i	−0.0972478	+	0.426070i	0.902744	+	0.430179i	$0.141549\pi$
$972$	−27.7422	+	15.5908i	−0.889833	+	0.500077i
$973$	7.99016	+	6.98165i	0.256153	+	0.223821i
$974$	−0.868542	−	27.4752i	−0.0278299	−	0.880363i
$975$	9.16731	−	7.31068i	0.293589	−	0.234129i
$976$	−3.29791	−	25.9508i	−0.105563	−	0.830666i
$977$	0.410090	+	0.514237i	0.0131200	+	0.0164519i	0.788348	−	0.615229i	$-0.210937\pi$
$977$	0.410090	+	0.514237i	0.0131200	+	0.0164519i	−0.775228	+	0.631681i	$0.782365\pi$
$978$	12.9886	+	9.70285i	0.415329	+	0.310263i
$979$	42.7761			1.36713
$980$	12.5979	+	3.23125i	0.402426	+	0.103218i
$981$	−14.3027			−0.456651
$982$	−11.3464	−	8.47607i	−0.362077	−	0.270482i
$983$	27.6479	+	34.6693i	0.881830	+	1.10578i	0.993702	+	0.112058i	$0.0357441\pi$
$983$	27.6479	+	34.6693i	0.881830	+	1.10578i	−0.111871	+	0.993723i	$0.535684\pi$
$984$	−26.7151	−	17.4416i	−0.851646	−	0.556019i
$985$	8.57432	−	6.83780i	0.273201	−	0.217870i
$986$	−2.14073	−	67.7194i	−0.0681748	−	2.15662i
$987$	−7.54808	+	14.0246i	−0.240258	+	0.446409i
$988$	−14.4760	−	25.7585i	−0.460543	−	0.819487i
$989$	3.08741	−	13.5268i	0.0981739	−	0.430128i
$990$	13.3307	−	0.421407i	0.423676	−	0.0133932i
$991$	−39.0231	+	8.90678i	−1.23961	+	0.282933i	−0.791569	−	0.611080i	$-0.790736\pi$
$991$	−39.0231	+	8.90678i	−1.23961	+	0.282933i	−0.448042	+	0.894013i	$0.647878\pi$
$992$	1.05383	−	15.8493i	0.0334591	−	0.503215i
$993$	−2.23452	+	0.510014i	−0.0709103	+	0.0161848i
$994$	5.24053	+	0.0699085i	0.166220	+	0.00221736i
$995$	−0.461851	−	0.105414i	−0.0146416	−	0.00334186i
$996$	−14.5624	−	16.0643i	−0.461428	−	0.509015i
$997$	−11.7307	+	24.3590i	−0.371514	+	0.771457i	−0.999980	−	0.00638019i	$-0.997969\pi$
$997$	−11.7307	+	24.3590i	−0.371514	+	0.771457i	0.628465	+	0.777838i	$0.283683\pi$
$998$	13.7904	−	11.7291i	0.436526	−	0.371277i
$999$	−28.2515			−0.893836

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	196.2.j.a.111.19	yes	156
4.3	odd	2	inner	196.2.j.a.111.5	yes	156
49.34	odd	14	inner	196.2.j.a.83.5	✓	156
196.83	even	14	inner	196.2.j.a.83.19	yes	156

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
196.2.j.a.83.5	✓	156	49.34	odd	14	inner
196.2.j.a.83.19	yes	156	196.83	even	14	inner
196.2.j.a.111.5	yes	156	4.3	odd	2	inner
196.2.j.a.111.19	yes	156	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 196 = 2^{2} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	196.j (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.846372 - 1.13298i) q^{2} +(0.635719 + 0.797166i) q^{3} +(-0.567307 - 1.91785i) q^{4} +(-0.726306 + 0.579209i) q^{5} +(1.44123 - 0.0455600i) q^{6} +(2.60326 - 0.472259i) q^{7} +(-2.65305 - 0.980468i) q^{8} +(0.436227 - 1.91124i) q^{9} +(0.0415101 + 1.31312i) q^{10} +(5.04868 - 1.15233i) q^{11} +(1.16820 - 1.67145i) q^{12} +(-2.71007 + 0.618555i) q^{13} +(1.66827 - 3.34916i) q^{14} +(-0.923453 - 0.210772i) q^{15} +(-3.35632 + 2.17602i) q^{16} +(-2.67586 + 5.55648i) q^{17} +(-1.79619 - 2.11186i) q^{18} -5.31475 q^{19} +(1.52288 + 1.06436i) q^{20} +(2.03141 + 1.77501i) q^{21} +(2.96750 - 6.69538i) q^{22} +(2.67158 + 5.54759i) q^{23} +(-0.904999 - 2.73823i) q^{24} +(-0.920568 + 4.03327i) q^{25} +(-1.59291 + 3.59399i) q^{26} +(4.55681 - 2.19445i) q^{27} +(-2.38257 - 4.72476i) q^{28} +(-6.99898 - 3.37053i) q^{29} +(-1.02039 + 0.867866i) q^{30} -2.80797 q^{31} +(-0.375299 + 5.64439i) q^{32} +(4.12814 + 3.29208i) q^{33} +(4.03063 + 7.73455i) q^{34} +(-1.61723 + 1.85084i) q^{35} +(-3.91295 + 0.247638i) q^{36} +(-5.03268 - 2.42361i) q^{37} +(-4.49826 + 6.02153i) q^{38} +(-2.21593 - 1.76715i) q^{39} +(2.49482 - 0.824553i) q^{40} +(8.64941 - 6.89767i) q^{41} +(3.73039 - 0.799240i) q^{42} +(-1.76174 - 1.40494i) q^{43} +(-5.07415 - 9.02891i) q^{44} +(0.790172 + 1.64081i) q^{45} +(8.54648 + 1.66847i) q^{46} +(1.31376 + 5.75595i) q^{47} +(-3.86833 - 1.29221i) q^{48} +(6.55394 - 2.45883i) q^{49} +(3.79049 + 4.45664i) q^{50} +(-6.13053 + 1.39925i) q^{51} +(2.72374 + 4.84660i) q^{52} +(3.53549 - 1.70260i) q^{53} +(1.37049 - 7.02012i) q^{54} +(-2.99945 + 3.76119i) q^{55} +(-7.36962 - 1.29949i) q^{56} +(-3.37869 - 4.23674i) q^{57} +(-9.74251 + 5.07701i) q^{58} +(3.63089 - 4.55299i) q^{59} +(0.119651 + 1.89062i) q^{60} +(-2.83755 + 5.89224i) q^{61} +(-2.37659 + 3.18138i) q^{62} +(0.233014 - 5.18146i) q^{63} +(6.07736 + 5.20247i) q^{64} +(1.61006 - 2.01896i) q^{65} +(7.22383 - 1.89079i) q^{66} +7.05842i q^{67} +(12.1745 + 1.97967i) q^{68} +(-2.72398 + 5.65640i) q^{69} +(0.728195 + 3.39879i) q^{70} +(0.607747 + 1.26200i) q^{71} +(-3.03124 + 4.64290i) q^{72} +(-4.23286 - 0.966123i) q^{73} +(-7.00543 + 3.65067i) q^{74} +(-3.80041 + 1.83018i) q^{75} +(3.01510 + 10.1929i) q^{76} +(12.5988 - 5.38410i) q^{77} +(-3.87766 + 1.01495i) q^{78} -1.47889i q^{79} +(1.17734 - 3.52447i) q^{80} +(-0.652553 - 0.314253i) q^{81} +(-0.494335 - 15.6376i) q^{82} +(2.36598 - 10.3660i) q^{83} +(2.25177 - 4.90293i) q^{84} +(-1.27487 - 5.58558i) q^{85} +(-3.08286 + 0.806921i) q^{86} +(-1.76251 - 7.72207i) q^{87} +(-14.5242 - 1.89289i) q^{88} +(8.05318 + 1.83809i) q^{89} +(2.52779 + 0.493483i) q^{90} +(-6.76290 + 2.89012i) q^{91} +(9.12386 - 8.27088i) q^{92} +(-1.78508 - 2.23842i) q^{93} +(7.63333 + 3.38321i) q^{94} +(3.86013 - 3.07835i) q^{95} +(-4.73810 + 3.28907i) q^{96} -11.4703i q^{97} +(2.76126 - 9.50660i) q^{98} -10.1519i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 156 q - 5 q^{2} - 5 q^{4} - 14 q^{5} - 7 q^{6} - 11 q^{8} - 32 q^{9} - 7 q^{10} - 42 q^{12} - 14 q^{13} + 21 q^{14} - 13 q^{16} - 14 q^{17} - 12 q^{18} - 7 q^{20} - 14 q^{21} + 3 q^{22} + 35 q^{24} - 7 q^{26}+ \cdots + 105 q^{98}+O(q^{100}) \) 156 * q - 5 * q^2 - 5 * q^4 - 14 * q^5 - 7 * q^6 - 11 * q^8 - 32 * q^9 - 7 * q^10 - 42 * q^12 - 14 * q^13 + 21 * q^14 - 13 * q^16 - 14 * q^17 - 12 * q^18 - 7 * q^20 - 14 * q^21 + 3 * q^22 + 35 * q^24 - 7 * q^26 + 42 * q^28 - 30 * q^29 - 4 * q^30 - 5 * q^32 - 14 * q^33 + 77 * q^34 - 11 * q^36 + 10 * q^37 - 21 * q^38 - 63 * q^40 - 14 * q^41 - 7 * q^42 - 55 * q^44 - 14 * q^45 - 19 * q^46 - 132 * q^50 - 7 * q^52 - 2 * q^53 + 14 * q^54 - 70 * q^56 - 64 * q^57 - 3 * q^58 - 107 * q^60 + 14 * q^61 - 21 * q^62 - 11 * q^64 - 22 * q^65 + 161 * q^66 - 70 * q^69 - 77 * q^70 + 114 * q^72 - 14 * q^73 + 5 * q^74 + 70 * q^76 - 42 * q^77 + 61 * q^78 + 92 * q^81 - 42 * q^82 + 70 * q^84 - 6 * q^85 + 47 * q^86 + 65 * q^88 - 14 * q^89 + 112 * q^90 - 70 * q^92 - 48 * q^93 - 28 * q^94 + 238 * q^96 + 105 * q^98

Introduction

L-functions

Modular forms

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Database

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