LMFDB - Embedded newform 504.2.cc.b.293.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [504,2,Mod(293,504)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(504, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 5, 3]))

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

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

chi := DirichletCharacter("504.293");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 504 = 2^{3} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	504.cc (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.02446026187$
Analytic rank:	$0$
Dimension:	$168$
Relative dimension:	$84$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			293.3
Character	$\chi$	$=$	504.293
Dual form			504.2.cc.b.461.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.39399 - 0.238316i) q^{2} +(-1.00341 - 1.41180i) q^{3} +(1.88641 + 0.664419i) q^{4} +(1.68580 + 0.973297i) q^{5} +(1.06229 + 2.20716i) q^{6} +(-2.24361 - 1.40222i) q^{7} +(-2.47129 - 1.37576i) q^{8} +(-0.986337 + 2.83322i) q^{9} +O(q^{10})$	\(q+(-1.39399 - 0.238316i) q^{2} +(-1.00341 - 1.41180i) q^{3} +(1.88641 + 0.664419i) q^{4} +(1.68580 + 0.973297i) q^{5} +(1.06229 + 2.20716i) q^{6} +(-2.24361 - 1.40222i) q^{7} +(-2.47129 - 1.37576i) q^{8} +(-0.986337 + 2.83322i) q^{9} +(-2.11804 - 1.75852i) q^{10} +(2.34300 + 4.05819i) q^{11} +(-0.954819 - 3.32991i) q^{12} +(-1.34974 + 2.33782i) q^{13} +(2.79340 + 2.48936i) q^{14} +(-0.317452 - 3.35662i) q^{15} +(3.11709 + 2.50674i) q^{16} -1.98946 q^{17} +(2.05014 - 3.71442i) q^{18} -8.19396 q^{19} +(2.53343 + 2.95612i) q^{20} +(0.271616 + 4.57452i) q^{21} +(-2.29898 - 6.21545i) q^{22} +(-0.167614 - 0.0967722i) q^{23} +(0.537436 + 4.86941i) q^{24} +(-0.605385 - 1.04856i) q^{25} +(2.43866 - 2.93723i) q^{26} +(4.98963 - 1.45038i) q^{27} +(-3.30071 - 4.13586i) q^{28} +(3.85703 + 6.68057i) q^{29} +(-0.357412 + 4.75475i) q^{30} +(-3.60768 - 2.08289i) q^{31} +(-3.74780 - 4.23722i) q^{32} +(3.37835 - 7.37987i) q^{33} +(2.77328 + 0.474119i) q^{34} +(-2.41750 - 4.54756i) q^{35} +(-3.74308 + 4.68928i) q^{36} +10.4166i q^{37} +(11.4223 + 1.95275i) q^{38} +(4.65486 - 0.440232i) q^{39} +(-2.82709 - 4.72455i) q^{40} +(-3.52851 + 6.11157i) q^{41} +(0.711551 - 6.44156i) q^{42} +(3.25676 - 1.88029i) q^{43} +(1.72352 + 9.21215i) q^{44} +(-4.42033 + 3.81625i) q^{45} +(0.210590 + 0.174845i) q^{46} +(3.66475 + 6.34753i) q^{47} +(0.411278 - 6.91599i) q^{48} +(3.06757 + 6.29206i) q^{49} +(0.594012 + 1.60595i) q^{50} +(1.99624 + 2.80871i) q^{51} +(-4.09946 + 3.51329i) q^{52} +6.47241 q^{53} +(-7.30114 + 0.832699i) q^{54} +9.12174i q^{55} +(3.61551 + 6.55195i) q^{56} +(8.22190 + 11.5682i) q^{57} +(-3.78457 - 10.2318i) q^{58} +(4.33741 + 2.50420i) q^{59} +(1.63136 - 6.54289i) q^{60} +(0.820789 + 1.42165i) q^{61} +(4.53268 + 3.76330i) q^{62} +(6.18575 - 4.97358i) q^{63} +(4.21460 + 6.79979i) q^{64} +(-4.55078 + 2.62740i) q^{65} +(-6.46813 + 9.48234i) q^{66} +(-4.04058 - 2.33283i) q^{67} +(-3.75293 - 1.32183i) q^{68} +(0.0315633 + 0.333739i) q^{69} +(2.28622 + 6.91538i) q^{70} -1.77476i q^{71} +(6.33535 - 5.64477i) q^{72} -13.4982i q^{73} +(2.48245 - 14.5207i) q^{74} +(-0.872900 + 1.90681i) q^{75} +(-15.4572 - 5.44422i) q^{76} +(0.433693 - 12.3904i) q^{77} +(-6.59375 - 0.495649i) q^{78} +(2.50088 + 4.33165i) q^{79} +(2.81500 + 7.25972i) q^{80} +(-7.05428 - 5.58902i) q^{81} +(6.37519 - 7.67855i) q^{82} +(-10.0584 + 5.80719i) q^{83} +(-2.52702 + 8.80989i) q^{84} +(-3.35382 - 1.93633i) q^{85} +(-4.98798 + 1.84497i) q^{86} +(5.56143 - 12.1487i) q^{87} +(-0.207161 - 13.2524i) q^{88} -13.1567 q^{89} +(7.07137 - 4.26637i) q^{90} +(6.30642 - 3.35252i) q^{91} +(-0.251892 - 0.293918i) q^{92} +(0.679359 + 7.18331i) q^{93} +(-3.59590 - 9.72176i) q^{94} +(-13.8134 - 7.97516i) q^{95} +(-2.22151 + 9.54279i) q^{96} +(-3.24250 + 1.87206i) q^{97} +(-2.77667 - 9.50211i) q^{98} +(-13.8087 + 2.63549i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	$ 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) $ 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/504\mathbb{Z}\right)^\times$.

$n$	$73$	$127$	$253$	$281$
$\chi(n)$	$-1$	$1$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.39399	−	0.238316i	−0.985699	−	0.168515i
$2$	−1.39399	−	0.238316i	−0.985699	−	0.168515i
$3$	−1.00341	−	1.41180i	−0.579319	−	0.815101i
$3$	−1.00341	−	1.41180i	−0.579319	−	0.815101i
$4$	1.88641	+	0.664419i	0.943206	+	0.332210i
$5$	1.68580	+	0.973297i	0.753913	+	0.435272i	0.827106	−	0.562046i	$-0.189986\pi$
$5$	1.68580	+	0.973297i	0.753913	+	0.435272i	−0.0731931	+	0.997318i	$0.523319\pi$
$6$	1.06229	+	2.20716i	0.433678	+	0.901068i
$7$	−2.24361	−	1.40222i	−0.848005	−	0.529988i
$7$	−2.24361	−	1.40222i	−0.848005	−	0.529988i
$8$	−2.47129	−	1.37576i	−0.873735	−	0.486403i
$9$	−0.986337	+	2.83322i	−0.328779	+	0.944407i
$10$	−2.11804	−	1.75852i	−0.669782	−	0.556092i
$11$	2.34300	+	4.05819i	0.706441	+	1.22359i	0.966169	+	0.257909i	$0.0830336\pi$
$11$	2.34300	+	4.05819i	0.706441	+	1.22359i	−0.259728	+	0.965682i	$0.583633\pi$
$12$	−0.954819	−	3.32991i	−0.275632	−	0.961263i
$13$	−1.34974	+	2.33782i	−0.374350	+	0.648394i	−0.990230	−	0.139447i	$-0.955468\pi$
$13$	−1.34974	+	2.33782i	−0.374350	+	0.648394i	0.615879	+	0.787841i	$0.288801\pi$
$14$	2.79340	+	2.48936i	0.746567	+	0.665310i
$15$	−0.317452	−	3.35662i	−0.0819656	−	0.866676i
$16$	3.11709	+	2.50674i	0.779273	+	0.626684i
$17$	−1.98946			−0.482514			−0.241257	−	0.970461i	$-0.577560\pi$
$17$	−1.98946			−0.482514			−0.241257	+	0.970461i	$0.577560\pi$
$18$	2.05014	−	3.71442i	0.483224	−	0.875497i
$19$	−8.19396			−1.87982			−0.939911	−	0.341419i	$-0.889093\pi$
$19$	−8.19396			−1.87982			−0.939911	+	0.341419i	$0.889093\pi$
$20$	2.53343	+	2.95612i	0.566493	+	0.661008i
$21$	0.271616	+	4.57452i	0.0592714	+	0.998242i
$22$	−2.29898	−	6.21545i	−0.490145	−	1.32514i
$23$	−0.167614	−	0.0967722i	−0.0349500	−	0.0201784i	0.482423	−	0.875938i	$-0.339757\pi$
$23$	−0.167614	−	0.0967722i	−0.0349500	−	0.0201784i	−0.517373	+	0.855760i	$0.673090\pi$
$24$	0.537436	+	4.86941i	0.109704	+	0.993964i
$25$	−0.605385	−	1.04856i	−0.121077	−	0.209711i
$26$	2.43866	−	2.93723i	0.478261	−	0.576038i
$27$	4.98963	−	1.45038i	0.960255	−	0.279125i
$28$	−3.30071	−	4.13586i	−0.623776	−	0.781603i
$29$	3.85703	+	6.68057i	0.716233	+	1.24055i	0.962482	+	0.271345i	$0.0874684\pi$
$29$	3.85703	+	6.68057i	0.716233	+	1.24055i	−0.246249	+	0.969206i	$0.579198\pi$
$30$	−0.357412	+	4.75475i	−0.0652543	+	0.868094i
$31$	−3.60768	−	2.08289i	−0.647958	−	0.374099i	0.139715	−	0.990192i	$-0.455381\pi$
$31$	−3.60768	−	2.08289i	−0.647958	−	0.374099i	−0.787674	+	0.616093i	$0.788715\pi$
$32$	−3.74780	−	4.23722i	−0.662524	−	0.749041i
$33$	3.37835	−	7.37987i	0.588096	−	1.28467i
$34$	2.77328	+	0.474119i	0.475613	+	0.0813107i
$35$	−2.41750	−	4.54756i	−0.408633	−	0.768678i
$36$	−3.74308	+	4.68928i	−0.623847	+	0.781546i
$37$			10.4166i			1.71249i	0.516574	+	0.856243i	$0.327207\pi$
$37$			10.4166i			1.71249i	−0.516574	+	0.856243i	$0.672793\pi$
$38$	11.4223	+	1.95275i	1.85294	+	0.316778i
$39$	4.65486	−	0.440232i	0.745375	−	0.0704936i
$40$	−2.82709	−	4.72455i	−0.447002	−	0.747017i
$41$	−3.52851	+	6.11157i	−0.551061	+	0.954466i	0.447137	+	0.894465i	$0.352444\pi$
$41$	−3.52851	+	6.11157i	−0.551061	+	0.954466i	−0.998198	+	0.0600007i	$0.980890\pi$
$42$	0.711551	−	6.44156i	0.109795	−	0.993954i
$43$	3.25676	−	1.88029i	0.496651	−	0.286741i	−0.230679	−	0.973030i	$-0.574095\pi$
$43$	3.25676	−	1.88029i	0.496651	−	0.286741i	0.727329	+	0.686289i	$0.240761\pi$
$44$	1.72352	+	9.21215i	0.259830	+	1.38878i
$45$	−4.42033	+	3.81625i	−0.658944	+	0.568892i
$46$	0.210590	+	0.174845i	0.0310498	+	0.0257794i
$47$	3.66475	+	6.34753i	0.534559	+	0.925882i	0.999185	+	0.0403755i	$0.0128554\pi$
$47$	3.66475	+	6.34753i	0.534559	+	0.925882i	−0.464626	+	0.885507i	$0.653811\pi$
$48$	0.411278	−	6.91599i	0.0593628	−	0.998236i
$49$	3.06757	+	6.29206i	0.438225	+	0.898865i
$50$	0.594012	+	1.60595i	0.0840060	+	0.227116i
$51$	1.99624	+	2.80871i	0.279529	+	0.393297i
$52$	−4.09946	+	3.51329i	−0.568492	+	0.487206i
$53$	6.47241			0.889054			0.444527	−	0.895765i	$-0.353372\pi$
$53$	6.47241			0.889054			0.444527	+	0.895765i	$0.353372\pi$
$54$	−7.30114	+	0.832699i	−0.993559	+	0.113316i
$55$			9.12174i			1.22997i
$56$	3.61551	+	6.55195i	0.483143	+	0.875541i
$57$	8.22190	+	11.5682i	1.08902	+	1.53225i
$58$	−3.78457	−	10.2318i	−0.496939	−	1.34351i
$59$	4.33741	+	2.50420i	0.564682	+	0.326019i	0.755023	−	0.655699i	$-0.227626\pi$
$59$	4.33741	+	2.50420i	0.564682	+	0.326019i	−0.190340	+	0.981718i	$0.560959\pi$
$60$	1.63136	−	6.54289i	0.210608	−	0.844684i
$61$	0.820789	+	1.42165i	0.105091	+	0.182023i	0.913775	−	0.406220i	$-0.133153\pi$
$61$	0.820789	+	1.42165i	0.105091	+	0.182023i	−0.808684	+	0.588243i	$0.799820\pi$
$62$	4.53268	+	3.76330i	0.575651	+	0.477940i
$63$	6.18575	−	4.97358i	0.779331	−	0.626613i
$64$	4.21460	+	6.79979i	0.526824	+	0.849974i
$65$	−4.55078	+	2.62740i	−0.564455	+	0.325888i
$66$	−6.46813	+	9.48234i	−0.796171	+	1.16720i
$67$	−4.04058	−	2.33283i	−0.493635	−	0.285001i	0.232446	−	0.972609i	$-0.425327\pi$
$67$	−4.04058	−	2.33283i	−0.493635	−	0.285001i	−0.726081	+	0.687609i	$0.758660\pi$
$68$	−3.75293	−	1.32183i	−0.455110	−	0.160296i
$69$	0.0315633	+	0.333739i	0.00379978	+	0.0401775i
$70$	2.28622	+	6.91538i	0.273256	+	0.826546i
$71$		−	1.77476i		−	0.210626i	−0.994439	−	0.105313i	$-0.966416\pi$
$71$		−	1.77476i		−	0.210626i	0.994439	−	0.105313i	$-0.0335844\pi$
$72$	6.33535	−	5.64477i	0.746628	−	0.665242i
$73$		−	13.4982i		−	1.57984i	−0.613208	−	0.789922i	$-0.710121\pi$
$73$		−	13.4982i		−	1.57984i	0.613208	−	0.789922i	$-0.289879\pi$
$74$	2.48245	−	14.5207i	0.288579	−	1.68799i
$75$	−0.872900	+	1.90681i	−0.100794	+	0.220180i
$76$	−15.4572	−	5.44422i	−1.77306	−	0.624495i
$77$	0.433693	−	12.3904i	0.0494239	−	1.41202i
$78$	−6.59375	−	0.495649i	−0.746595	−	0.0561212i
$79$	2.50088	+	4.33165i	0.281371	+	0.487349i	0.971723	−	0.236125i	$-0.0758775\pi$
$79$	2.50088	+	4.33165i	0.281371	+	0.487349i	−0.690352	+	0.723474i	$0.742544\pi$
$80$	2.81500	+	7.25972i	0.314726	+	0.811661i
$81$	−7.05428	−	5.58902i	−0.783809	−	0.621002i
$82$	6.37519	−	7.67855i	0.704022	−	0.847954i
$83$	−10.0584	+	5.80719i	−1.10405	+	0.637422i	−0.937281	−	0.348574i	$-0.886666\pi$
$83$	−10.0584	+	5.80719i	−1.10405	+	0.637422i	−0.166766	+	0.985996i	$0.553333\pi$
$84$	−2.52702	+	8.80989i	−0.275721	+	0.961238i
$85$	−3.35382	−	1.93633i	−0.363773	−	0.210025i
$86$	−4.98798	+	1.84497i	−0.537868	+	0.198948i
$87$	5.56143	−	12.1487i	0.596247	−	1.30248i
$88$	−0.207161	−	13.2524i	−0.0220834	−	1.41271i
$89$	−13.1567			−1.39461			−0.697306	−	0.716773i	$-0.745618\pi$
$89$	−13.1567			−1.39461			−0.697306	+	0.716773i	$0.745618\pi$
$90$	7.07137	−	4.26637i	0.745388	−	0.449715i
$91$	6.30642	−	3.35252i	0.661092	−	0.351440i
$92$	−0.251892	−	0.293918i	−0.0262616	−	0.0306431i
$93$	0.679359	+	7.18331i	0.0704462	+	0.744874i
$94$	−3.59590	−	9.72176i	−0.370889	−	1.00272i
$95$	−13.8134	−	7.97516i	−1.41722	−	0.818234i
$96$	−2.22151	+	9.54279i	−0.226731	+	0.973957i
$97$	−3.24250	+	1.87206i	−0.329226	+	0.190079i	−0.655498	−	0.755197i	$-0.727541\pi$
$97$	−3.24250	+	1.87206i	−0.329226	+	0.190079i	0.326271	+	0.945276i	$0.394208\pi$
$98$	−2.77667	−	9.50211i	−0.280486	−	0.959858i
$99$	−13.8087	+	2.63549i	−1.38783	+	0.264876i
$100$	−0.445323	−	2.38024i	−0.0445323	−	0.238024i
$101$	8.75485	−	5.05462i	0.871141	−	0.502953i	0.00341347	−	0.999994i	$-0.498913\pi$
$101$	8.75485	−	5.05462i	0.871141	−	0.502953i	0.867727	+	0.497041i	$0.165580\pi$
$102$	−2.11338	−	4.39104i	−0.209255	−	0.434778i
$103$	11.9302	+	6.88790i	1.17552	+	0.678685i	0.954973	−	0.296692i	$-0.0958833\pi$
$103$	11.9302	+	6.88790i	1.17552	+	0.678685i	0.220544	+	0.975377i	$0.429217\pi$
$104$	6.55187	−	3.92053i	0.642464	−	0.384439i
$105$	−3.99448	+	7.97609i	−0.389821	+	0.778387i
$106$	−9.02247	−	1.54248i	−0.876340	−	0.149819i
$107$	−13.5091			−1.30597			−0.652985	−	0.757371i	$-0.726484\pi$
$107$	−13.5091			−1.30597			−0.652985	+	0.757371i	$0.726484\pi$
$108$	10.3762	+	0.579203i	0.998446	+	0.0557338i
$109$		−	7.21435i		−	0.691009i	−0.938417	−	0.345505i	$-0.887708\pi$
$109$		−	7.21435i		−	0.691009i	0.938417	−	0.345505i	$-0.112292\pi$
$110$	2.17385	−	12.7156i	0.207269	−	1.21239i
$111$	14.7062	−	10.4522i	1.39585	−	0.992075i
$112$	−3.47855	−	9.99498i	−0.328692	−	0.944437i
$113$	−6.09107	−	3.51668i	−0.573000	−	0.330822i	0.185347	−	0.982673i	$-0.440659\pi$
$113$	−6.09107	−	3.51668i	−0.573000	−	0.330822i	−0.758347	+	0.651851i	$0.773993\pi$
$114$	−8.70435	−	18.0853i	−0.815237	−	1.69385i
$115$	−0.188376	−	0.326277i	−0.0175662	−	0.0304255i
$116$	2.83724	+	15.1650i	0.263431	+	1.40803i
$117$	−5.29226	−	6.12999i	−0.489269	−	0.566717i
$118$	−5.44951	−	4.52450i	−0.501668	−	0.416514i
$119$	4.46356	+	2.78965i	0.409174	+	0.255727i
$120$	−3.83337	+	8.73194i	−0.349938	+	0.797113i
$121$	−5.47929	+	9.49040i	−0.498117	+	0.862764i
$122$	−0.805369	−	2.17737i	−0.0729147	−	0.197130i
$123$	12.1688	−	1.15086i	1.09723	−	0.103770i
$124$	−5.42165	−	6.32621i	−0.486879	−	0.568110i
$125$		−	12.0899i		−	1.08135i
$126$	−9.80815	+	5.45896i	−0.873779	+	0.486323i
$127$	−4.75537			−0.421971			−0.210986	−	0.977489i	$-0.567667\pi$
$127$	−4.75537			−0.421971			−0.210986	+	0.977489i	$0.567667\pi$
$128$	−4.25460	−	10.4832i	−0.376057	−	0.926596i
$129$	−5.92245	−	2.71117i	−0.521442	−	0.238706i
$130$	6.96989	−	2.57804i	0.611300	−	0.226109i
$131$	11.7477	+	6.78254i	1.02640	+	0.592593i	0.915952	−	0.401289i	$-0.131438\pi$
$131$	11.7477	+	6.78254i	1.02640	+	0.592593i	0.110450	+	0.993882i	$0.464771\pi$
$132$	11.2763	−	11.6768i	0.981475	−	1.01634i
$133$	18.3840	+	11.4897i	1.59410	+	0.996284i
$134$	5.07657	+	4.21487i	0.438549	+	0.364110i
$135$	9.82317	+	2.41135i	0.845444	+	0.207536i
$136$	4.91653	+	2.73700i	0.421589	+	0.234696i
$137$	8.79499	−	5.07779i	0.751407	−	0.433825i	−0.0747953	−	0.997199i	$-0.523830\pi$
$137$	8.79499	−	5.07779i	0.751407	−	0.433825i	0.826202	+	0.563374i	$0.190497\pi$
$138$	0.0355365	−	0.472751i	0.00302507	−	0.0402433i
$139$	1.44274	−	2.49891i	0.122372	−	0.211954i	−0.798331	−	0.602219i	$-0.794283\pi$
$139$	1.44274	−	2.49891i	0.122372	−	0.211954i	0.920703	+	0.390265i	$0.127617\pi$
$140$	−1.53892	−	10.1848i	−0.130063	−	0.860773i
$141$	5.28417	−	11.5431i	0.445008	−	0.972100i
$142$	−0.422954	+	2.47400i	−0.0354935	+	0.207614i
$143$	−12.6498			−1.05783
$144$	−10.1766	+	6.35893i	−0.848053	+	0.529911i
$145$			15.0162i			1.24702i
$146$	−3.21683	+	18.8163i	−0.266227	+	1.55725i
$147$	5.80507	−	10.6443i	0.478794	−	0.877927i
$148$	−6.92102	+	19.6501i	−0.568904	+	1.61523i
$149$	−2.82095	+	4.88603i	−0.231101	+	0.400279i	−0.958133	−	0.286325i	$-0.907566\pi$
$149$	−2.82095	+	4.88603i	−0.231101	+	0.400279i	0.727031	+	0.686605i	$0.240900\pi$
$150$	1.67124	−	2.45005i	0.136456	−	0.200046i
$151$	−8.35895	−	14.4781i	−0.680241	−	1.17821i	−0.974907	−	0.222612i	$-0.928542\pi$
$151$	−8.35895	−	14.4781i	−0.680241	−	1.17821i	0.294666	−	0.955600i	$-0.404792\pi$
$152$	20.2497	+	11.2729i	1.64247	+	0.914351i
$153$	1.96227	−	5.63657i	0.158640	−	0.455689i
$154$	−3.55739	+	17.1687i	−0.286663	+	1.38349i
$155$	−4.05455	−	7.02269i	−0.325669	−	0.564076i
$156$	9.07349	+	2.26232i	0.726460	+	0.181131i
$157$	−6.72536	+	11.6487i	−0.536742	+	0.929665i	0.462334	+	0.886706i	$0.347012\pi$
$157$	−6.72536	+	11.6487i	−0.536742	+	0.929665i	−0.999077	+	0.0429595i	$0.986321\pi$
$158$	−2.45390	−	6.63428i	−0.195222	−	0.527795i
$159$	−6.49448	−	9.13773i	−0.515046	−	0.724669i
$160$	−2.19397	−	10.7908i	−0.173449	−	0.853090i
$161$	0.240366	+	0.452151i	0.0189435	+	0.0356345i
$162$	8.50164	+	9.47218i	0.667952	+	0.744205i
$163$			1.82026i			0.142574i	0.997456	+	0.0712869i	$0.0227106\pi$
$163$			1.82026i			0.142574i	−0.997456	+	0.0712869i	$0.977289\pi$
$164$	−10.7169	+	9.18451i	−0.836847	+	0.717190i
$165$	12.8780	−	9.15284i	1.00255	−	0.712548i
$166$	15.4052	−	5.69810i	1.19567	−	0.442258i
$167$	−0.492874	+	0.853684i	−0.0381398	+	0.0660600i	−0.884465	−	0.466606i	$-0.845477\pi$
$167$	−0.492874	+	0.853684i	−0.0381398	+	0.0660600i	0.846325	+	0.532666i	$0.178810\pi$
$168$	5.62218	−	11.6787i	0.433760	−	0.901028i
$169$	2.85640	+	4.94744i	0.219723	+	0.380572i
$170$	4.21374	+	3.49849i	0.323179	+	0.268322i
$171$	8.08200	−	23.2153i	0.618046	−	1.77532i
$172$	7.39288	−	1.38315i	0.563702	−	0.105464i
$173$	0.873495	−	0.504313i	0.0664106	−	0.0383422i	−0.466427	−	0.884560i	$-0.654459\pi$
$173$	0.873495	−	0.504313i	0.0664106	−	0.0383422i	0.532838	+	0.846217i	$0.321126\pi$
$174$	−10.6478	+	15.6098i	−0.807207	+	1.18337i
$175$	−0.112058	+	3.20143i	−0.00847076	+	0.242006i
$176$	−2.86947	+	18.5230i	−0.216295	+	1.39623i
$177$	−0.816773	−	8.63627i	−0.0613924	−	0.649142i
$178$	18.3404	+	3.13546i	1.37467	+	0.235013i
$179$	−8.09264			−0.604872			−0.302436	−	0.953170i	$-0.597800\pi$
$179$	−8.09264			−0.604872			−0.302436	+	0.953170i	$0.597800\pi$
$180$	−10.8742	+	4.26205i	−0.810512	+	0.317675i
$181$	3.26485			0.242675			0.121337	−	0.992611i	$-0.461282\pi$
$181$	3.26485			0.242675			0.121337	+	0.992611i	$0.461282\pi$
$182$	−9.59004	+	3.17046i	−0.710861	+	0.235010i
$183$	1.18349	−	2.58528i	0.0874861	−	0.191110i
$184$	0.281090	+	0.469749i	0.0207222	+	0.0346303i
$185$	−10.1385	+	17.5604i	−0.745396	+	1.29106i
$186$	0.764877	−	10.1754i	0.0560835	−	0.746093i
$187$	−4.66129	−	8.07359i	−0.340867	−	0.590400i
$188$	2.69580	+	14.4090i	0.196611	+	1.05088i
$189$	−13.2285	−	3.74247i	−0.962234	−	0.272225i
$190$	17.3551	+	14.4092i	1.25907	+	1.04536i
$191$	4.78085	−	2.76023i	0.345930	−	0.199723i	−0.316961	−	0.948439i	$-0.602662\pi$
$191$	4.78085	−	2.76023i	0.345930	−	0.199723i	0.662891	+	0.748716i	$0.269329\pi$
$192$	5.37095	−	12.7731i	0.387615	−	0.921821i
$193$	−0.950689	+	1.64664i	−0.0684321	+	0.118528i	−0.898211	−	0.439564i	$-0.855133\pi$
$193$	−0.950689	+	1.64664i	−0.0684321	+	0.118528i	0.829779	+	0.558092i	$0.188466\pi$
$194$	4.96615	−	1.83689i	0.356549	−	0.131881i
$195$	8.27565	+	3.78842i	0.592632	+	0.271295i
$196$	1.60614	+	13.9076i	0.114724	+	0.993397i
$197$	−16.5454			−1.17881			−0.589407	−	0.807836i	$-0.700639\pi$
$197$	−16.5454			−1.17881			−0.589407	+	0.807836i	$0.700639\pi$
$198$	19.8773	−	0.382999i	1.41262	−	0.0272185i
$199$			1.93136i			0.136911i	0.997654	+	0.0684554i	$0.0218071\pi$
$199$			1.93136i			0.136911i	−0.997654	+	0.0684554i	$0.978193\pi$
$200$	0.0535263	+	3.42415i	0.00378488	+	0.242124i
$201$	0.760878	+	8.04526i	0.0536682	+	0.567469i
$202$	−13.4088	+	4.95966i	−0.943438	+	0.348961i
$203$	0.713943	−	20.3970i	0.0501089	−	1.43159i
$204$	1.89957	+	6.62471i	0.132996	+	0.463823i
$205$	−11.8967	+	6.86859i	−0.830904	+	0.479723i
$206$	−14.9891	−	12.4448i	−1.04434	−	0.867072i
$207$	0.439501	−	0.379438i	0.0305474	−	0.0263728i
$208$	−10.0676	+	3.90376i	−0.698060	+	0.270677i
$209$	−19.1984	−	33.2527i	−1.32798	−	2.30013i
$210$	7.46909	−	10.1666i	0.515416	−	0.701564i
$211$	−14.1815	−	8.18769i	−0.976294	−	0.563664i	−0.0751449	−	0.997173i	$-0.523942\pi$
$211$	−14.1815	−	8.18769i	−0.976294	−	0.563664i	−0.901149	+	0.433509i	$0.857275\pi$
$212$	12.2096	+	4.30040i	0.838561	+	0.295352i
$213$	−2.50560	+	1.78082i	−0.171681	+	0.122019i
$214$	18.8315	+	3.21942i	1.28729	+	0.220075i
$215$	7.32032			0.499242
$216$	−14.3262	−	3.28020i	−0.974775	−	0.223190i
$217$	5.17356	+	9.73196i	0.351204	+	0.660648i
$218$	−1.71929	+	10.0567i	−0.116445	+	0.681127i
$219$	−19.0567	+	13.5442i	−1.28773	+	0.915234i
$220$	−6.06066	+	17.2073i	−0.408610	+	1.16012i
$221$	2.68525	−	4.65098i	0.180629	−	0.312859i
$222$	−22.9912	+	11.0655i	−1.54307	+	0.742667i
$223$	−13.1940	+	7.61755i	−0.883535	+	0.510109i	−0.871822	−	0.489822i	$-0.837062\pi$
$223$	−13.1940	+	7.61755i	−0.883535	+	0.510109i	−0.0117127	+	0.999931i	$0.503728\pi$
$224$	2.46710	+	14.7619i	0.164840	+	0.986320i
$225$	3.56791	−	0.680958i	0.237860	−	0.0453972i
$226$	7.65281	+	6.35382i	0.509057	+	0.422650i
$227$	−8.72916	+	5.03978i	−0.579375	+	0.334502i	−0.760885	−	0.648887i	$-0.775235\pi$
$227$	−8.72916	+	5.03978i	−0.579375	+	0.334502i	0.181510	+	0.983389i	$0.441902\pi$
$228$	7.82375	+	27.2852i	0.518140	+	1.80700i
$229$	13.0477	−	22.5993i	0.862219	−	1.49341i	−0.00756367	−	0.999971i	$-0.502408\pi$
$229$	13.0477	−	22.5993i	0.862219	−	1.49341i	0.869782	−	0.493435i	$-0.164259\pi$
$230$	0.184837	+	0.499720i	0.0121878	+	0.0329506i
$231$	−17.9279	+	11.8204i	−1.17957	+	0.777723i
$232$	−0.341027	−	21.8160i	−0.0223895	−	1.43229i
$233$		−	11.2017i		−	0.733850i	−0.930251	−	0.366925i	$-0.880411\pi$
$233$		−	11.2017i		−	0.733850i	0.930251	−	0.366925i	$-0.119589\pi$
$234$	5.91647	+	9.80636i	0.386772	+	0.641062i
$235$			14.2676i			0.930713i
$236$	6.51829	+	7.60581i	0.424305	+	0.495096i
$237$	3.60600	−	7.87716i	0.234235	−	0.511677i
$238$	−5.55734	−	4.95248i	−0.360229	−	0.321021i
$239$	26.3169	+	15.1941i	1.70230	+	0.982824i	0.943423	+	0.331591i	$0.107585\pi$
$239$	26.3169	+	15.1941i	1.70230	+	0.982824i	0.758878	+	0.651233i	$0.225748\pi$
$240$	7.42464	−	11.2587i	0.479259	−	0.726744i
$241$	23.3477	−	13.4798i	1.50395	−	0.868309i	0.503965	−	0.863724i	$-0.331874\pi$
$241$	23.3477	−	13.4798i	1.50395	−	0.868309i	0.999989	−	0.00458447i	$-0.00145929\pi$
$242$	9.89978	−	11.9237i	0.636382	−	0.766485i
$243$	−0.812222	+	15.5673i	−0.0521041	+	0.998642i
$244$	0.603775	+	3.22716i	0.0386527	+	0.206598i
$245$	−0.952728	+	13.5928i	−0.0608675	+	0.868413i
$246$	−17.2375	−	1.29573i	−1.09902	−	0.0826130i
$247$	11.0597	−	19.1560i	0.703712	−	1.21887i
$248$	6.05009	+	10.1107i	0.384181	+	0.642032i
$249$	18.2912	+	8.37335i	1.15916	+	0.530639i
$250$	−2.88120	+	16.8531i	−0.182223	+	1.06588i
$251$			11.2959i			0.712992i	0.934297	+	0.356496i	$0.116029\pi$
$251$			11.2959i			0.712992i	−0.934297	+	0.356496i	$0.883971\pi$
$252$	14.9734	−	5.27229i	0.943236	−	0.332123i
$253$		−	0.906948i		−	0.0570194i
$254$	6.62894	+	1.13328i	0.415937	+	0.0711084i
$255$	0.631556	+	6.67785i	0.0395495	+	0.418183i
$256$	3.43255	+	15.6275i	0.214534	+	0.976716i
$257$	4.12362	−	7.14231i	0.257224	−	0.445525i	−0.708273	−	0.705938i	$-0.750525\pi$
$257$	4.12362	−	7.14231i	0.257224	−	0.445525i	0.965497	+	0.260413i	$0.0838588\pi$
$258$	7.60971	+	5.19076i	0.473760	+	0.323163i
$259$	14.6064	−	23.3709i	0.907597	−	1.45220i
$260$	−10.3303	+	1.93272i	−0.640661	+	0.119862i
$261$	−22.7319	+	4.33852i	−1.40707	+	0.268548i
$262$	−14.7598	−	12.2544i	−0.911862	−	0.757082i
$263$	−2.96849	+	1.71386i	−0.183045	+	0.105681i	−0.588723	−	0.808335i	$-0.700369\pi$
$263$	−2.96849	+	1.71386i	−0.183045	+	0.105681i	0.405677	+	0.914016i	$0.367036\pi$
$264$	−18.5018	+	13.5900i	−1.13871	+	0.836409i
$265$	10.9112	+	6.29958i	0.670269	+	0.386980i
$266$	−22.8890	−	20.3977i	−1.40341	−	1.25067i
$267$	13.2016	+	18.5746i	0.807925	+	1.13675i
$268$	−6.07222	−	7.08532i	−0.370920	−	0.432805i
$269$			0.554740i			0.0338231i	0.999857	+	0.0169115i	$0.00538337\pi$
$269$			0.554740i			0.0338231i	−0.999857	+	0.0169115i	$0.994617\pi$
$270$	−13.1187	−	5.70241i	−0.798380	−	0.347038i
$271$			19.3489i			1.17536i	0.809092	+	0.587682i	$0.199959\pi$
$271$			19.3489i			1.17536i	−0.809092	+	0.587682i	$0.800041\pi$
$272$	−6.20132	−	4.98704i	−0.376010	−	0.302384i
$273$	−11.0610	−	5.53942i	−0.669442	−	0.335261i
$274$	−13.4702	+	4.98240i	−0.813767	+	0.300998i
$275$	2.83683	−	4.91353i	0.171067	−	0.296297i
$276$	−0.162202	+	0.650541i	−0.00976339	+	0.0391580i
$277$	−11.4482	+	6.60962i	−0.687855	+	0.397134i	−0.802808	−	0.596237i	$-0.796662\pi$
$277$	−11.4482	+	6.60962i	−0.687855	+	0.397134i	0.114953	+	0.993371i	$0.463328\pi$
$278$	−2.60670	+	3.13962i	−0.156339	+	0.188302i
$279$	9.45969	−	8.16692i	0.566337	−	0.488941i
$280$	−0.281960	+	14.5643i	−0.0168504	+	0.870381i
$281$	10.5582	−	6.09580i	0.629852	−	0.363645i	−0.150843	−	0.988558i	$-0.548199\pi$
$281$	10.5582	−	6.09580i	0.629852	−	0.363645i	0.780695	+	0.624913i	$0.214865\pi$
$282$	−10.1170	+	14.8316i	−0.602457	+	0.883208i
$283$	6.37639	−	11.0442i	0.379037	−	0.656512i	−0.611885	−	0.790946i	$-0.709589\pi$
$283$	6.37639	−	11.0442i	0.379037	−	0.656512i	0.990922	+	0.134435i	$0.0429219\pi$
$284$	1.17919	−	3.34793i	0.0699719	−	0.198663i
$285$	2.60118	+	27.5040i	0.154081	+	1.62920i
$286$	17.6336	+	3.01464i	1.04270	+	0.178259i
$287$	16.4864	−	8.76423i	0.973159	−	0.517336i
$288$	15.7016	−	6.43902i	0.925223	−	0.379423i
$289$	−13.0421			−0.767180
$290$	3.57859	−	20.9324i	0.210142	−	1.22919i
$291$	5.89653	+	2.69931i	0.345660	+	0.158236i
$292$	8.96846	−	25.4631i	0.524839	−	1.49012i
$293$	1.35392	+	0.781686i	0.0790968	+	0.0456666i	0.539027	−	0.842289i	$-0.318792\pi$
$293$	1.35392	+	0.781686i	0.0790968	+	0.0456666i	−0.459930	+	0.887955i	$0.652125\pi$
$294$	−10.6289	+	13.4546i	−0.619891	+	0.784688i
$295$	4.87467	+	8.44317i	0.283814	+	0.491580i
$296$	14.3307	−	25.7426i	0.832958	−	1.49626i
$297$	17.5766	+	16.8507i	1.01990	+	0.977774i
$298$	5.09680	−	6.13880i	0.295249	−	0.355611i
$299$	0.452471	−	0.261235i	0.0261671	−	0.0151076i
$300$	−2.91357	+	3.01706i	−0.168215	+	0.174190i
$301$	−9.94346	−	0.348044i	−0.573132	−	0.0200609i
$302$	8.20192	+	22.1744i	0.471967	+	1.27599i
$303$	−15.9208	−	7.28822i	−0.914626	−	0.418697i
$304$	−25.5413	−	20.5401i	−1.46490	−	1.17805i
$305$			3.19549i			0.182973i
$306$	−4.07867	+	7.38967i	−0.233162	+	0.422439i
$307$	−26.8470			−1.53224			−0.766121	−	0.642697i	$-0.777816\pi$
$307$	−26.8470			−1.53224			−0.766121	+	0.642697i	$0.777816\pi$
$308$	9.05054	−	23.0852i	0.515703	−	1.31540i
$309$	−2.24657	−	23.7544i	−0.127803	−	1.35134i
$310$	3.97838	+	10.7558i	0.225957	+	0.610889i
$311$	−5.57185	+	9.65072i	−0.315951	+	0.547242i	−0.979639	−	0.200767i	$-0.935657\pi$
$311$	−5.57185	+	9.65072i	−0.315951	+	0.547242i	0.663689	+	0.748009i	$0.268990\pi$
$312$	−12.1092	−	5.31601i	−0.685548	−	0.300960i
$313$	14.9760	−	8.64637i	0.846491	−	0.488722i	−0.0129743	−	0.999916i	$-0.504130\pi$
$313$	14.9760	−	8.64637i	0.846491	−	0.488722i	0.859465	+	0.511194i	$0.170797\pi$
$314$	12.1511	−	14.6354i	0.685729	−	0.825921i
$315$	15.2687	−	2.36390i	0.860294	−	0.133191i
$316$	1.83966	+	9.83292i	0.103489	+	0.553145i
$317$	9.27338	+	16.0620i	0.520845	+	0.902129i	0.999706	+	0.0242389i	$0.00771625\pi$
$317$	9.27338	+	16.0620i	0.520845	+	0.902129i	−0.478862	+	0.877890i	$0.658950\pi$
$318$	6.87557	+	14.2856i	0.385563	+	0.801098i
$319$	−18.0740	+	31.3052i	−1.01195	+	1.75275i
$320$	0.486747	+	15.5651i	0.0272100	+	0.870118i
$321$	13.5551	+	19.0720i	0.756573	+	1.06450i
$322$	−0.227312	−	0.687576i	−0.0126676	−	0.0383171i
$323$	16.3015			0.907040
$324$	−9.59382	−	15.2302i	−0.532990	−	0.846122i
$325$	3.26845			0.181301
$326$	0.433797	−	2.53742i	0.0240258	−	0.140535i
$327$	−10.1852	+	7.23895i	−0.563242	+	0.400315i
$328$	17.1280	−	10.2491i	0.945736	−	0.565912i
$329$	0.678351	−	19.3802i	0.0373987	−	1.06846i
$330$	−20.1331	+	9.68992i	−1.10829	+	0.533413i
$331$	1.35306	−	0.781188i	0.0743708	−	0.0429380i	−0.462353	−	0.886696i	$-0.652995\pi$
$331$	1.35306	−	0.781188i	0.0743708	−	0.0429380i	0.536724	+	0.843758i	$0.319662\pi$
$332$	−22.8326	+	4.27179i	−1.25310	+	0.234445i
$333$	−29.5126	−	10.2743i	−1.61728	−	0.563029i
$334$	0.890508	−	1.07257i	0.0487264	−	0.0586882i
$335$	−4.54107	−	7.86537i	−0.248105	−	0.429731i
$336$	−10.6205	+	14.9401i	−0.579394	+	0.815048i
$337$	−10.0259	+	17.3653i	−0.546144	+	0.945950i	0.452390	+	0.891820i	$0.350572\pi$
$337$	−10.0259	+	17.3653i	−0.546144	+	0.945950i	−0.998534	+	0.0541294i	$0.982762\pi$
$338$	−2.80274	−	7.57740i	−0.152449	−	0.412156i
$339$	1.14700	+	12.1280i	0.0622967	+	0.658704i
$340$	−5.04016	−	5.88106i	−0.273341	−	0.318945i
$341$		−	19.5209i		−	1.05711i
$342$	−16.7988	+	30.4358i	−0.908375	+	1.64578i
$343$	1.94040	−	18.4183i	0.104772	−	0.994496i
$344$	−10.6352	+	0.166250i	−0.573413	+	0.00896357i
$345$	−0.271618	+	0.593339i	−0.0146234	+	0.0319443i
$346$	−1.33783	+	0.494839i	−0.0719221	+	0.0266027i
$347$	−8.97338	+	15.5423i	−0.481716	+	0.834357i	−0.999780	−	0.0209851i	$-0.993320\pi$
$347$	−8.97338	+	15.5423i	−0.481716	+	0.834357i	0.518064	+	0.855342i	$0.326653\pi$
$348$	18.5630	−	19.2223i	0.995079	−	1.03042i
$349$	4.49126	+	7.77909i	0.240412	+	0.416405i	0.960832	−	0.277133i	$-0.0893842\pi$
$349$	4.49126	+	7.77909i	0.240412	+	0.416405i	−0.720420	+	0.693538i	$0.756051\pi$
$350$	0.919160	−	4.43606i	0.0491311	−	0.237117i
$351$	−3.34399	+	13.6225i	−0.178489	+	0.727114i
$352$	8.41435	−	25.1371i	0.448486	−	1.33981i
$353$	10.7938	+	18.6954i	0.574496	+	0.995057i	0.996096	+	0.0882749i	$0.0281354\pi$
$353$	10.7938	+	18.6954i	0.574496	+	0.995057i	−0.421600	+	0.906782i	$0.638531\pi$
$354$	−0.919589	+	12.2335i	−0.0488756	+	0.650204i
$355$	1.72737	−	2.99190i	0.0916794	−	0.158793i
$356$	−24.8190	−	8.74160i	−1.31541	−	0.463304i
$357$	−0.540367	−	9.10080i	−0.0285993	−	0.481665i
$358$	11.2811	+	1.92860i	0.596222	+	0.101930i
$359$			5.14131i			0.271348i	0.990754	+	0.135674i	$0.0433200\pi$
$359$			5.14131i			0.271348i	−0.990754	+	0.135674i	$0.956680\pi$
$360$	16.1742	−	3.34977i	0.852453	−	0.176548i
$361$	48.1409			2.53373
$362$	−4.55117	−	0.778067i	−0.239204	−	0.0408943i
$363$	18.8965	−	1.78713i	0.991808	−	0.0937999i
$364$	14.1240	−	2.13413i	0.740298	−	0.111859i
$365$	13.1378	−	22.7553i	0.687661	−	1.19106i
$366$	−2.26589	+	3.32181i	−0.118440	+	0.173634i
$367$	9.50106	−	5.48544i	0.495952	−	0.286338i	−0.231089	−	0.972933i	$-0.574229\pi$
$367$	9.50106	−	5.48544i	0.495952	−	0.286338i	0.727040	+	0.686595i	$0.240895\pi$
$368$	−0.279887	−	0.721813i	−0.0145901	−	0.0376271i
$369$	−13.8351	−	16.0251i	−0.720227	−	0.834234i
$370$	18.3179	−	22.0628i	0.952300	−	1.14699i
$371$	−14.5216	−	9.07573i	−0.753922	−	0.471188i
$372$	−3.49118	+	14.0020i	−0.181009	+	0.725972i
$373$	25.7387	+	14.8602i	1.33270	+	0.769434i	0.985713	−	0.168435i	$-0.0538715\pi$
$373$	25.7387	+	14.8602i	1.33270	+	0.769434i	0.346987	+	0.937870i	$0.387205\pi$
$374$	4.57372	+	12.3654i	0.236502	+	0.639398i
$375$	−17.0684	+	12.1311i	−0.881409	+	0.626446i
$376$	−0.324026	−	20.7284i	−0.0167104	−	1.06899i
$377$	−20.8240			−1.07249
$378$	17.5485	+	8.36953i	0.902599	+	0.430482i
$379$			2.95230i			0.151650i	0.997121	+	0.0758248i	$0.0241590\pi$
$379$			2.95230i			0.151650i	−0.997121	+	0.0758248i	$0.975841\pi$
$380$	−20.7589	−	24.2223i	−1.06491	−	1.24258i
$381$	4.77159	+	6.71362i	0.244456	+	0.343949i
$382$	−7.32226	+	2.70837i	−0.374640	+	0.138572i
$383$	9.99957	−	17.3198i	0.510954	−	0.884999i	−0.488965	−	0.872303i	$-0.662625\pi$
$383$	9.99957	−	17.3198i	0.510954	−	0.884999i	0.999919	−	0.0126955i	$-0.00404122\pi$
$384$	−10.5311	+	16.5256i	−0.537412	+	0.843320i
$385$	12.7907	−	20.4656i	0.651872	−	1.04302i
$386$	1.71767	−	2.06884i	0.0874271	−	0.105301i
$387$	2.11502	+	11.0817i	0.107512	+	0.563315i
$388$	−7.36052	+	1.37709i	−0.373674	+	0.0699113i
$389$	1.63665	+	2.83477i	0.0829816	+	0.143728i	0.904529	−	0.426411i	$-0.140222\pi$
$389$	1.63665	+	2.83477i	0.0829816	+	0.143728i	−0.821548	+	0.570140i	$0.806889\pi$
$390$	−10.6333	−	7.25324i	−0.538439	−	0.367282i
$391$	0.333461	+	0.192524i	0.0168639	+	0.00973635i
$392$	1.07545	−	19.7698i	0.0543187	−	0.998524i
$393$	−2.21220	−	23.3910i	−0.111591	−	1.17992i
$394$	23.0642	+	3.94304i	1.16196	+	0.198648i
$395$			9.73641i			0.489892i
$396$	−27.8000	−	4.20318i	−1.39700	−	0.211218i
$397$	18.7992			0.943505			0.471753	−	0.881731i	$-0.343622\pi$
$397$	18.7992			0.943505			0.471753	+	0.881731i	$0.343622\pi$
$398$	0.460275	−	2.69230i	0.0230715	−	0.134953i
$399$	−2.22561	−	37.4834i	−0.111420	−	1.87652i
$400$	0.741415	−	4.78599i	0.0370708	−	0.239299i
$401$	−1.59338	−	0.919937i	−0.0795695	−	0.0459395i	0.459687	−	0.888081i	$-0.347961\pi$
$401$	−1.59338	−	0.919937i	−0.0795695	−	0.0459395i	−0.539257	+	0.842141i	$0.681295\pi$
$402$	0.856658	−	11.3963i	0.0427262	−	0.568398i
$403$	9.73886	−	5.62273i	0.485127	−	0.280088i
$404$	19.8736	−	3.71819i	0.988751	−	0.184987i
$405$	−6.45233	−	16.2879i	−0.320619	−	0.809351i
$406$	−5.85616	+	28.2631i	−0.290636	+	1.40267i
$407$	−42.2727	+	24.4062i	−2.09538	+	1.20977i
$408$	−1.06920	−	9.68747i	−0.0529335	−	0.479601i
$409$	−13.7628	−	7.94598i	−0.680529	−	0.392904i	0.119525	−	0.992831i	$-0.461863\pi$
$409$	−13.7628	−	7.94598i	−0.680529	−	0.392904i	−0.800054	+	0.599928i	$0.795196\pi$
$410$	18.2208	−	6.73955i	0.899862	−	0.332843i
$411$	−15.9938	−	7.32163i	−0.788915	−	0.361149i
$412$	17.9288	+	20.9201i	0.883289	+	1.03066i
$413$	−6.22001	−	11.7004i	−0.306067	−	0.575741i
$414$	−0.703086	+	0.424193i	−0.0345548	+	0.0208479i
$415$	−22.6085			−1.10981
$416$	14.9644	−	3.04253i	0.733690	−	0.149172i
$417$	−4.97561	+	0.470567i	−0.243657	+	0.0230437i
$418$	18.8378	+	50.9291i	0.921385	+	2.49103i
$419$	−0.501299	−	0.289425i	−0.0244901	−	0.0141394i	0.487705	−	0.873009i	$-0.337834\pi$
$419$	−0.501299	−	0.289425i	−0.0244901	−	0.0141394i	−0.512195	+	0.858869i	$0.671168\pi$
$420$	−12.8347	+	12.3922i	−0.626269	+	0.604676i
$421$	−2.27938	+	1.31600i	−0.111090	+	0.0641378i	−0.554515	−	0.832173i	$-0.687096\pi$
$421$	−2.27938	+	1.31600i	−0.111090	+	0.0641378i	0.443426	+	0.896311i	$0.353763\pi$
$422$	17.8176	+	14.7932i	0.867347	+	0.720123i
$423$	−21.5986	+	4.12224i	−1.05016	+	0.200430i
$424$	−15.9952	−	8.90445i	−0.776797	−	0.432439i
$425$	1.20439	+	2.08606i	0.0584213	+	0.101189i
$426$	3.91718	−	1.88531i	0.189788	−	0.0913436i
$427$	0.151929	−	4.34055i	0.00735238	−	0.210054i
$428$	−25.4836	−	8.97568i	−1.23180	−	0.433856i
$429$	12.6929	+	17.8589i	0.612819	+	0.862235i
$430$	−10.2044	−	1.74455i	−0.492102	−	0.0841296i
$431$			16.0670i			0.773920i	0.922096	+	0.386960i	$0.126475\pi$
$431$			16.0670i			0.773920i	−0.922096	+	0.386960i	$0.873525\pi$
$432$	19.1889	+	7.98673i	0.923224	+	0.384262i
$433$		−	0.381922i		−	0.0183540i	−0.999958	−	0.00917700i	$-0.997079\pi$
$433$		−	0.381922i		−	0.0183540i	0.999958	−	0.00917700i	$-0.00292117\pi$
$434$	−4.89260	−	14.7992i	−0.234852	−	0.710383i
$435$	21.1997	−	15.0674i	1.01645	−	0.722424i
$436$	4.79335	−	13.6092i	0.229560	−	0.651764i
$437$	1.37342	+	0.792947i	0.0656998	+	0.0379318i
$438$	29.7926	−	14.3390i	1.42355	−	0.685143i
$439$	0.787279	−	0.454536i	0.0375748	−	0.0216938i	−0.481095	−	0.876668i	$-0.659761\pi$
$439$	0.787279	−	0.454536i	0.0375748	−	0.0216938i	0.518670	+	0.854975i	$0.326427\pi$
$440$	12.5493	−	22.5425i	0.598263	−	1.07467i
$441$	−20.8524	+	2.48502i	−0.992974	+	0.118334i
$442$	−4.85161	+	5.84348i	−0.230767	+	0.277946i
$443$	11.3107	+	19.5908i	0.537389	+	0.930785i	0.999044	+	0.0437254i	$0.0139227\pi$
$443$	11.3107	+	19.5908i	0.537389	+	0.930785i	−0.461655	+	0.887060i	$0.652744\pi$
$444$	34.6865	−	9.94600i	1.64615	−	0.472016i
$445$	−22.1796	−	12.8054i	−1.05142	−	0.607035i
$446$	20.2077	−	7.47445i	0.956861	−	0.353925i
$447$	9.72865	−	0.920084i	0.460150	−	0.0435185i
$448$	0.0788780	−	21.1659i	0.00372663	−	0.999993i
$449$		−	33.1002i		−	1.56210i	−0.624470	−	0.781049i	$-0.714685\pi$
$449$		−	33.1002i		−	1.56210i	0.624470	−	0.781049i	$-0.285315\pi$
$450$	−5.13591	+	0.0989593i	−0.242109	+	0.00466498i
$451$	−33.0692			−1.55717
$452$	−9.15372	−	10.6809i	−0.430555	−	0.502389i
$453$	−12.0527	+	26.3286i	−0.566285	+	1.23703i
$454$	13.3694	−	4.94511i	0.627458	−	0.232085i
$455$	13.8944	+	0.486335i	0.651378	+	0.0227997i
$456$	−4.40373	−	39.8997i	−0.206223	−	1.86848i
$457$	−0.667913	−	1.15686i	−0.0312436	−	0.0541156i	0.849981	−	0.526814i	$-0.176613\pi$
$457$	−0.667913	−	1.15686i	−0.0312436	−	0.0541156i	−0.881224	+	0.472698i	$0.843280\pi$
$458$	−23.5742	+	28.3938i	−1.10155	+	1.32675i
$459$	−9.92665	+	2.88546i	−0.463336	+	0.134682i
$460$	−0.138570	−	0.740654i	−0.00646086	−	0.0345332i
$461$	23.8734	−	13.7833i	1.11190	−	0.641953i	0.172576	−	0.984996i	$-0.444791\pi$
$461$	23.8734	−	13.7833i	1.11190	−	0.641953i	0.939320	+	0.343043i	$0.111458\pi$
$462$	27.8083	−	12.2050i	1.29376	−	0.567826i
$463$	19.0453	−	32.9874i	0.885109	−	1.53305i	0.0395197	−	0.999219i	$-0.487417\pi$
$463$	19.0453	−	32.9874i	0.885109	−	1.53305i	0.845589	−	0.533834i	$-0.179249\pi$
$464$	−4.72371	+	30.4925i	−0.219293	+	1.41558i
$465$	−5.84623	+	12.7708i	−0.271112	+	0.592233i
$466$	−2.66955	+	15.6151i	−0.123664	+	0.723355i
$467$		−	5.54016i		−	0.256368i	−0.991750	−	0.128184i	$-0.959085\pi$
$467$		−	5.54016i		−	0.256368i	0.991750	−	0.128184i	$-0.0409148\pi$
$468$	−5.91049	−	15.0800i	−0.273212	−	0.697071i
$469$	5.79435	+	10.8997i	0.267558	+	0.503303i
$470$	3.40019	−	19.8888i	0.156839	−	0.917403i
$471$	23.1938	−	2.19355i	1.06872	−	0.101073i
$472$	−7.27384	−	12.1558i	−0.334806	−	0.559517i
$473$	15.2611	+	8.81103i	0.701708	+	0.405132i
$474$	−6.90398	+	10.1213i	−0.317110	+	0.464887i
$475$	4.96050	+	8.59183i	0.227603	+	0.394220i
$476$	6.56662	+	8.22810i	0.300980	+	0.377134i
$477$	−6.38398	+	18.3378i	−0.292302	+	0.839629i
$478$	−33.0645	−	27.4521i	−1.51234	−	1.25563i
$479$	15.4215	+	26.7109i	0.704627	+	1.22045i	0.966826	+	0.255436i	$0.0822191\pi$
$479$	15.4215	+	26.7109i	0.704627	+	1.22045i	−0.262199	+	0.965014i	$0.584448\pi$
$480$	−13.0330	+	13.9251i	−0.594872	+	0.635589i
$481$	−24.3522	−	14.0598i	−1.11037	−	0.641070i
$482$	−35.7588	+	13.2265i	−1.62877	+	0.602452i
$483$	0.397160	−	0.793040i	0.0180714	−	0.0360846i
$484$	−16.6418	+	14.2623i	−0.756445	+	0.648284i
$485$	−7.28828			−0.330944
$486$	4.84216	−	21.5071i	0.219645	−	0.975580i
$487$	−27.3946			−1.24137			−0.620683	−	0.784062i	$-0.713145\pi$
$487$	−27.3946			−1.24137			−0.620683	+	0.784062i	$0.713145\pi$
$488$	−0.0725717	−	4.64252i	−0.00328517	−	0.210157i
$489$	2.56984	−	1.82647i	0.116212	−	0.0825957i
$490$	4.56748	−	18.7212i	0.206338	−	0.845737i
$491$	1.96713	−	3.40717i	0.0887752	−	0.153763i	−0.818218	−	0.574907i	$-0.805038\pi$
$491$	1.96713	−	3.40717i	0.0887752	−	0.153763i	0.906994	+	0.421144i	$0.138371\pi$
$492$	23.7201	+	5.91421i	1.06938	+	0.266633i
$493$	−7.67339	−	13.2907i	−0.345592	−	0.598583i
$494$	−19.9823	+	24.0675i	−0.899046	+	1.08285i
$495$	−25.8439	−	8.99711i	−1.16160	−	0.404390i
$496$	−6.02421	−	15.5361i	−0.270495	−	0.697591i
$497$	−2.48860	+	3.98188i	−0.111629	+	0.178612i
$498$	−23.5023	−	16.0314i	−1.05316	−	0.718386i
$499$	−7.13543	−	4.11964i	−0.319426	−	0.184421i	0.331711	−	0.943381i	$-0.392374\pi$
$499$	−7.13543	−	4.11964i	−0.319426	−	0.184421i	−0.651137	+	0.758961i	$0.725708\pi$
$500$	8.03273	−	22.8064i	0.359235	−	1.01993i
$501$	1.69978	−	0.160756i	0.0759407	−	0.00718206i
$502$	2.69200	−	15.7464i	0.120150	−	0.702796i
$503$	−1.51243			−0.0674359			−0.0337179	−	0.999431i	$-0.510735\pi$
$503$	−1.51243			−0.0674359			−0.0337179	+	0.999431i	$0.510735\pi$
$504$	−22.1292	+	3.78112i	−0.985715	+	0.168424i
$505$	19.6786			0.875685
$506$	−0.216140	+	1.26428i	−0.00960860	+	0.0562039i
$507$	4.11863	−	8.99697i	0.182915	−	0.399569i
$508$	−8.97059	−	3.15956i	−0.398005	−	0.140183i
$509$	−16.3076	−	9.41518i	−0.722821	−	0.417321i	0.0929694	−	0.995669i	$-0.470364\pi$
$509$	−16.3076	−	9.41518i	−0.722821	−	0.417321i	−0.815790	+	0.578348i	$0.803697\pi$
$510$	0.711056	−	9.45936i	0.0314861	−	0.418868i
$511$	−18.9274	+	30.2847i	−0.837299	+	1.33972i
$512$	−1.06066	−	22.6025i	−0.0468749	−	0.998901i
$513$	−40.8848	+	11.8843i	−1.80511	+	0.524705i
$514$	−7.45040	+	8.97358i	−0.328623	+	0.395808i
$515$	13.4080	+	23.2233i	0.590825	+	1.02334i
$516$	−9.37081	−	9.04938i	−0.412527	−	0.398377i
$517$	−17.1730	+	29.7445i	−0.755268	+	1.30816i
$518$	−25.9308	+	29.0978i	−1.13933	+	1.27848i
$519$	−1.58846	−	0.727165i	−0.0697257	−	0.0319190i
$520$	14.8610	−	0.232307i	0.651697	−	0.0101873i
$521$	14.7752			0.647313			0.323657	−	0.946175i	$-0.395088\pi$
$521$	14.7752			0.647313			0.323657	+	0.946175i	$0.395088\pi$
$522$	32.7219	−	0.630490i	1.43220	−	0.0275958i
$523$	11.2414			0.491551			0.245776	−	0.969327i	$-0.420957\pi$
$523$	11.2414			0.491551			0.245776	+	0.969327i	$0.420957\pi$
$524$	17.6545	+	20.6001i	0.771242	+	0.899917i
$525$	4.63221	−	3.05415i	0.202166	−	0.133294i
$526$	4.54649	−	1.68166i	0.198236	−	0.0733240i
$527$	7.17732	+	4.14383i	0.312649	+	0.180508i
$528$	29.0300	−	14.5351i	1.26337	−	0.632559i
$529$	−11.4813	−	19.8861i	−0.499186	−	0.864615i
$530$	−13.7088	−	11.3819i	−0.595472	−	0.494396i
$531$	−11.3731	+	9.81884i	−0.493551	+	0.426101i
$532$	27.0459	+	33.8890i	1.17259	+	1.46928i
$533$	−9.52515	−	16.4980i	−0.412580	−	0.714610i
$534$	−13.9763	−	29.0390i	−0.604812	−	1.25664i
$535$	−22.7736	−	13.1483i	−0.984588	−	0.568452i
$536$	6.77606	+	11.3240i	0.292681	+	0.489121i
$537$	8.12024	+	11.4252i	0.350414	+	0.493032i
$538$	0.132203	−	0.773301i	0.00569969	−	0.0333394i
$539$	−18.3471	+	27.1911i	−0.790264	+	1.17120i
$540$	16.9284	+	11.0755i	0.728482	+	0.476614i
$541$		−	4.55500i		−	0.195835i	−0.995195	−	0.0979173i	$-0.968782\pi$
$541$		−	4.55500i		−	0.195835i	0.995195	−	0.0979173i	$-0.0312181\pi$
$542$	4.61116	−	26.9722i	0.198066	−	1.15855i
$543$	−3.27599	−	4.60931i	−0.140586	−	0.197804i
$544$	7.45608	+	8.42975i	0.319677	+	0.361423i
$545$	7.02171	−	12.1620i	0.300777	−	0.520961i
$546$	14.0988	+	10.3579i	0.603372	+	0.443277i
$547$	27.1016	−	15.6471i	1.15878	−	0.669023i	0.207770	−	0.978178i	$-0.433380\pi$
$547$	27.1016	−	15.6471i	1.15878	−	0.669023i	0.951012	+	0.309155i	$0.100046\pi$
$548$	19.9647	−	3.73524i	0.852852	−	0.159561i
$549$	−4.83742	+	0.923252i	−0.206456	+	0.0394034i
$550$	−5.12548	+	6.17335i	−0.218551	+	0.263233i
$551$	−31.6043	−	54.7403i	−1.34639	−	2.33202i
$552$	0.381142	−	0.868192i	0.0162225	−	0.0369527i
$553$	0.462917	−	13.2253i	0.0196852	−	0.562398i
$554$	17.5338	−	6.48545i	0.744941	−	0.275540i
$555$	34.9647	−	3.30678i	1.48417	−	0.140365i
$556$	4.38193	−	3.75538i	0.185835	−	0.159263i
$557$	−0.935343			−0.0396318			−0.0198159	−	0.999804i	$-0.506308\pi$
$557$	−0.935343			−0.0396318			−0.0198159	+	0.999804i	$0.506308\pi$
$558$	−15.1330	+	9.13020i	−0.640631	+	0.386512i
$559$			10.1516i			0.429367i
$560$	3.86394	−	20.2352i	0.163281	−	0.855094i
$561$	−6.72108	+	14.6819i	−0.283764	+	0.619871i
$562$	−16.1708	+	5.98129i	−0.682124	+	0.252305i
$563$	33.8328	+	19.5334i	1.42588	+	0.823235i	0.996793	−	0.0800263i	$-0.0255004\pi$
$563$	33.8328	+	19.5334i	1.42588	+	0.823235i	0.429092	+	0.903261i	$0.358834\pi$
$564$	17.6376	−	18.2640i	0.742675	−	0.769055i
$565$	−6.84556	−	11.8569i	−0.287995	−	0.498822i
$566$	−11.5206	+	13.8759i	−0.484248	+	0.583249i
$567$	7.99003	+	22.4312i	0.335550	+	0.942022i
$568$	−2.44164	+	4.38596i	−0.102449	+	0.184031i
$569$	−12.7197	+	7.34372i	−0.533238	+	0.307865i	−0.742334	−	0.670030i	$-0.766281\pi$
$569$	−12.7197	+	7.34372i	−0.533238	+	0.307865i	0.209096	+	0.977895i	$0.432948\pi$
$570$	2.92862	−	38.9602i	0.122667	−	1.63186i
$571$	37.0416	+	21.3860i	1.55014	+	0.894975i	0.998129	+	0.0611403i	$0.0194737\pi$
$571$	37.0416	+	21.3860i	1.55014	+	0.894975i	0.552014	+	0.833835i	$0.313860\pi$
$572$	−23.8626	−	8.40474i	−0.997747	−	0.351420i
$573$	−8.69403	−	3.97995i	−0.363198	−	0.166265i
$574$	−25.0704	+	8.28828i	−1.04642	+	0.345946i
$575$			0.234338i			0.00977255i
$576$	−23.4223	+	5.23399i	−0.975930	+	0.218083i
$577$		−	24.6712i		−	1.02707i	−0.858067	−	0.513537i	$-0.828335\pi$
$577$		−	24.6712i		−	1.02707i	0.858067	−	0.513537i	$-0.171665\pi$
$578$	18.1805	+	3.10813i	0.756209	+	0.129281i
$579$	3.27865	−	0.310078i	0.136256	−	0.0128864i
$580$	−9.97702	+	28.3266i	−0.414273	+	1.17620i
$581$	30.7100	+	1.07492i	1.27406	+	0.0445952i
$582$	−7.57640	−	5.16804i	−0.314052	−	0.214222i
$583$	15.1649	+	26.2663i	0.628064	+	1.08784i
$584$	−18.5702	+	33.3580i	−0.768441	+	1.38036i
$585$	−2.95539	−	15.4849i	−0.122190	−	0.640221i
$586$	−1.70106	−	1.41232i	−0.0702702	−	0.0583425i
$587$	−21.6542	+	12.5020i	−0.893763	+	0.516014i	−0.875171	−	0.483813i	$-0.839251\pi$
$587$	−21.6542	+	12.5020i	−0.893763	+	0.516014i	−0.0185914	+	0.999827i	$0.505918\pi$
$588$	18.0230	−	16.2225i	0.743257	−	0.669006i
$589$	29.5612	+	17.0672i	1.21805	+	0.703240i
$590$	−4.78309	−	12.9314i	−0.196917	−	0.532377i
$591$	16.6019	+	23.3588i	0.682909	+	0.960852i
$592$	−26.1118	+	32.4696i	−1.07319	+	1.33449i
$593$	29.9312			1.22913			0.614564	−	0.788867i	$-0.289332\pi$
$593$	29.9312			1.22913			0.614564	+	0.788867i	$0.289332\pi$
$594$	−20.4858	−	27.6784i	−0.840543	−	1.13566i
$595$	4.80952	+	9.04716i	0.197171	+	0.370898i
$596$	−8.56785	+	7.34277i	−0.350953	+	0.300772i
$597$	2.72669	−	1.93795i	0.111596	−	0.0793150i
$598$	−0.692997	+	0.256327i	−0.0283387	+	0.0104820i
$599$	−3.42279	−	1.97615i	−0.139851	−	0.0807432i	0.428442	−	0.903569i	$-0.359063\pi$
$599$	−3.42279	−	1.97615i	−0.139851	−	0.0807432i	−0.568293	+	0.822826i	$0.692396\pi$
$600$	4.78050	−	3.51140i	0.195163	−	0.143352i
$601$	−17.3493	+	10.0166i	−0.707693	+	0.408587i	−0.810206	−	0.586145i	$-0.800645\pi$
$601$	−17.3493	+	10.0166i	−0.707693	+	0.408587i	0.102513	+	0.994732i	$0.467312\pi$
$602$	13.7781	+	2.85486i	0.561555	+	0.116355i
$603$	10.5948	−	9.14690i	0.431453	−	0.372491i
$604$	−6.14887	−	32.8655i	−0.250194	−	1.33728i
$605$	−18.4740	+	10.6659i	−0.751074	+	0.433632i
$606$	20.4565	+	13.9539i	0.830989	+	0.566837i
$607$	−2.94782	−	1.70192i	−0.119648	−	0.0690789i	0.438982	−	0.898496i	$-0.355339\pi$
$607$	−2.94782	−	1.70192i	−0.119648	−	0.0690789i	−0.558630	+	0.829417i	$0.688673\pi$
$608$	30.7093	+	34.7196i	1.24543	+	1.40806i
$609$	−29.5128	+	19.4586i	−1.19592	+	0.788503i
$610$	0.761535	−	4.45447i	0.0308337	−	0.180356i
$611$	−19.7858			−0.800449
$612$	7.44670	−	9.32911i	0.301015	−	0.377107i
$613$		−	26.1261i		−	1.05522i	−0.849485	−	0.527612i	$-0.823088\pi$
$613$		−	26.1261i		−	1.05522i	0.849485	−	0.527612i	$-0.176912\pi$
$614$	37.4245	+	6.39807i	1.51033	+	0.258205i
$615$	21.6344	+	9.90376i	0.872381	+	0.399358i
$616$	−18.1179	+	30.0237i	−0.729992	+	1.20969i
$617$	31.9558	+	18.4497i	1.28649	+	0.742757i	0.978027	−	0.208478i	$-0.0668511\pi$
$617$	31.9558	+	18.4497i	1.28649	+	0.742757i	0.308466	+	0.951235i	$0.400184\pi$
$618$	−2.52936	+	33.6488i	−0.101746	+	1.35355i
$619$	5.97378	+	10.3469i	0.240107	+	0.415877i	0.960744	−	0.277435i	$-0.0894843\pi$
$619$	5.97378	+	10.3469i	0.240107	+	0.415877i	−0.720638	+	0.693312i	$0.756151\pi$
$620$	−2.98254	−	15.9416i	−0.119782	−	0.640230i
$621$	−0.976690	−	0.239754i	−0.0391932	−	0.00962098i
$622$	10.0670	−	12.1251i	0.403651	−	0.486174i
$623$	29.5186	+	18.4486i	1.18264	+	0.739128i
$624$	15.6132	+	10.2963i	0.625028	+	0.412181i
$625$	8.74010	−	15.1383i	0.349604	−	0.605532i
$626$	−22.9369	+	8.48394i	−0.916742	+	0.339086i
$627$	−27.6821	+	60.4703i	−1.10552	+	2.41495i
$628$	−20.4264	+	17.5057i	−0.815102	+	0.698554i
$629$		−	20.7234i		−	0.826298i
$630$	−21.8478	−	0.343526i	−0.870436	−	0.0136864i
$631$	−6.71690			−0.267396			−0.133698	−	0.991022i	$-0.542685\pi$
$631$	−6.71690			−0.267396			−0.133698	+	0.991022i	$0.542685\pi$
$632$	−0.221121	−	14.1454i	−0.00879570	−	0.562674i
$633$	2.67050	+	28.2370i	0.106143	+	1.12232i
$634$	−9.09916	−	24.6002i	−0.361374	−	0.976998i
$635$	−8.01661	−	4.62839i	−0.318129	−	0.183672i
$636$	−6.17998	−	21.5526i	−0.245052	−	0.854615i
$637$	−18.8501	−	1.32121i	−0.746869	−	0.0523484i
$638$	32.6555	−	39.3317i	1.29284	−	1.55716i
$639$	5.02830	+	1.75051i	0.198916	+	0.0692493i
$640$	3.03090	−	21.8136i	0.119807	−	0.862260i
$641$	4.72968	−	2.73068i	0.186811	−	0.107855i	−0.403678	−	0.914901i	$-0.632268\pi$
$641$	4.72968	−	2.73068i	0.186811	−	0.107855i	0.590489	+	0.807046i	$0.298935\pi$
$642$	−14.3505	−	29.8166i	−0.566370	−	1.17677i
$643$	10.3266	−	17.8861i	0.407240	−	0.705360i	−0.587340	−	0.809341i	$-0.699825\pi$
$643$	10.3266	−	17.8861i	0.407240	−	0.705360i	0.994579	+	0.103981i	$0.0331580\pi$
$644$	0.153011	+	1.01265i	0.00602946	+	0.0399038i
$645$	−7.34528	−	10.3348i	−0.289220	−	0.406932i
$646$	−22.7241	−	3.88491i	−0.894069	−	0.152850i
$647$	42.4737			1.66981			0.834907	−	0.550391i	$-0.185521\pi$
$647$	42.4737			1.66981			0.834907	+	0.550391i	$0.185521\pi$
$648$	9.74408	+	23.5171i	0.382784	+	0.923838i
$649$			23.4694i			0.921253i
$650$	−4.55618	−	0.778923i	−0.178708	−	0.0305519i
$651$	8.54834	−	17.0691i	0.335036	−	0.668993i
$652$	−1.20942	+	3.43376i	−0.0473644	+	0.134476i
$653$	−14.2286	+	24.6446i	−0.556806	+	0.964417i	0.440954	+	0.897530i	$0.354640\pi$
$653$	−14.2286	+	24.6446i	−0.556806	+	0.964417i	−0.997761	+	0.0668873i	$0.978693\pi$
$654$	15.9232	−	7.66372i	0.622646	−	0.299675i
$655$	13.2028	+	22.8680i	0.515878	+	0.893527i
$656$	−26.3188	+	10.2053i	−1.02758	+	0.398449i
$657$	38.2434	+	13.3138i	1.49202	+	0.519419i
$658$	−5.56421	+	26.8541i	−0.216916	+	1.04688i
$659$	5.13331	+	8.89116i	0.199965	+	0.346350i	0.948517	−	0.316726i	$-0.102584\pi$
$659$	5.13331	+	8.89116i	0.199965	+	0.346350i	−0.748552	+	0.663077i	$0.769250\pi$
$660$	30.3746	−	8.70961i	1.18233	−	0.339021i
$661$	5.43674	−	9.41671i	0.211465	−	0.366267i	−0.740708	−	0.671827i	$-0.765510\pi$
$661$	5.43674	−	9.41671i	0.211465	−	0.366267i	0.952173	+	0.305559i	$0.0988433\pi$
$662$	−2.07232	+	0.766513i	−0.0805429	+	0.0297914i
$663$	−9.26064	+	0.875823i	−0.359654	+	0.0340141i
$664$	32.8464	−	0.513455i	1.27469	−	0.0199259i
$665$	19.8089	+	37.2625i	0.768157	+	1.44498i
$666$	38.6918	+	21.3556i	1.49928	+	0.827513i
$667$		−	1.49301i		−	0.0578097i
$668$	−1.49697	+	1.28292i	−0.0579194	+	0.0496378i
$669$	23.9934	+	10.9837i	0.927639	+	0.424654i
$670$	4.45577	+	12.0465i	0.172141	+	0.465395i
$671$	−3.84621	+	6.66184i	−0.148481	+	0.257177i
$672$	18.3653	−	18.2953i	0.708455	−	0.705756i
$673$	−15.3165	−	26.5290i	−0.590409	−	1.02262i	−0.994177	−	0.107756i	$-0.965633\pi$
$673$	−15.3165	−	26.5290i	−0.590409	−	1.02262i	0.403769	−	0.914861i	$-0.367700\pi$
$674$	18.1144	−	21.8178i	0.697741	−	0.840389i
$675$	−4.54145	−	4.35388i	−0.174800	−	0.167581i
$676$	2.10118	+	11.2308i	0.0808146	+	0.431952i
$677$	−39.7862	+	22.9706i	−1.52911	+	0.882830i	−0.529708	+	0.848180i	$0.677698\pi$
$677$	−39.7862	+	22.9706i	−1.52911	+	0.882830i	−0.999400	+	0.0346500i	$0.988968\pi$
$678$	1.29139	−	17.1797i	0.0495955	−	0.659782i
$679$	9.89995	+	0.346521i	0.379925	+	0.0132983i
$680$	5.62437	+	9.39929i	0.215685	+	0.360446i
$681$	15.8741	+	7.26683i	0.608296	+	0.278465i
$682$	−4.65214	+	27.2119i	−0.178139	+	1.04200i
$683$	−10.1985			−0.390236			−0.195118	−	0.980780i	$-0.562509\pi$
$683$	−10.1985			−0.390236			−0.195118	+	0.980780i	$0.562509\pi$
$684$	30.6707	−	38.4237i	1.17272	−	1.46917i
$685$	19.7688			0.755327
$686$	−7.09427	+	25.2125i	−0.270861	+	0.962619i
$687$	−44.9979	+	4.25566i	−1.71678	+	0.162364i
$688$	14.8650	+	2.30279i	0.566723	+	0.0877931i
$689$	−8.73607	+	15.1313i	−0.332818	+	0.576457i
$690$	0.520035	−	0.762377i	0.0197974	−	0.0290232i
$691$	18.7407	+	32.4598i	0.712929	+	1.23483i	0.963753	+	0.266796i	$0.0859651\pi$
$691$	18.7407	+	32.4598i	0.712929	+	1.23483i	−0.250824	+	0.968033i	$0.580702\pi$
$692$	1.98285	−	0.370974i	0.0753765	−	0.0141023i
$693$	34.6770	+	13.4499i	1.31727	+	0.510918i
$694$	16.2128	−	19.5274i	0.615429	−	0.741249i
$695$	4.86436	−	2.80844i	0.184516	−	0.106530i
$696$	−30.4576	+	22.3719i	−1.15449	+	0.848003i
$697$	7.01982	−	12.1587i	0.265895	−	0.460543i
$698$	−4.40689	−	11.9143i	−0.166803	−	0.450963i
$699$	−15.8146	+	11.2399i	−0.598162	+	0.425133i
$700$	−2.33848	+	5.96477i	−0.0883863	+	0.225447i
$701$	8.98189			0.339241			0.169621	−	0.985509i	$-0.445746\pi$
$701$	8.98189			0.339241			0.169621	+	0.985509i	$0.445746\pi$
$702$	7.90794	−	18.1927i	0.298466	−	0.686638i
$703$		−	85.3535i		−	3.21917i
$704$	−17.7201	+	33.0355i	−0.667851	+	1.24507i
$705$	20.1429	−	14.3162i	0.758625	−	0.539180i
$706$	−10.5910	−	28.6335i	−0.398599	−	1.07764i
$707$	−26.7302	−	0.935618i	−1.00529	−	0.0351875i
$708$	4.19734	−	16.8342i	0.157746	−	0.632670i
$709$	−42.0356	+	24.2692i	−1.57868	+	0.911451i	−0.583635	+	0.812016i	$0.698370\pi$
$709$	−42.0356	+	24.2692i	−1.57868	+	0.911451i	−0.995044	+	0.0994345i	$0.968297\pi$
$710$	−3.12095	+	3.75901i	−0.117127	+	0.141073i
$711$	−14.7392	+	2.81308i	−0.552765	+	0.105499i
$712$	32.5142	+	18.1005i	1.21852	+	0.678343i
$713$	0.403133	+	0.698246i	0.0150974	+	0.0261495i
$714$	−1.41560	+	12.8152i	−0.0529775	+	0.479597i
$715$	−21.3250	−	12.3120i	−0.797508	−	0.460442i
$716$	−15.2660	−	5.37691i	−0.570519	−	0.200944i
$717$	−4.95572	−	52.4001i	−0.185075	−	1.95692i
$718$	1.22526	−	7.16694i	0.0457262	−	0.267468i
$719$	21.1814			0.789931			0.394966	−	0.918696i	$-0.370756\pi$
$719$	21.1814			0.789931			0.394966	+	0.918696i	$0.370756\pi$
$720$	−23.3449	+	0.814985i	−0.870014	+	0.0303727i
$721$	−17.1084	−	32.1825i	−0.637149	−	1.19854i
$722$	−67.1079	−	11.4727i	−2.49750	−	0.426971i
$723$	−42.4580	−	19.4364i	−1.57903	−	0.722847i
$724$	6.15886	+	2.16923i	0.228892	+	0.0806189i
$725$	4.66997	−	8.08863i	0.173438	−	0.300404i
$726$	−26.7674	−	2.01209i	−0.993431	−	0.0746758i
$727$	−45.2874	+	26.1467i	−1.67962	+	0.969726i	−0.717711	+	0.696341i	$0.754810\pi$
$727$	−45.2874	+	26.1467i	−1.67962	+	0.969726i	−0.961905	+	0.273385i	$0.911857\pi$
$728$	−20.1973	−	0.391014i	−0.748561	−	0.0144920i
$729$	22.7928	−	14.4737i	0.844179	−	0.536062i
$730$	−23.7368	+	28.5896i	−0.878539	+	1.05815i
$731$	−6.47917	+	3.74075i	−0.239641	+	0.138357i
$732$	3.95026	−	4.09057i	0.146006	−	0.151192i
$733$	−5.16760	+	8.95055i	−0.190870	+	0.330596i	−0.945539	−	0.325510i	$-0.894464\pi$
$733$	−5.16760	+	8.95055i	−0.190870	+	0.330596i	0.754669	+	0.656106i	$0.227798\pi$
$734$	−14.5516	+	5.38239i	−0.537111	+	0.198668i
$735$	20.1463	−	12.2941i	0.743106	−	0.453475i
$736$	0.218140	+	1.07290i	0.00804076	+	0.0395477i
$737$		−	21.8633i		−	0.805344i
$738$	15.4670	+	25.6360i	0.569346	+	0.943673i
$739$			18.1093i			0.666162i	0.942898	+	0.333081i	$0.108088\pi$
$739$			18.1093i			0.666162i	−0.942898	+	0.333081i	$0.891912\pi$
$740$	−30.7928	+	26.3899i	−1.13197	+	0.970111i
$741$	−38.1418	+	3.60724i	−1.40117	+	0.132515i
$742$	18.0800	+	16.1122i	0.663738	+	0.591497i
$743$	−25.6144	−	14.7885i	−0.939699	−	0.542536i	−0.0498334	−	0.998758i	$-0.515869\pi$
$743$	−25.6144	−	14.7885i	−0.939699	−	0.542536i	−0.889866	+	0.456222i	$0.849202\pi$
$744$	8.20357	−	18.6867i	0.300758	−	0.685088i
$745$	−9.51113	+	5.49125i	−0.348461	+	0.201184i
$746$	−32.3380	−	26.8490i	−1.18398	−	0.983010i
$747$	−6.53213	−	34.2254i	−0.238998	−	1.25224i
$748$	−3.42886	−	18.3272i	−0.125372	−	0.670108i
$749$	30.3091	+	18.9426i	1.10747	+	0.692149i
$750$	26.6842	−	12.8429i	0.974369	−	0.468957i
$751$	16.9685	−	29.3903i	0.619189	−	1.07247i	−0.370445	−	0.928854i	$-0.620795\pi$
$751$	16.9685	−	29.3903i	0.619189	−	1.07247i	0.989634	−	0.143612i	$-0.0458719\pi$
$752$	−4.48822	+	28.9724i	−0.163669	+	1.05651i
$753$	15.9475	−	11.3344i	0.581161	−	0.413050i
$754$	29.0284	+	4.96268i	1.05715	+	0.180730i
$755$		−	32.5430i		−	1.18436i
$756$	−22.4679	−	15.8491i	−0.817149	−	0.576427i
$757$		−	21.7705i		−	0.791263i	−0.918409	−	0.395631i	$-0.870526\pi$
$757$		−	21.7705i		−	0.791263i	0.918409	−	0.395631i	$-0.129474\pi$
$758$	0.703580	−	4.11548i	0.0255552	−	0.149481i
$759$	−1.28043	+	0.910041i	−0.0464765	+	0.0330324i
$760$	23.1651	+	38.7128i	0.840285	+	1.40426i
$761$	−6.34558	+	10.9909i	−0.230027	+	0.398418i	−0.957816	−	0.287383i	$-0.907215\pi$
$761$	−6.34558	+	10.9909i	−0.230027	+	0.398418i	0.727789	+	0.685801i	$0.240548\pi$
$762$	−5.05158	−	10.4959i	−0.182999	−	0.380225i
$763$	−10.1161	+	16.1862i	−0.366227	+	0.585979i
$764$	10.8526	−	2.03043i	0.392633	−	0.0734584i
$765$	8.79405	−	7.59225i	0.317950	−	0.274498i
$766$	−18.0669	+	21.7605i	−0.652783	+	0.786239i
$767$	−11.7087	+	6.76004i	−0.422778	+	0.244091i
$768$	18.6185	−	20.5268i	0.671839	−	0.740697i
$769$	10.8274	+	6.25121i	0.390446	+	0.225424i	0.682354	−	0.731022i	$-0.260957\pi$
$769$	10.8274	+	6.25121i	0.390446	+	0.225424i	−0.291907	+	0.956447i	$0.594290\pi$
$770$	−22.7073	+	25.4806i	−0.818315	+	0.918258i
$771$	−14.2212	+	1.34496i	−0.512163	+	0.0484376i
$772$	−2.88745	+	2.47459i	−0.103922	+	0.0890623i
$773$			47.8090i			1.71957i	0.510657	+	0.859784i	$0.329402\pi$
$773$			47.8090i			1.71957i	−0.510657	+	0.859784i	$0.670598\pi$
$774$	−0.307362	−	15.9518i	−0.0110479	−	0.573376i
$775$			5.04381i			0.181179i
$776$	10.5887	−	0.165522i	0.380111	−	0.00594189i
$777$	−47.6511	+	2.82932i	−1.70947	+	0.101501i
$778$	−1.60591	−	4.34167i	−0.0575745	−	0.155657i
$779$	28.9125	−	50.0779i	1.03590	−	1.79423i
$780$	13.0942	+	12.6450i	0.468847	+	0.452765i
$781$	7.20233	−	4.15827i	0.257720	−	0.148795i
$782$	−0.418960	−	0.347845i	−0.0149820	−	0.0124389i
$783$	28.9345	+	27.7395i	1.03403	+	0.991327i
$784$	−6.21062	+	27.3025i	−0.221808	+	0.975090i
$785$	−22.6752	+	13.0916i	−0.809314	+	0.467258i
$786$	−2.49067	+	33.1340i	−0.0888393	+	1.18185i
$787$	−11.8273	+	20.4854i	−0.421597	+	0.730227i	−0.996096	−	0.0882784i	$-0.971864\pi$
$787$	−11.8273	+	20.4854i	−0.421597	+	0.730227i	0.574499	+	0.818505i	$0.305197\pi$
$788$	−31.2115	−	10.9931i	−1.11186	−	0.391613i
$789$	5.39824	+	2.47120i	0.192182	+	0.0879772i
$790$	2.32034	−	13.5724i	0.0825540	−	0.482886i
$791$	8.73484	+	16.4311i	0.310575	+	0.584222i
$792$	37.7513	+	12.4844i	1.34143	+	0.443613i
$793$	−4.43141			−0.157364
$794$	−26.2059	−	4.48015i	−0.930012	−	0.158995i
$795$	−2.05468	−	21.7254i	−0.0728719	−	0.770522i
$796$	−1.28324	+	3.64335i	−0.0454831	+	0.129135i
$797$	41.4021	+	23.9035i	1.46654	+	0.846706i	0.999299	−	0.0374249i	$-0.0119155\pi$
$797$	41.4021	+	23.9035i	1.46654	+	0.846706i	0.467239	+	0.884131i	$0.345249\pi$
$798$	−5.83042	+	52.7819i	−0.206395	+	1.86846i
$799$	−7.29085	−	12.6281i	−0.257932	−	0.446751i
$800$	−2.17410	+	6.49493i	−0.0768661	+	0.229630i
$801$	12.9770	−	37.2760i	0.458519	−	1.31708i
$802$	2.00192	+	1.66211i	0.0706901	+	0.0586911i
$803$	54.7783	−	31.6262i	1.93308	−	1.11607i
$804$	−3.91010	+	15.6822i	−0.137899	+	0.553069i
$805$	−0.0348687	+	0.996183i	−0.00122896	+	0.0351108i
$806$	−14.9158	+	5.51710i	−0.525388	+	0.194332i
$807$	0.783179	−	0.556631i	0.0275692	−	0.0195943i
$808$	−28.5897	+	0.446914i	−1.00578	+	0.0157224i
$809$			7.39118i			0.259860i	0.991523	+	0.129930i	$0.0414752\pi$
$809$			7.39118i			0.259860i	−0.991523	+	0.129930i	$0.958525\pi$
$810$	5.11282	+	24.2428i	0.179646	+	0.851806i
$811$	29.5707			1.03837			0.519185	−	0.854662i	$-0.326236\pi$
$811$	29.5707			1.03837			0.519185	+	0.854662i	$0.326236\pi$
$812$	14.8990	−	38.0028i	0.522851	−	1.33364i
$813$	27.3167	−	19.4149i	0.958040	−	0.680910i
$814$	64.7441	−	23.9477i	2.26928	−	0.839366i
$815$	−1.77166	+	3.06860i	−0.0620584	+	0.107488i
$816$	−0.818219	+	13.7590i	−0.0286434	+	0.481663i
$817$	−26.6857	+	15.4070i	−0.933615	+	0.539023i
$818$	17.2916	+	14.3565i	0.604587	+	0.501964i
$819$	3.27819	+	21.1742i	0.114549	+	0.739886i
$820$	−27.0058	+	5.05255i	−0.943082	+	0.176443i
$821$	6.70781	+	11.6183i	0.234104	+	0.405481i	0.959012	−	0.283365i	$-0.0914509\pi$
$821$	6.70781	+	11.6183i	0.234104	+	0.405481i	−0.724908	+	0.688846i	$0.758118\pi$
$822$	20.5503	+	14.0178i	0.716774	+	0.488928i
$823$	25.2681	−	43.7656i	0.880790	−	1.52557i	0.0303252	−	0.999540i	$-0.490346\pi$
$823$	25.2681	−	43.7656i	0.880790	−	1.52557i	0.850465	−	0.526032i	$-0.176321\pi$
$824$	−20.0070	−	33.4351i	−0.696976	−	1.16477i
$825$	−9.78341	+	0.925263i	−0.340615	+	0.0322135i
$826$	5.88223	+	17.7926i	0.204669	+	0.619084i
$827$	3.67588			0.127823			0.0639114	−	0.997956i	$-0.479642\pi$
$827$	3.67588			0.127823			0.0639114	+	0.997956i	$0.479642\pi$
$828$	1.08119	−	0.423764i	0.0375738	−	0.0147268i
$829$	9.84373			0.341887			0.170944	−	0.985281i	$-0.445318\pi$
$829$	9.84373			0.341887			0.170944	+	0.985281i	$0.445318\pi$
$830$	31.5160	+	5.38796i	1.09394	+	0.187019i
$831$	20.8187	+	9.53036i	0.722192	+	0.330605i
$832$	−21.5853	+	0.675006i	−0.748335	+	0.0234016i
$833$	−6.10280	−	12.5178i	−0.211449	−	0.433715i
$834$	7.04809	+	0.529802i	0.244055	+	0.0183455i
$835$	−1.66178	+	0.959427i	−0.0575081	+	0.0332023i
$836$	−14.1224	−	75.4840i	−0.488434	−	2.61067i
$837$	−21.0220	−	5.16039i	−0.726626	−	0.178369i
$838$	0.629831	+	0.522923i	0.0217572	+	0.0180641i
$839$	−2.69662	−	4.67069i	−0.0930977	−	0.161250i	0.815715	−	0.578453i	$-0.196344\pi$
$839$	−2.69662	−	4.67069i	−0.0930977	−	0.161250i	−0.908813	+	0.417203i	$0.863010\pi$
$840$	20.8447	−	14.2158i	0.719210	−	0.490493i
$841$	−15.2534	+	26.4196i	−0.525979	+	0.911022i
$842$	3.49105	−	1.29128i	0.120309	−	0.0445003i
$843$	−19.2003	−	8.78950i	−0.661293	−	0.302726i
$844$	−21.3121	−	24.8678i	−0.733591	−	0.855985i
$845$			11.1205i			0.382558i
$846$	31.0907	−	0.599059i	1.06892	−	0.0205961i
$847$	25.6010	−	13.6096i	0.879660	−	0.467632i
$848$	20.1751	+	16.2246i	0.692816	+	0.557156i
$849$	−21.9903	+	2.07973i	−0.754707	+	0.0713761i
$850$	−1.18176	−	3.19496i	−0.0405340	−	0.109586i
$851$	1.00804	−	1.74598i	0.0345552	−	0.0598514i
$852$	−5.90981	+	1.69458i	−0.202467	+	0.0580553i
$853$	−12.0597	−	20.8881i	−0.412918	−	0.715194i	0.582290	−	0.812981i	$-0.302157\pi$
$853$	−12.0597	−	20.8881i	−0.412918	−	0.715194i	−0.995207	+	0.0977871i	$0.968824\pi$
$854$	−1.24621	+	6.01447i	−0.0426444	+	0.205811i
$855$	36.2200	−	31.2702i	1.23870	−	1.06942i
$856$	33.3849	+	18.5852i	1.14107	+	0.635228i
$857$	−0.305103	−	0.528453i	−0.0104221	−	0.0180516i	0.860767	−	0.508999i	$-0.169984\pi$
$857$	−0.305103	−	0.528453i	−0.0104221	−	0.0180516i	−0.871189	+	0.490947i	$0.836651\pi$
$858$	−13.4377	−	27.9200i	−0.458755	−	0.953173i
$859$	−15.7563	+	27.2908i	−0.537599	+	0.931149i	0.461433	+	0.887175i	$0.347335\pi$
$859$	−15.7563	+	27.2908i	−0.537599	+	0.931149i	−0.999033	+	0.0439745i	$0.985998\pi$
$860$	13.8091	+	4.86376i	0.470888	+	0.165853i
$861$	−28.9159	−	14.4813i	−0.985450	−	0.493520i
$862$	3.82902	−	22.3972i	0.130417	−	0.762853i
$863$			13.0678i			0.444832i	0.974952	+	0.222416i	$0.0713943\pi$
$863$			13.0678i			0.444832i	−0.974952	+	0.222416i	$0.928606\pi$
$864$	−24.8457	−	15.7064i	−0.845267	−	0.534343i
$865$	1.96339			0.0667571
$866$	−0.0910181	+	0.532395i	−0.00309292	+	0.0180915i
$867$	13.0865	+	18.4127i	0.444442	+	0.625330i
$868$	3.29335	+	21.7959i	0.111784	+	0.739800i
$869$	−11.7191	+	20.2981i	−0.397544	+	0.688567i
$870$	−33.1430	+	15.9515i	−1.12365	+	0.540806i
$871$	10.9075	−	6.29743i	0.369585	−	0.213380i
$872$	−9.92518	+	17.8288i	−0.336109	+	0.603759i
$873$	−2.10576	−	11.0332i	−0.0712691	−	0.373417i
$874$	−1.72557	−	1.43267i	−0.0583682	−	0.0484607i
$875$	−16.9526	+	27.1249i	−0.573102	+	0.916989i
$876$	−44.9478	+	12.8883i	−1.51865	+	0.435456i
$877$	12.4502	+	7.18814i	0.420414	+	0.242726i	0.695255	−	0.718764i	$-0.255292\pi$
$877$	12.4502	+	7.18814i	0.420414	+	0.242726i	−0.274840	+	0.961490i	$0.588625\pi$
$878$	−1.20578	+	0.445997i	−0.0406931	+	0.0150517i
$879$	−0.254955	−	2.69581i	−0.00859943	−	0.0909274i
$880$	−22.8658	+	28.4333i	−0.770806	+	0.958487i
$881$	−18.8451			−0.634907			−0.317454	−	0.948274i	$-0.602828\pi$
$881$	−18.8451			−0.634907			−0.317454	+	0.948274i	$0.602828\pi$
$882$	29.6603	+	1.50538i	0.998715	+	0.0506886i
$883$			16.4261i			0.552782i	0.961045	+	0.276391i	$0.0891385\pi$
$883$			16.4261i			0.552782i	−0.961045	+	0.276391i	$0.910862\pi$
$884$	8.15568	−	6.98954i	0.274305	−	0.235084i
$885$	7.02875	−	15.3540i	0.236269	−	0.516119i
$886$	−11.0982	−	30.0048i	−0.372853	−	1.00803i
$887$	−2.87446	+	4.97871i	−0.0965149	+	0.167169i	−0.910240	−	0.414081i	$-0.864103\pi$
$887$	−2.87446	+	4.97871i	−0.0965149	+	0.167169i	0.813725	+	0.581250i	$0.197436\pi$
$888$	−50.7229	+	5.59828i	−1.70215	+	0.187866i
$889$	10.6692	+	6.66807i	0.357834	+	0.223640i
$890$	27.8664	+	23.1364i	0.934085	+	0.775533i
$891$	6.15315	−	41.7227i	0.206138	−	1.39776i
$892$	−29.9505	+	5.60350i	−1.00282	+	0.187619i
$893$	−30.0288	−	52.0114i	−1.00488	−	1.74049i
$894$	−13.7809	−	1.03591i	−0.460903	−	0.0346458i
$895$	−13.6426	−	7.87654i	−0.456021	−	0.263284i
$896$	−5.15412	+	29.4862i	−0.172187	+	0.985064i
$897$	−0.822824	−	0.376672i	−0.0274733	−	0.0125767i
$898$	−7.88831	+	46.1414i	−0.263236	+	1.53976i
$899$		−	32.1352i		−	1.07177i
$900$	7.18298	+	1.08602i	0.239433	+	0.0362007i
$901$	−12.8766			−0.428981
$902$	46.0981	+	7.88092i	1.53490	+	0.262406i
$903$	9.48600	+	14.3874i	0.315674	+	0.478782i
$904$	10.2147	+	17.0706i	0.339737	+	0.567759i
$905$	5.50389	+	3.17767i	0.182956	+	0.105629i
$906$	23.0759	−	33.8295i	0.766644	−	1.12391i
$907$	−50.2899	+	29.0349i	−1.66985	+	0.964087i	−0.702131	+	0.712047i	$0.747768\pi$
$907$	−50.2899	+	29.0349i	−1.66985	+	0.964087i	−0.967717	+	0.252040i	$0.918899\pi$
$908$	−19.8153	+	3.70728i	−0.657595	+	0.123030i
$909$	5.68561	+	29.7900i	0.188580	+	0.988072i
$910$	−19.2527	−	3.98919i	−0.638221	−	0.132240i
$911$	34.0582	−	19.6635i	1.12840	−	0.651481i	0.184867	−	0.982764i	$-0.440815\pi$
$911$	34.0582	−	19.6635i	1.12840	−	0.651481i	0.943532	+	0.331282i	$0.107481\pi$
$912$	−3.36999	+	56.6693i	−0.111592	+	1.87651i
$913$	−47.1334	−	27.2125i	−1.55989	−	0.900602i
$914$	0.655365	+	1.77182i	0.0216776	+	0.0586067i
$915$	4.51138	−	3.20638i	0.149141	−	0.106000i
$916$	39.6288	−	33.9625i	1.30937	−	1.12215i
$917$	−16.8467	−	31.6902i	−0.556326	−	1.04650i
$918$	14.5253	−	1.65662i	0.479406	−	0.0546765i
$919$	20.5765			0.678754			0.339377	−	0.940650i	$-0.389784\pi$
$919$	20.5765			0.678754			0.339377	+	0.940650i	$0.389784\pi$
$920$	0.0166557	+	1.06549i	0.000549121	+	0.0351281i
$921$	26.9386	+	37.9025i	0.887657	+	1.24893i
$922$	−36.5641	+	13.5244i	−1.20417	+	0.445402i
$923$	4.14907	+	2.39547i	0.136568	+	0.0788478i
$924$	−41.6730	+	10.3864i	−1.37094	+	0.341688i
$925$	10.9224	−	6.30607i	0.359128	−	0.207342i
$926$	−34.4103	+	41.4452i	−1.13079	+	1.36198i
$927$	−31.2822	+	27.0071i	−1.02744	+	0.887029i
$928$	13.8517	−	41.3805i	0.454703	−	1.35838i
$929$	17.4880	+	30.2900i	0.573762	+	0.993784i	0.996175	+	0.0873810i	$0.0278497\pi$
$929$	17.4880	+	30.2900i	0.573762	+	0.993784i	−0.422413	+	0.906403i	$0.638817\pi$
$930$	11.1931	−	16.4092i	0.367035	−	0.538078i
$931$	−25.1356	−	51.5569i	−0.823785	−	1.68971i
$932$	7.44265	−	21.1311i	0.243792	−	0.692171i
$933$	19.2157	−	1.81732i	0.629094	−	0.0594964i
$934$	−1.32031	+	7.72293i	−0.0432018	+	0.252702i
$935$		−	18.1473i		−	0.593480i
$936$	4.64536	+	22.4299i	0.151838	+	0.733143i
$937$			56.6280i			1.84995i	0.380022	+	0.924977i	$0.375916\pi$
$937$			56.6280i			1.84995i	−0.380022	+	0.924977i	$0.624084\pi$
$938$	−5.47968	−	16.5750i	−0.178918	−	0.541193i
$939$	−27.2339	−	12.4671i	−0.888746	−	0.406850i
$940$	−9.47964	+	26.9145i	−0.309192	+	0.877854i
$941$	−13.5147	−	7.80273i	−0.440567	−	0.254362i	0.263271	−	0.964722i	$-0.415199\pi$
$941$	−13.5147	−	7.80273i	−0.440567	−	0.254362i	−0.703838	+	0.710360i	$0.748532\pi$
$942$	−32.8547	−	2.46968i	−1.07046	−	0.0804664i
$943$	1.18286	−	0.682924i	0.0385192	−	0.0222391i
$944$	7.24273	+	18.6786i	0.235731	+	0.607936i
$945$	−18.6581	−	19.1843i	−0.606949	−	0.624067i
$946$	−19.1741	−	15.9195i	−0.623403	−	0.517586i
$947$	12.1113	+	20.9774i	0.393564	+	0.681673i	0.992917	−	0.118812i	$-0.0379086\pi$
$947$	12.1113	+	20.9774i	0.393564	+	0.681673i	−0.599353	+	0.800485i	$0.704575\pi$
$948$	12.0361	−	12.4637i	0.390916	−	0.404801i
$949$	31.5563	+	18.2190i	1.02436	+	0.591415i
$950$	−4.86731	−	13.1591i	−0.157916	−	0.426937i
$951$	13.3712	−	29.2088i	0.433591	−	0.947162i
$952$	−7.19290	−	13.0348i	−0.233123	−	0.422461i
$953$			35.4223i			1.14744i	0.819051	+	0.573720i	$0.194500\pi$
$953$			35.4223i			1.14744i	−0.819051	+	0.573720i	$0.805500\pi$
$954$	13.2694	−	24.0413i	0.429612	−	0.778364i
$955$	10.7461			0.347735
$956$	39.5493	+	46.1478i	1.27912	+	1.49253i
$957$	62.3322	−	5.89504i	2.01491	−	0.190560i
$958$	−15.1318	−	40.9098i	−0.488887	−	1.32174i
$959$	−26.8527	−	0.939907i	−0.867119	−	0.0303512i
$960$	21.4864	−	16.3054i	0.693471	−	0.526255i
$961$	−6.82310	−	11.8180i	−0.220100	−	0.381224i
$962$	30.5960	+	25.4027i	0.986456	+	0.819015i
$963$	13.3245	−	38.2742i	0.429376	−	1.23337i
$964$	52.9995	−	9.91576i	1.70700	−	0.319365i
$965$	−3.20534	+	1.85061i	−0.103184	+	0.0595731i
$966$	−0.742630	+	1.01084i	−0.0238937	+	0.0325232i
$967$	−5.73743	+	9.93753i	−0.184503	+	0.319569i	−0.943409	−	0.331631i	$-0.892401\pi$
$967$	−5.73743	+	9.93753i	−0.184503	+	0.319569i	0.758906	+	0.651201i	$0.225734\pi$
$968$	26.5974	−	15.9154i	0.854873	−	0.511541i
$969$	−16.3571	−	23.0144i	−0.525466	−	0.739329i
$970$	10.1598	+	1.73691i	0.326211	+	0.0557689i
$971$		−	1.25058i		−	0.0401329i	−0.999799	−	0.0200665i	$-0.993612\pi$
$971$		−	1.25058i		−	0.0401329i	0.999799	−	0.0200665i	$-0.00638778\pi$
$972$	−11.8754	+	28.8266i	−0.380903	+	0.924615i
$973$	−6.74096	+	3.58353i	−0.216105	+	0.114883i
$974$	38.1877	+	6.52856i	1.22361	+	0.209189i
$975$	−3.27959	−	4.61438i	−0.105031	−	0.147778i
$976$	−1.00522	+	6.48891i	−0.0321763	+	0.207705i
$977$	9.02430	+	5.21018i	0.288713	+	0.166689i	0.637361	−	0.770565i	$-0.280026\pi$
$977$	9.02430	+	5.21018i	0.288713	+	0.166689i	−0.348648	+	0.937254i	$0.613359\pi$
$978$	−4.01760	+	1.93364i	−0.128469	+	0.0618311i
$979$	−30.8262	−	53.3926i	−0.985211	−	1.70644i
$980$	−10.8286	+	25.0086i	−0.345906	+	0.798871i
$981$	20.4398	+	7.11578i	0.652594	+	0.227189i
$982$	−3.55414	+	4.28075i	−0.113417	+	0.136604i
$983$	25.7276	+	44.5616i	0.820584	+	1.42129i	0.905248	+	0.424884i	$0.139685\pi$
$983$	25.7276	+	44.5616i	0.820584	+	1.42129i	−0.0846634	+	0.996410i	$0.526981\pi$
$984$	−31.6561	−	13.8972i	−1.00916	−	0.443027i
$985$	−27.8923	−	16.1036i	−0.888723	−	0.513104i
$986$	7.52924	+	20.3558i	0.239780	+	0.648260i
$987$	−28.0415	+	18.4886i	−0.892571	+	0.588497i
$988$	33.5908	−	28.7878i	1.06866	−	0.915861i
$989$	−0.727839			−0.0231439
$990$	33.8820	+	18.7009i	1.07684	+	0.594353i
$991$	−22.6225			−0.718629			−0.359314	−	0.933217i	$-0.616989\pi$
$991$	−22.6225			−0.718629			−0.359314	+	0.933217i	$0.616989\pi$
$992$	4.69518	+	23.0928i	0.149072	+	0.733197i
$993$	−2.46055	−	1.12639i	−0.0780832	−	0.0357449i
$994$	4.41803	−	4.95762i	0.140131	−	0.157246i
$995$	−1.87979	+	3.25589i	−0.0595934	+	0.103219i
$996$	28.9413	+	27.9486i	0.917042	+	0.885586i
$997$	14.3531	+	24.8603i	0.454568	+	0.787334i	0.998663	−	0.0516889i	$-0.0164604\pi$
$997$	14.3531	+	24.8603i	0.454568	+	0.787334i	−0.544096	+	0.839023i	$0.683127\pi$
$998$	8.96494	+	7.44322i	0.283780	+	0.235611i
$999$	15.1080	+	51.9752i	0.477997	+	1.64442i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	504.2.cc.b.293.3	✓	168
7.6	odd	2	inner	504.2.cc.b.293.4	yes	168
8.5	even	2	inner	504.2.cc.b.293.32	yes	168
9.2	odd	6	inner	504.2.cc.b.461.31	yes	168
56.13	odd	2	inner	504.2.cc.b.293.31	yes	168
63.20	even	6	inner	504.2.cc.b.461.32	yes	168
72.29	odd	6	inner	504.2.cc.b.461.4	yes	168
504.461	even	6	inner	504.2.cc.b.461.3	yes	168

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
504.2.cc.b.293.3	✓	168	1.1	even	1	trivial
504.2.cc.b.293.4	yes	168	7.6	odd	2	inner
504.2.cc.b.293.31	yes	168	56.13	odd	2	inner
504.2.cc.b.293.32	yes	168	8.5	even	2	inner
504.2.cc.b.461.3	yes	168	504.461	even	6	inner
504.2.cc.b.461.4	yes	168	72.29	odd	6	inner
504.2.cc.b.461.31	yes	168	9.2	odd	6	inner
504.2.cc.b.461.32	yes	168	63.20	even	6	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 504 = 2^{3} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	504.cc (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.39399 - 0.238316i) q^{2} +(-1.00341 - 1.41180i) q^{3} +(1.88641 + 0.664419i) q^{4} +(1.68580 + 0.973297i) q^{5} +(1.06229 + 2.20716i) q^{6} +(-2.24361 - 1.40222i) q^{7} +(-2.47129 - 1.37576i) q^{8} +(-0.986337 + 2.83322i) q^{9} +O(q^{10})\)	\(q+(-1.39399 - 0.238316i) q^{2} +(-1.00341 - 1.41180i) q^{3} +(1.88641 + 0.664419i) q^{4} +(1.68580 + 0.973297i) q^{5} +(1.06229 + 2.20716i) q^{6} +(-2.24361 - 1.40222i) q^{7} +(-2.47129 - 1.37576i) q^{8} +(-0.986337 + 2.83322i) q^{9} +(-2.11804 - 1.75852i) q^{10} +(2.34300 + 4.05819i) q^{11} +(-0.954819 - 3.32991i) q^{12} +(-1.34974 + 2.33782i) q^{13} +(2.79340 + 2.48936i) q^{14} +(-0.317452 - 3.35662i) q^{15} +(3.11709 + 2.50674i) q^{16} -1.98946 q^{17} +(2.05014 - 3.71442i) q^{18} -8.19396 q^{19} +(2.53343 + 2.95612i) q^{20} +(0.271616 + 4.57452i) q^{21} +(-2.29898 - 6.21545i) q^{22} +(-0.167614 - 0.0967722i) q^{23} +(0.537436 + 4.86941i) q^{24} +(-0.605385 - 1.04856i) q^{25} +(2.43866 - 2.93723i) q^{26} +(4.98963 - 1.45038i) q^{27} +(-3.30071 - 4.13586i) q^{28} +(3.85703 + 6.68057i) q^{29} +(-0.357412 + 4.75475i) q^{30} +(-3.60768 - 2.08289i) q^{31} +(-3.74780 - 4.23722i) q^{32} +(3.37835 - 7.37987i) q^{33} +(2.77328 + 0.474119i) q^{34} +(-2.41750 - 4.54756i) q^{35} +(-3.74308 + 4.68928i) q^{36} +10.4166i q^{37} +(11.4223 + 1.95275i) q^{38} +(4.65486 - 0.440232i) q^{39} +(-2.82709 - 4.72455i) q^{40} +(-3.52851 + 6.11157i) q^{41} +(0.711551 - 6.44156i) q^{42} +(3.25676 - 1.88029i) q^{43} +(1.72352 + 9.21215i) q^{44} +(-4.42033 + 3.81625i) q^{45} +(0.210590 + 0.174845i) q^{46} +(3.66475 + 6.34753i) q^{47} +(0.411278 - 6.91599i) q^{48} +(3.06757 + 6.29206i) q^{49} +(0.594012 + 1.60595i) q^{50} +(1.99624 + 2.80871i) q^{51} +(-4.09946 + 3.51329i) q^{52} +6.47241 q^{53} +(-7.30114 + 0.832699i) q^{54} +9.12174i q^{55} +(3.61551 + 6.55195i) q^{56} +(8.22190 + 11.5682i) q^{57} +(-3.78457 - 10.2318i) q^{58} +(4.33741 + 2.50420i) q^{59} +(1.63136 - 6.54289i) q^{60} +(0.820789 + 1.42165i) q^{61} +(4.53268 + 3.76330i) q^{62} +(6.18575 - 4.97358i) q^{63} +(4.21460 + 6.79979i) q^{64} +(-4.55078 + 2.62740i) q^{65} +(-6.46813 + 9.48234i) q^{66} +(-4.04058 - 2.33283i) q^{67} +(-3.75293 - 1.32183i) q^{68} +(0.0315633 + 0.333739i) q^{69} +(2.28622 + 6.91538i) q^{70} -1.77476i q^{71} +(6.33535 - 5.64477i) q^{72} -13.4982i q^{73} +(2.48245 - 14.5207i) q^{74} +(-0.872900 + 1.90681i) q^{75} +(-15.4572 - 5.44422i) q^{76} +(0.433693 - 12.3904i) q^{77} +(-6.59375 - 0.495649i) q^{78} +(2.50088 + 4.33165i) q^{79} +(2.81500 + 7.25972i) q^{80} +(-7.05428 - 5.58902i) q^{81} +(6.37519 - 7.67855i) q^{82} +(-10.0584 + 5.80719i) q^{83} +(-2.52702 + 8.80989i) q^{84} +(-3.35382 - 1.93633i) q^{85} +(-4.98798 + 1.84497i) q^{86} +(5.56143 - 12.1487i) q^{87} +(-0.207161 - 13.2524i) q^{88} -13.1567 q^{89} +(7.07137 - 4.26637i) q^{90} +(6.30642 - 3.35252i) q^{91} +(-0.251892 - 0.293918i) q^{92} +(0.679359 + 7.18331i) q^{93} +(-3.59590 - 9.72176i) q^{94} +(-13.8134 - 7.97516i) q^{95} +(-2.22151 + 9.54279i) q^{96} +(-3.24250 + 1.87206i) q^{97} +(-2.77667 - 9.50211i) q^{98} +(-13.8087 + 2.63549i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9}+O(q^{10}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9	\( 168 q - 6 q^{2} - 18 q^{4} - 2 q^{7} - 8 q^{9} + 12 q^{14} - 4 q^{15} + 30 q^{16} - 2 q^{18} + 6 q^{22} - 84 q^{23} + 32 q^{25} + 4 q^{28} - 52 q^{30} + 24 q^{32} - 26 q^{36} + 44 q^{39} - 16 q^{46} + 54 q^{49} + 108 q^{50} - 24 q^{56} - 40 q^{57} + 6 q^{58} - 4 q^{60} - 86 q^{63} + 120 q^{64} + 60 q^{65} - 6 q^{70} + 52 q^{72} + 48 q^{74} - 184 q^{78} - 4 q^{79} - 104 q^{81} - 72 q^{84} - 144 q^{86} - 18 q^{88} - 90 q^{92} - 72 q^{95}+O(q^{100}) \) 168 * q - 6 * q^2 - 18 * q^4 - 2 * q^7 - 8 * q^9 + 12 * q^14 - 4 * q^15 + 30 * q^16 - 2 * q^18 + 6 * q^22 - 84 * q^23 + 32 * q^25 + 4 * q^28 - 52 * q^30 + 24 * q^32 - 26 * q^36 + 44 * q^39 - 16 * q^46 + 54 * q^49 + 108 * q^50 - 24 * q^56 - 40 * q^57 + 6 * q^58 - 4 * q^60 - 86 * q^63 + 120 * q^64 + 60 * q^65 - 6 * q^70 + 52 * q^72 + 48 * q^74 - 184 * q^78 - 4 * q^79 - 104 * q^81 - 72 * q^84 - 144 * q^86 - 18 * q^88 - 90 * q^92 - 72 * q^95

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