LMFDB - Embedded newform 540.2.be.a.11.43

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [540,2,Mod(11,540)] 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("540.11"); S:= CuspForms(chi, 2); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(540, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([9, 13, 0])) N = Newforms(chi, 2, names="a")

Level:	$ N $	$=$	$ 540 = 2^{2} \cdot 3^{3} \cdot 5 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	540.be (of order $18$, 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:	$4.31192170915$
Analytic rank:	$0$
Dimension:	$432$
Relative dimension:	$72$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			11.43
Character	$\chi$	$=$	540.11
Dual form			540.2.be.a.491.43

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(0.349180 + 1.37043i) q^{2} +(-1.59941 + 0.664741i) q^{3} +(-1.75615 + 0.957052i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-1.46946 - 1.95977i) q^{6} +(-2.87648 - 0.507202i) q^{7} +(-1.92478 - 2.07249i) q^{8} +(2.11624 - 2.12639i) q^{9} +(1.40721 + 0.140592i) q^{10} +(1.13791 - 0.414164i) q^{11} +(2.17261 - 2.69810i) q^{12} +(1.94642 - 1.63324i) q^{13} +(-0.309327 - 4.11912i) q^{14} +(0.0776213 + 1.73031i) q^{15} +(2.16810 - 3.36145i) q^{16} +(-0.0896428 + 0.0517553i) q^{17} +(3.65301 + 2.15766i) q^{18} +(0.733915 + 0.423726i) q^{19} +(0.298697 + 1.97757i) q^{20} +(4.93784 - 1.10089i) q^{21} +(0.964916 + 1.41480i) q^{22} +(-0.839030 - 4.75837i) q^{23} +(4.45619 + 2.03528i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(2.91790 + 2.09714i) q^{26} +(-1.97124 + 4.80773i) q^{27} +(5.53695 - 1.86222i) q^{28} +(1.79670 - 2.14122i) q^{29} +(-2.34416 + 0.710564i) q^{30} +(6.37237 - 1.12362i) q^{31} +(5.36368 + 1.79748i) q^{32} +(-1.54467 + 1.41883i) q^{33} +(-0.102228 - 0.104777i) q^{34} +(-1.46043 + 2.52954i) q^{35} +(-1.68136 + 5.75960i) q^{36} +(-0.227440 - 0.393937i) q^{37} +(-0.324418 + 1.15373i) q^{38} +(-2.02745 + 3.90610i) q^{39} +(-2.60582 + 1.09987i) q^{40} +(-2.50219 - 2.98199i) q^{41} +(3.23289 + 6.38255i) q^{42} +(-4.23504 - 11.6357i) q^{43} +(-1.60195 + 1.81637i) q^{44} +(-1.27436 - 2.71588i) q^{45} +(6.22804 - 2.81136i) q^{46} +(-0.930514 + 5.27721i) q^{47} +(-1.23320 + 6.81757i) q^{48} +(1.43906 + 0.523776i) q^{49} +(0.613407 - 1.27426i) q^{50} +(0.108972 - 0.142367i) q^{51} +(-1.85511 + 4.73104i) q^{52} +4.33094i q^{53} +(-7.27696 - 1.02268i) q^{54} -1.21094i q^{55} +(4.48543 + 6.93774i) q^{56} +(-1.45550 - 0.189849i) q^{57} +(3.56176 + 1.71457i) q^{58} +(1.13544 + 0.413268i) q^{59} +(-1.79231 - 2.96439i) q^{60} +(2.31898 - 13.1516i) q^{61} +(3.76494 + 8.34052i) q^{62} +(-7.16584 + 5.04317i) q^{63} +(-0.590430 + 7.97818i) q^{64} +(-0.869031 - 2.38764i) q^{65} +(-2.48378 - 1.62143i) q^{66} +(-3.66108 - 4.36310i) q^{67} +(0.107893 - 0.176683i) q^{68} +(4.50504 + 7.05286i) q^{69} +(-3.97650 - 1.11815i) q^{70} +(3.66807 + 6.35329i) q^{71} +(-8.48022 - 0.293045i) q^{72} +(7.73645 - 13.3999i) q^{73} +(0.460445 - 0.449245i) q^{74} +(1.65251 + 0.518861i) q^{75} +(-1.69439 - 0.0417305i) q^{76} +(-3.48324 + 0.614189i) q^{77} +(-6.06097 - 1.41454i) q^{78} +(3.85350 - 4.59243i) q^{79} +(-2.41719 - 3.18703i) q^{80} +(-0.0430716 - 8.99990i) q^{81} +(3.21289 - 4.47032i) q^{82} +(-6.85563 - 5.75256i) q^{83} +(-7.61796 + 6.65910i) q^{84} +(0.0179744 + 0.101938i) q^{85} +(14.4671 - 9.86675i) q^{86} +(-1.45030 + 4.61903i) q^{87} +(-3.04857 - 1.56112i) q^{88} +(6.85757 + 3.95922i) q^{89} +(3.27694 - 2.69475i) q^{90} +(-6.42724 + 3.71077i) q^{91} +(6.02747 + 7.55341i) q^{92} +(-9.44512 + 6.03311i) q^{93} +(-7.55695 + 0.567492i) q^{94} +(0.649186 - 0.544731i) q^{95} +(-9.77359 + 0.690546i) q^{96} +(-12.0807 + 4.39700i) q^{97} +(-0.215306 + 2.15502i) q^{98} +(1.52741 - 3.29610i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) $ 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/540\mathbb{Z}\right)^\times$.

$n$	$217$	$271$	$461$
$\chi(n)$	$1$	$-1$	$e\left(\frac{13}{18}\right)$

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 $

$2$	0.349180	+	1.37043i	0.246907	+	0.969039i
$2$	0.349180	+	1.37043i	0.246907	+	0.969039i
$3$	−1.59941	+	0.664741i	−0.923421	+	0.383789i
$3$	−1.59941	+	0.664741i	−0.923421	+	0.383789i
$4$	−1.75615	+	0.957052i	−0.878073	+	0.478526i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$5$	0.342020	−	0.939693i	0.152956	−	0.420243i
$6$	−1.46946	−	1.95977i	−0.599906	−	0.800071i
$7$	−2.87648	−	0.507202i	−1.08721	−	0.191704i	−0.398808	−	0.917034i	$-0.630576\pi$
$7$	−2.87648	−	0.507202i	−1.08721	−	0.191704i	−0.688401	+	0.725330i	$0.741687\pi$
$8$	−1.92478	−	2.07249i	−0.680513	−	0.732736i
$9$	2.11624	−	2.12639i	0.705413	−	0.708797i
$10$	1.40721	+	0.140592i	0.444998	+	0.0444592i
$11$	1.13791	−	0.414164i	0.343092	−	0.124875i	−0.164727	−	0.986339i	$-0.552674\pi$
$11$	1.13791	−	0.414164i	0.343092	−	0.124875i	0.507819	+	0.861464i	$0.330452\pi$
$12$	2.17261	−	2.69810i	0.627179	−	0.778875i
$13$	1.94642	−	1.63324i	0.539841	−	0.452980i	−0.331643	−	0.943405i	$-0.607603\pi$
$13$	1.94642	−	1.63324i	0.539841	−	0.452980i	0.871484	+	0.490425i	$0.163158\pi$
$14$	−0.309327	−	4.11912i	−0.0826710	−	1.10088i
$15$	0.0776213	+	1.73031i	0.0200417	+	0.446764i
$16$	2.16810	−	3.36145i	0.542026	−	0.840362i
$17$	−0.0896428	+	0.0517553i	−0.0217416	+	0.0125525i	−0.510831	−	0.859681i	$-0.670662\pi$
$17$	−0.0896428	+	0.0517553i	−0.0217416	+	0.0125525i	0.489090	+	0.872233i	$0.337329\pi$
$18$	3.65301	+	2.15766i	0.861023	+	0.508565i
$19$	0.733915	+	0.423726i	0.168372	+	0.0972094i	0.581818	−	0.813319i	$-0.302342\pi$
$19$	0.733915	+	0.423726i	0.168372	+	0.0972094i	−0.413446	+	0.910529i	$0.635675\pi$
$20$	0.298697	+	1.97757i	0.0667906	+	0.442198i
$21$	4.93784	−	1.10089i	1.07753	−	0.240235i
$22$	0.964916	+	1.41480i	0.205721	+	0.301637i
$23$	−0.839030	−	4.75837i	−0.174950	−	0.992190i	−0.938202	−	0.346089i	$-0.887510\pi$
$23$	−0.839030	−	4.75837i	−0.174950	−	0.992190i	0.763252	−	0.646101i	$-0.223601\pi$
$24$	4.45619	+	2.03528i	0.909616	+	0.415451i
$25$	−0.766044	−	0.642788i	−0.153209	−	0.128558i
$26$	2.91790	+	2.09714i	0.572246	+	0.411283i
$27$	−1.97124	+	4.80773i	−0.379365	+	0.925247i
$28$	5.53695	−	1.86222i	1.04638	−	0.351927i
$29$	1.79670	−	2.14122i	0.333638	−	0.397615i	−0.572978	−	0.819571i	$-0.694212\pi$
$29$	1.79670	−	2.14122i	0.333638	−	0.397615i	0.906616	+	0.421956i	$0.138656\pi$
$30$	−2.34416	+	0.710564i	−0.427984	+	0.129731i
$31$	6.37237	−	1.12362i	1.14451	−	0.201808i	0.430933	−	0.902384i	$-0.358185\pi$
$31$	6.37237	−	1.12362i	1.14451	−	0.201808i	0.713578	+	0.700576i	$0.247073\pi$
$32$	5.36368	+	1.79748i	0.948174	+	0.317753i
$33$	−1.54467	+	1.41883i	−0.268893	+	0.246987i
$34$	−0.102228	−	0.104777i	−0.0175320	−	0.0179691i
$35$	−1.46043	+	2.52954i	−0.246858	+	0.427570i
$36$	−1.68136	+	5.75960i	−0.280227	+	0.959934i
$37$	−0.227440	−	0.393937i	−0.0373909	−	0.0647629i	0.846724	−	0.532032i	$-0.178571\pi$
$37$	−0.227440	−	0.393937i	−0.0373909	−	0.0647629i	−0.884115	+	0.467269i	$0.845238\pi$
$38$	−0.324418	+	1.15373i	−0.0526275	+	0.187160i
$39$	−2.02745	+	3.90610i	−0.324652	+	0.625476i
$40$	−2.60582	+	1.09987i	−0.412016	+	0.173905i
$41$	−2.50219	−	2.98199i	−0.390776	−	0.465709i	0.534409	−	0.845226i	$-0.320534\pi$
$41$	−2.50219	−	2.98199i	−0.390776	−	0.465709i	−0.925184	+	0.379518i	$0.876090\pi$
$42$	3.23289	+	6.38255i	0.498846	+	0.984849i
$43$	−4.23504	−	11.6357i	−0.645837	−	1.77442i	−0.632561	−	0.774511i	$-0.717996\pi$
$43$	−4.23504	−	11.6357i	−0.645837	−	1.77442i	−0.0132760	−	0.999912i	$-0.504226\pi$
$44$	−1.60195	+	1.81637i	−0.241504	+	0.273828i
$45$	−1.27436	−	2.71588i	−0.189970	−	0.404860i
$46$	6.22804	−	2.81136i	0.918274	−	0.414512i
$47$	−0.930514	+	5.27721i	−0.135729	+	0.769760i	0.838620	+	0.544717i	$0.183363\pi$
$47$	−0.930514	+	5.27721i	−0.135729	+	0.769760i	−0.974349	+	0.225042i	$0.927748\pi$
$48$	−1.23320	+	6.81757i	−0.177997	+	0.984031i
$49$	1.43906	+	0.523776i	0.205580	+	0.0748251i
$50$	0.613407	−	1.27426i	0.0867489	−	0.180207i
$51$	0.108972	−	0.142367i	0.0152591	−	0.0199354i
$52$	−1.85511	+	4.73104i	−0.257257	+	0.656078i
$53$			4.33094i			0.594900i	0.954737	+	0.297450i	$0.0961361\pi$
$53$			4.33094i			0.594900i	−0.954737	+	0.297450i	$0.903864\pi$
$54$	−7.27696	−	1.02268i	−0.990269	−	0.139169i
$55$		−	1.21094i		−	0.163282i
$56$	4.48543	+	6.93774i	0.599391	+	0.927094i
$57$	−1.45550	−	0.189849i	−0.192786	−	0.0251461i
$58$	3.56176	+	1.71457i	0.467682	+	0.225135i
$59$	1.13544	+	0.413268i	0.147822	+	0.0538029i	0.414872	−	0.909880i	$-0.363826\pi$
$59$	1.13544	+	0.413268i	0.147822	+	0.0538029i	−0.267049	+	0.963683i	$0.586049\pi$
$60$	−1.79231	−	2.96439i	−0.231386	−	0.382701i
$61$	2.31898	−	13.1516i	0.296915	−	1.68389i	−0.362400	−	0.932023i	$-0.618043\pi$
$61$	2.31898	−	13.1516i	0.296915	−	1.68389i	0.659315	−	0.751867i	$-0.270846\pi$
$62$	3.76494	+	8.34052i	0.478148	+	1.05925i
$63$	−7.16584	+	5.04317i	−0.902810	+	0.635380i
$64$	−0.590430	+	7.97818i	−0.0738038	+	0.997273i
$65$	−0.869031	−	2.38764i	−0.107790	−	0.296151i
$66$	−2.48378	−	1.62143i	−0.305732	−	0.199584i
$67$	−3.66108	−	4.36310i	−0.447272	−	0.533038i	0.494551	−	0.869149i	$-0.335333\pi$
$67$	−3.66108	−	4.36310i	−0.447272	−	0.533038i	−0.941822	+	0.336111i	$0.890888\pi$
$68$	0.107893	−	0.176683i	0.0130840	−	0.0214259i
$69$	4.50504	+	7.05286i	0.542343	+	0.849065i
$70$	−3.97650	−	1.11815i	−0.475283	−	0.133645i
$71$	3.66807	+	6.35329i	0.435320	+	0.753997i	0.997322	−	0.0731396i	$-0.0233018\pi$
$71$	3.66807	+	6.35329i	0.435320	+	0.753997i	−0.562002	+	0.827136i	$0.689969\pi$
$72$	−8.48022	−	0.293045i	−0.999403	−	0.0345357i
$73$	7.73645	−	13.3999i	0.905483	−	1.56834i	0.0852159	−	0.996363i	$-0.472842\pi$
$73$	7.73645	−	13.3999i	0.905483	−	1.56834i	0.820267	−	0.571980i	$-0.193825\pi$
$74$	0.460445	−	0.449245i	0.0535257	−	0.0522236i
$75$	1.65251	+	0.518861i	0.190815	+	0.0599129i
$76$	−1.69439	−	0.0417305i	−0.194360	−	0.00478681i
$77$	−3.48324	+	0.614189i	−0.396952	+	0.0699933i
$78$	−6.06097	−	1.41454i	−0.686270	−	0.160166i
$79$	3.85350	−	4.59243i	0.433553	−	0.516688i	−0.504391	−	0.863475i	$-0.668283\pi$
$79$	3.85350	−	4.59243i	0.433553	−	0.516688i	0.937944	+	0.346787i	$0.112727\pi$
$80$	−2.41719	−	3.18703i	−0.270250	−	0.356321i
$81$	−0.0430716	−	8.99990i	−0.00478573	−	0.999989i
$82$	3.21289	−	4.47032i	0.354804	−	0.493664i
$83$	−6.85563	−	5.75256i	−0.752503	−	0.631425i	0.183661	−	0.982990i	$-0.441205\pi$
$83$	−6.85563	−	5.75256i	−0.752503	−	0.631425i	−0.936164	+	0.351565i	$0.885650\pi$
$84$	−7.61796	+	6.65910i	−0.831188	+	0.726567i
$85$	0.0179744	+	0.101938i	0.00194960	+	0.0110567i
$86$	14.4671	−	9.86675i	1.56002	−	1.06396i
$87$	−1.45030	+	4.61903i	−0.155489	+	0.495212i
$88$	−3.04857	−	1.56112i	−0.324979	−	0.166416i
$89$	6.85757	+	3.95922i	0.726901	+	0.419676i	0.817287	−	0.576230i	$-0.195477\pi$
$89$	6.85757	+	3.95922i	0.726901	+	0.419676i	−0.0903866	+	0.995907i	$0.528810\pi$
$90$	3.27694	−	2.69475i	0.345420	−	0.284051i
$91$	−6.42724	+	3.71077i	−0.673758	+	0.388994i
$92$	6.02747	+	7.55341i	0.628407	+	0.787497i
$93$	−9.44512	+	6.03311i	−0.979414	+	0.625604i
$94$	−7.55695	+	0.567492i	−0.779440	+	0.0585323i
$95$	0.649186	−	0.544731i	0.0666050	−	0.0558883i
$96$	−9.77359	+	0.690546i	−0.997513	+	0.0704785i
$97$	−12.0807	+	4.39700i	−1.22660	+	0.446448i	−0.872433	−	0.488733i	$-0.837459\pi$
$97$	−12.0807	+	4.39700i	−1.22660	+	0.446448i	−0.354171	+	0.935181i	$0.615237\pi$
$98$	−0.215306	+	2.15502i	−0.0217492	+	0.217690i
$99$	1.52741	−	3.29610i	0.153510	−	0.331271i
$100$	1.96047	+	0.395685i	0.196047	+	0.0395685i
$101$	−10.6992	−	1.88656i	−1.06461	−	0.187719i	−0.386208	−	0.922412i	$-0.626215\pi$
$101$	−10.6992	−	1.88656i	−1.06461	−	0.187719i	−0.678400	+	0.734692i	$0.737327\pi$
$102$	0.233155	+	0.0996264i	0.0230858	+	0.00986449i
$103$	5.37436	−	14.7659i	0.529551	−	1.45493i	−0.330049	−	0.943964i	$-0.607065\pi$
$103$	5.37436	−	14.7659i	0.529551	−	1.45493i	0.859600	−	0.510967i	$-0.170712\pi$
$104$	−7.13132	−	0.890307i	−0.699284	−	0.0873018i
$105$	0.654340	−	5.01658i	0.0638571	−	0.489568i
$106$	−5.93524	+	1.51228i	−0.576481	+	0.146885i
$107$	−11.1722			−1.08006			−0.540030	−	0.841646i	$-0.681587\pi$
$107$	−11.1722			−1.08006			−0.540030	+	0.841646i	$0.681587\pi$
$108$	−1.13946	−	10.3296i	−0.109644	−	0.993971i
$109$	−0.961755			−0.0921195			−0.0460597	−	0.998939i	$-0.514666\pi$
$109$	−0.961755			−0.0921195			−0.0460597	+	0.998939i	$0.514666\pi$
$110$	1.65950	−	0.422834i	0.158227	−	0.0403157i
$111$	0.625636	+	0.478879i	0.0593827	+	0.0454532i
$112$	−7.94145	+	8.56948i	−0.750396	+	0.809740i
$113$	−6.83345	+	18.7747i	−0.642837	+	1.76618i	−0.000209607		1.00000i	$0.500067\pi$
$113$	−6.83345	+	18.7747i	−0.642837	+	1.76618i	−0.642627	+	0.766179i	$0.722156\pi$
$114$	−0.248057	−	2.06095i	−0.0232327	−	0.193026i
$115$	−4.75837	−	0.839030i	−0.443721	−	0.0782399i
$116$	−1.10601	+	5.47983i	−0.102690	+	0.508790i
$117$	0.646183	−	7.59519i	0.0597397	−	0.702176i
$118$	−0.169880	+	1.70035i	−0.0156387	+	0.156530i
$119$	0.284107	−	0.103406i	0.0260440	−	0.00947925i
$120$	3.43665	−	3.49134i	0.313722	−	0.318714i
$121$	−7.30319	+	6.12810i	−0.663926	+	0.557100i
$122$	18.8331	−	1.41427i	1.70507	−	0.128042i
$123$	5.98428	+	3.10612i	0.539584	+	0.280070i
$124$	−10.1154	+	8.07193i	−0.908394	+	0.724880i
$125$	−0.866025	+	0.500000i	−0.0774597	+	0.0447214i
$126$	−9.41347	−	8.05929i	−0.838618	−	0.717979i
$127$	8.51273	+	4.91483i	0.755383	+	0.436120i	0.827635	−	0.561266i	$-0.189686\pi$
$127$	8.51273	+	4.91483i	0.755383	+	0.436120i	−0.0722529	+	0.997386i	$0.523019\pi$
$128$	−11.1397	+	1.97668i	−0.984619	+	0.174715i
$129$	14.5083	+	15.7950i	1.27738	+	1.39067i
$130$	2.96864	−	2.02466i	0.260367	−	0.177575i
$131$	−2.52630	−	14.3274i	−0.220724	−	1.25179i	−0.870692	−	0.491828i	$-0.836329\pi$
$131$	−2.52630	−	14.3274i	−0.220724	−	1.25179i	0.649968	−	0.759961i	$-0.274782\pi$
$132$	1.35477	−	3.97001i	0.117918	−	0.345545i
$133$	−1.89618	−	1.59108i	−0.164420	−	0.137964i
$134$	4.70094	−	6.54075i	0.406100	−	0.565035i
$135$	3.84358	+	3.49670i	0.330803	+	0.300948i
$136$	0.279805	+	0.0861662i	0.0239931	+	0.00738869i
$137$	−3.15192	+	3.75631i	−0.269286	+	0.320923i	−0.883693	−	0.468066i	$-0.844951\pi$
$137$	−3.15192	+	3.75631i	−0.269286	+	0.320923i	0.614407	+	0.788989i	$0.289395\pi$
$138$	−8.09237	+	8.63655i	−0.688869	+	0.735192i
$139$	20.2391	−	3.56870i	1.71666	−	0.302694i	0.773196	−	0.634167i	$-0.218657\pi$
$139$	20.2391	−	3.56870i	1.71666	−	0.302694i	0.943464	+	0.331474i	$0.107546\pi$
$140$	0.143830	−	5.83995i	0.0121558	−	0.493566i
$141$	−2.01970	−	9.05898i	−0.170090	−	0.762904i
$142$	−7.42591	+	7.24527i	−0.623168	+	0.608010i
$143$	1.53842	−	2.66462i	0.128649	−	0.222827i
$144$	−2.55952	−	11.7239i	−0.213294	−	0.976988i
$145$	−1.39758	−	2.42068i	−0.116063	−	0.201027i
$146$	21.0651	+	5.92327i	1.74336	+	0.490213i
$147$	−2.64983	+	0.118871i	−0.218554	+	0.00980428i
$148$	0.776436	+	0.474140i	0.0638226	+	0.0389741i
$149$	−6.87090	−	8.18842i	−0.562886	−	0.670821i	0.407269	−	0.913308i	$-0.366481\pi$
$149$	−6.87090	−	8.18842i	−0.562886	−	0.670821i	−0.970155	+	0.242487i	$0.922037\pi$
$150$	−0.134039	+	2.44582i	−0.0109443	+	0.199700i
$151$	−2.43599	−	6.69283i	−0.198238	−	0.544655i	0.800247	−	0.599670i	$-0.204701\pi$
$151$	−2.43599	−	6.69283i	−0.198238	−	0.544655i	−0.998486	+	0.0550153i	$0.982479\pi$
$152$	−0.534458	−	2.33661i	−0.0433503	−	0.189524i
$153$	−0.0796536	+	0.300142i	−0.00643961	+	0.0242651i
$154$	−2.05798	−	4.55906i	−0.165837	−	0.367380i
$155$	1.12362	−	6.37237i	0.0902513	−	0.511841i
$156$	−0.177838	−	8.80006i	−0.0142385	−	0.704568i
$157$	−5.35278	−	1.94825i	−0.427198	−	0.155488i	0.119468	−	0.992838i	$-0.461881\pi$
$157$	−5.35278	−	1.94825i	−0.427198	−	0.155488i	−0.546666	+	0.837351i	$0.684103\pi$
$158$	7.63916	+	3.67737i	0.607739	+	0.292556i
$159$	−2.87895	−	6.92695i	−0.228316	−	0.549343i
$160$	3.52357	−	4.42544i	0.278562	−	0.349861i
$161$			14.1129i			1.11226i
$162$	12.3187	−	3.20161i	0.967846	−	0.251542i
$163$			2.37802i			0.186261i	0.995654	+	0.0931304i	$0.0296873\pi$
$163$			2.37802i			0.186261i	−0.995654	+	0.0931304i	$0.970313\pi$
$164$	7.24813	+	2.84209i	0.565984	+	0.221930i
$165$	0.804959	+	1.93678i	0.0626659	+	0.150778i
$166$	5.48962	−	11.4038i	0.426077	−	0.885108i
$167$	17.3710	+	6.32252i	1.34421	+	0.489251i	0.911135	−	0.412108i	$-0.135207\pi$
$167$	17.3710	+	6.32252i	1.34421	+	0.489251i	0.433072	+	0.901359i	$0.357430\pi$
$168$	−11.7859	−	8.11465i	−0.909299	−	0.626059i
$169$	−1.13634	+	6.44453i	−0.0874111	+	0.495733i
$170$	−0.133423	+	0.0602274i	−0.0102330	+	0.00461923i
$171$	2.45414	−	0.663884i	0.187673	−	0.0507685i
$172$	18.5733	+	16.3808i	1.41620	+	1.24902i
$173$	3.44742	+	9.47170i	0.262102	+	0.720120i	0.999025	+	0.0441434i	$0.0140559\pi$
$173$	3.44742	+	9.47170i	0.262102	+	0.720120i	−0.736923	+	0.675977i	$0.763722\pi$
$174$	−6.83647	−	0.374662i	−0.518272	−	0.0284030i
$175$	1.87749	+	2.23751i	0.141925	+	0.169140i
$176$	1.07491	−	4.72296i	0.0810243	−	0.356007i
$177$	−2.09076	+	0.0937909i	−0.157151	+	0.00704975i
$178$	−3.03130	+	10.7803i	−0.227206	+	0.808016i
$179$	−4.32705	−	7.49467i	−0.323419	−	0.560178i	0.657772	−	0.753217i	$-0.271499\pi$
$179$	−4.32705	−	7.49467i	−0.323419	−	0.560178i	−0.981191	+	0.193039i	$0.938166\pi$
$180$	4.83720	+	3.54986i	0.360543	+	0.264591i
$181$	1.01701	−	1.76151i	0.0755936	−	0.130932i	−0.825751	−	0.564035i	$-0.809248\pi$
$181$	1.01701	−	1.76151i	0.0755936	−	0.130932i	0.901344	+	0.433103i	$0.142581\pi$
$182$	−7.32961	−	7.51235i	−0.543307	−	0.556852i
$183$	5.03340	+	22.5763i	0.372080	+	1.66889i
$184$	−8.24673	+	10.8977i	−0.607957	+	0.803390i
$185$	−0.447969	+	0.0789890i	−0.0329353	+	0.00580738i
$186$	−11.5660	−	10.8372i	−0.848059	−	0.794624i
$187$	−0.0805700	+	0.0960196i	−0.00589186	+	0.00702165i
$188$	−3.41644	−	10.1581i	−0.249170	−	0.740856i
$189$	8.10872	−	12.8295i	0.589823	−	0.933211i
$190$	0.973198	+	0.699453i	0.0706032	+	0.0507437i
$191$	−4.99033	−	4.18738i	−0.361088	−	0.302988i	0.444136	−	0.895959i	$-0.353511\pi$
$191$	−4.99033	−	4.18738i	−0.361088	−	0.302988i	−0.805224	+	0.592971i	$0.797955\pi$
$192$	−4.35909	−	13.1529i	−0.314590	−	0.949228i
$193$	4.23290	+	24.0060i	0.304691	+	1.72799i	0.624956	+	0.780660i	$0.285117\pi$
$193$	4.23290	+	24.0060i	0.304691	+	1.72799i	−0.320265	+	0.947328i	$0.603772\pi$
$194$	−10.2441	−	15.0203i	−0.735483	−	1.07840i
$195$	2.97710	+	3.24114i	0.213195	+	0.232103i
$196$	−3.02848	+	0.457430i	−0.216320	+	0.0326735i
$197$	23.4395	+	13.5328i	1.67000	+	0.964174i	0.967635	+	0.252355i	$0.0812051\pi$
$197$	23.4395	+	13.5328i	1.67000	+	0.964174i	0.702363	+	0.711819i	$0.252128\pi$
$198$	5.05041	+	0.942269i	0.358917	+	0.0669641i
$199$	−6.83785	+	3.94784i	−0.484723	+	0.279855i	−0.722382	−	0.691494i	$-0.756953\pi$
$199$	−6.83785	+	3.94784i	−0.484723	+	0.279855i	0.237660	+	0.971348i	$0.423620\pi$
$200$	0.142297	+	2.82485i	0.0100619	+	0.199747i
$201$	8.75591	+	4.54473i	0.617594	+	0.320561i
$202$	−1.15055	−	15.3212i	−0.0809525	−	1.07800i
$203$	−6.25421	+	5.24790i	−0.438959	+	0.368330i
$204$	−0.0551178	+	0.354310i	−0.00385902	+	0.0248067i
$205$	−3.65795	+	1.33139i	−0.255483	+	0.0929880i
$206$	22.1123	+	2.20921i	1.54063	+	0.153923i
$207$	−11.8937	−	8.28575i	−0.826673	−	0.575899i
$208$	−1.27001	−	10.0838i	−0.0880595	−	0.699189i
$209$	1.01062	+	0.178199i	0.0699060	+	0.0123263i
$210$	7.10335	−	0.854963i	0.490178	−	0.0589980i
$211$	−7.37653	+	20.2669i	−0.507822	+	1.39523i	0.375658	+	0.926758i	$0.377417\pi$
$211$	−7.37653	+	20.2669i	−0.507822	+	1.39523i	−0.883479	+	0.468470i	$0.844805\pi$
$212$	−4.14493	−	7.60576i	−0.284675	−	0.522366i
$213$	−10.0901	−	7.72321i	−0.691359	−	0.529185i
$214$	−3.90112	−	15.3107i	−0.266675	−	1.04662i
$215$	−12.3824			−0.844474
$216$	13.7582	−	5.16845i	0.936125	−	0.351669i
$217$	−18.8999			−1.28301
$218$	−0.335826	−	1.31802i	−0.0227450	−	0.0892673i
$219$	−3.46629	+	26.5747i	−0.234230	+	1.79575i
$220$	1.15893	+	2.12658i	0.0781349	+	0.143374i
$221$	−0.0899539	+	0.247146i	−0.00605096	+	0.0166249i
$222$	−0.437810	+	1.02460i	−0.0293839	+	0.0687669i
$223$	26.9024	+	4.74362i	1.80152	+	0.317656i	0.970953	−	0.239268i	$-0.0769076\pi$
$223$	26.9024	+	4.74362i	1.80152	+	0.317656i	0.830563	+	0.556924i	$0.188019\pi$
$224$	−14.5169	−	7.89090i	−0.969948	−	0.527233i
$225$	−2.98795	+	0.268618i	−0.199197	+	0.0179079i
$226$	−28.1155	−	2.80899i	−1.87022	−	0.186851i
$227$	−13.4682	+	4.90201i	−0.893913	+	0.325358i	−0.747811	−	0.663912i	$-0.768895\pi$
$227$	−13.4682	+	4.90201i	−0.893913	+	0.325358i	−0.146102	+	0.989270i	$0.546673\pi$
$228$	2.73777	−	1.05959i	0.181313	−	0.0701728i
$229$	−1.39433	+	1.16998i	−0.0921401	+	0.0773147i	−0.687694	−	0.726001i	$-0.741377\pi$
$229$	−1.39433	+	1.16998i	−0.0921401	+	0.0773147i	0.595554	+	0.803315i	$0.296933\pi$
$230$	−0.511698	−	6.81398i	−0.0337404	−	0.449301i
$231$	5.16285	−	3.29779i	0.339691	−	0.216979i
$232$	−7.89591	+	0.397745i	−0.518392	+	0.0261132i
$233$	23.4757	−	13.5537i	1.53794	−	0.887932i	0.538985	−	0.842315i	$-0.318808\pi$
$233$	23.4757	−	13.5537i	1.53794	−	0.887932i	0.998959	−	0.0456170i	$-0.0145254\pi$
$234$	10.6343	−	1.76654i	0.695186	−	0.115482i
$235$	4.64070	+	2.67931i	0.302726	+	0.174779i
$236$	−2.38952	+	0.360920i	−0.155545	+	0.0234939i
$237$	−3.11056	+	9.90676i	−0.202053	+	0.643513i
$238$	0.240915	+	0.353240i	0.0156162	+	0.0228972i
$239$	2.29474	+	13.0141i	0.148434	+	0.841813i	0.964545	+	0.263918i	$0.0850147\pi$
$239$	2.29474	+	13.0141i	0.148434	+	0.841813i	−0.816111	+	0.577895i	$0.803874\pi$
$240$	5.98464	+	3.49057i	0.386307	+	0.225316i
$241$	0.343944	+	0.288604i	0.0221554	+	0.0185906i	0.653798	−	0.756669i	$-0.273175\pi$
$241$	0.343944	+	0.288604i	0.0221554	+	0.0185906i	−0.631643	+	0.775260i	$0.717619\pi$
$242$	−10.9483	−	7.86869i	−0.703780	−	0.505818i
$243$	6.05149	+	14.3659i	0.388203	+	0.921574i
$244$	8.51429	+	25.3155i	0.545071	+	1.62066i
$245$	0.984376	−	1.17313i	0.0628895	−	0.0749488i
$246$	−2.16713	+	9.28562i	−0.138171	+	0.592030i
$247$	2.12056	−	0.373911i	0.134928	−	0.0237914i
$248$	−14.5941	−	11.0439i	−0.926727	−	0.701291i
$249$	14.7889	+	4.64349i	0.937211	+	0.294269i
$250$	−0.987613	−	1.01224i	−0.0624621	−	0.0640194i
$251$	12.4150	−	21.5034i	0.783626	−	1.35728i	−0.146191	−	0.989256i	$-0.546701\pi$
$251$	12.4150	−	21.5034i	0.783626	−	1.35728i	0.929817	−	0.368023i	$-0.119965\pi$
$252$	7.75769	−	15.7146i	0.488688	−	0.989928i
$253$	−2.92549	−	5.06709i	−0.183924	−	0.318565i
$254$	−3.76294	+	13.3822i	−0.236108	+	0.839677i
$255$	−0.0965110	−	0.151093i	−0.00604375	−	0.00946179i
$256$	−6.59865	−	14.5759i	−0.412416	−	0.910996i
$257$	−8.05793	−	9.60307i	−0.502640	−	0.599023i	0.453745	−	0.891132i	$-0.350088\pi$
$257$	−8.05793	−	9.60307i	−0.502640	−	0.599023i	−0.956385	+	0.292108i	$0.905643\pi$
$258$	−16.5799	+	25.3979i	−1.03222	+	1.58120i
$259$	0.454421	+	1.24851i	0.0282364	+	0.0775787i
$260$	3.81124	+	3.36134i	0.236363	+	0.208462i
$261$	−0.750831	−	8.35182i	−0.0464753	−	0.516964i
$262$	18.7525	−	8.46495i	1.15853	−	0.522967i
$263$	−1.84330	+	10.4539i	−0.113663	+	0.644613i	0.873741	+	0.486392i	$0.161687\pi$
$263$	−1.84330	+	10.4539i	−0.113663	+	0.644613i	−0.987404	+	0.158222i	$0.949424\pi$
$264$	5.91367	+	0.470370i	0.363961	+	0.0289492i
$265$	4.06975	+	1.48127i	0.250003	+	0.0909935i
$266$	1.51836	−	3.15415i	0.0930965	−	0.193394i
$267$	−13.5999	−	1.77391i	−0.832302	−	0.108562i
$268$	10.6051	+	4.15841i	0.647810	+	0.254015i
$269$			21.0278i			1.28208i	0.767505	+	0.641042i	$0.221498\pi$
$269$			21.0278i			1.28208i	−0.767505	+	0.641042i	$0.778502\pi$
$270$	−3.44987	+	6.48833i	−0.209952	+	0.394867i
$271$			24.9251i			1.51409i	0.653360	+	0.757047i	$0.273359\pi$
$271$			24.9251i			1.51409i	−0.653360	+	0.757047i	$0.726641\pi$
$272$	−0.0203822	+	0.413541i	−0.00123585	+	0.0250746i
$273$	7.81311	−	10.2075i	0.472871	−	0.617786i
$274$	−6.24834	−	3.00785i	−0.377476	−	0.181711i
$275$	−1.13791	−	0.414164i	−0.0686184	−	0.0249750i
$276$	−14.6615	−	8.07431i	−0.882517	−	0.486016i
$277$	4.62328	−	26.2199i	0.277786	−	1.57540i	−0.452184	−	0.891925i	$-0.649355\pi$
$277$	4.62328	−	26.2199i	0.277786	−	1.57540i	0.729970	−	0.683479i	$-0.239534\pi$
$278$	11.9577	+	26.4902i	0.717178	+	1.58877i
$279$	11.0962	−	15.9280i	0.664312	−	0.953584i
$280$	8.05345	−	1.84208i	0.481286	−	0.110086i
$281$	5.05136	+	13.8785i	0.301339	+	0.827921i	0.994268	+	0.106916i	$0.0340975\pi$
$281$	5.05136	+	13.8785i	0.301339	+	0.827921i	−0.692929	+	0.721005i	$0.743680\pi$
$282$	11.7094	−	5.93107i	0.697287	−	0.353190i
$283$	−12.5248	−	14.9265i	−0.744524	−	0.887289i	0.252241	−	0.967665i	$-0.418833\pi$
$283$	−12.5248	−	14.9265i	−0.744524	−	0.887289i	−0.996765	+	0.0803753i	$0.974388\pi$
$284$	−12.5221	−	7.64677i	−0.743050	−	0.453752i
$285$	−0.676210	+	1.30279i	−0.0400552	+	0.0771706i
$286$	4.18885	+	1.17786i	0.247692	+	0.0696484i
$287$	5.68503	+	9.84676i	0.335577	+	0.581236i
$288$	15.1730	−	7.60138i	0.894076	−	0.447916i
$289$	−8.49464	+	14.7132i	−0.499685	+	0.865480i
$290$	2.82937	−	2.76054i	0.166146	−	0.162105i
$291$	16.3991	−	15.0631i	0.961331	−	0.883016i
$292$	−0.761922	+	30.9364i	−0.0445881	+	1.81042i
$293$	−7.79480	+	1.37443i	−0.455377	+	0.0802953i	−0.396632	−	0.917978i	$-0.629821\pi$
$293$	−7.79480	+	1.37443i	−0.455377	+	0.0802953i	−0.0587452	+	0.998273i	$0.518710\pi$
$294$	−1.08817	−	3.58989i	−0.0634634	−	0.209367i
$295$	0.776689	−	0.925622i	0.0452206	−	0.0538918i
$296$	−0.378659	+	1.22961i	−0.0220091	+	0.0714696i
$297$	−0.251897	+	6.28716i	−0.0146166	+	0.364818i
$298$	8.82246	−	12.2753i	0.511071	−	0.711089i
$299$	−9.40469	−	7.89147i	−0.543887	−	0.456376i
$300$	−3.39862	+	0.670340i	−0.196220	+	0.0387021i
$301$	6.28038	+	35.6178i	0.361995	+	2.05298i
$302$	8.32144	−	5.67535i	0.478845	−	0.326580i
$303$	18.3665	−	4.09481i	1.05513	−	0.235241i
$304$	3.01554	−	1.54833i	0.172953	−	0.0888030i
$305$	−11.5653	−	6.67724i	−0.662228	−	0.382338i
$306$	−0.439137	−	0.00435592i	−0.0251038	−	0.000249011i
$307$	19.8140	−	11.4396i	1.13084	−	0.652893i	0.186696	−	0.982418i	$-0.440222\pi$
$307$	19.8140	−	11.4396i	1.13084	−	0.652893i	0.944147	+	0.329525i	$0.106889\pi$
$308$	5.52926	−	4.41224i	0.315059	−	0.251411i
$309$	1.21971	+	27.1894i	0.0693867	+	1.54675i
$310$	9.12522	−	0.685261i	0.518277	−	0.0389202i
$311$	−2.81537	+	2.36238i	−0.159645	+	0.133958i	−0.719111	−	0.694895i	$-0.755451\pi$
$311$	−2.81537	+	2.36238i	−0.159645	+	0.133958i	0.559466	+	0.828853i	$0.311006\pi$
$312$	11.9977	−	3.31652i	0.679239	−	0.187761i
$313$	23.4919	−	8.55035i	1.32784	−	0.483294i	0.421878	−	0.906653i	$-0.361371\pi$
$313$	23.4919	−	8.55035i	1.32784	−	0.483294i	0.905962	+	0.423359i	$0.139149\pi$
$314$	0.800858	−	8.01589i	0.0451950	−	0.452363i
$315$	2.28817	+	8.45855i	0.128924	+	0.476585i
$316$	−2.37213	+	11.7530i	−0.133443	+	0.661157i
$317$	−23.1396	−	4.08013i	−1.29965	−	0.229163i	−0.519345	−	0.854565i	$-0.673824\pi$
$317$	−23.1396	−	4.08013i	−1.29965	−	0.229163i	−0.780303	+	0.625402i	$0.784935\pi$
$318$	8.48762	−	6.36415i	0.475962	−	0.356884i
$319$	1.15766	−	3.18064i	0.0648164	−	0.178082i
$320$	7.29510	+	3.28352i	0.407808	+	0.183554i
$321$	17.8690	−	7.42664i	0.997350	−	0.414515i
$322$	−19.3408	+	4.92796i	−1.07782	+	0.274624i
$323$	−0.0877203			−0.00488089
$324$	8.68901	+	15.7639i	0.482723	+	0.875773i
$325$	−2.54088			−0.140942
$326$	−3.25890	+	0.830356i	−0.180494	+	0.0459892i
$327$	1.53824	−	0.639318i	0.0850650	−	0.0353544i
$328$	−1.36398	+	10.9254i	−0.0753133	+	0.603256i
$329$	5.35322	−	14.7078i	0.295132	−	0.810870i
$330$	−2.37315	+	1.77942i	−0.130638	+	0.0979541i
$331$	−13.5456	−	2.38846i	−0.744536	−	0.131282i	−0.211504	−	0.977377i	$-0.567836\pi$
$331$	−13.5456	−	2.38846i	−0.744536	−	0.131282i	−0.533032	+	0.846095i	$0.678947\pi$
$332$	17.5450	+	3.54114i	0.962906	+	0.194345i
$333$	−1.31898	−	0.350039i	−0.0722797	−	0.0191820i
$334$	−2.59896	+	26.0134i	−0.142209	+	1.42339i
$335$	−5.35214	+	1.94802i	−0.292419	+	0.106432i
$336$	7.00516	−	18.9851i	0.382163	−	1.03572i
$337$	−4.44002	+	3.72562i	−0.241863	+	0.202947i	−0.755659	−	0.654965i	$-0.772683\pi$
$337$	−4.44002	+	3.72562i	−0.241863	+	0.202947i	0.513796	+	0.857912i	$0.328239\pi$
$338$	−9.22856	+	0.693021i	−0.501967	+	0.0376954i
$339$	−1.55085	−	34.5710i	−0.0842304	−	1.87764i
$340$	−0.129126	−	0.161816i	−0.00700283	−	0.00877569i
$341$	6.78580	−	3.91778i	0.367471	−	0.212160i
$342$	1.76674	+	3.13141i	0.0955345	+	0.169327i
$343$	13.8330	+	7.98648i	0.746911	+	0.431229i
$344$	−15.9633	+	31.1732i	−0.860682	+	1.68075i
$345$	8.16834	−	1.82113i	0.439769	−	0.0980465i
$346$	−11.7765	+	8.03177i	−0.633110	+	0.431790i
$347$	4.21175	+	23.8860i	0.226098	+	1.28227i	0.860574	+	0.509325i	$0.170105\pi$
$347$	4.21175	+	23.8860i	0.226098	+	1.28227i	−0.634476	+	0.772943i	$0.718784\pi$
$348$	−1.87371	−	9.49972i	−0.100441	−	0.509238i
$349$	−13.6099	−	11.4200i	−0.728519	−	0.611300i	0.201209	−	0.979548i	$-0.435513\pi$
$349$	−13.6099	−	11.4200i	−0.728519	−	0.611300i	−0.929727	+	0.368249i	$0.879958\pi$
$350$	−2.41076	+	3.35426i	−0.128861	+	0.179293i
$351$	4.01532	+	12.5774i	0.214322	+	0.671331i
$352$	6.84782	−	0.176078i	0.364990	−	0.00938499i
$353$	17.2940	−	20.6102i	0.920468	−	1.09697i	−0.0745443	−	0.997218i	$-0.523750\pi$
$353$	17.2940	−	20.6102i	0.920468	−	1.09697i	0.995012	−	0.0997533i	$-0.0318053\pi$
$354$	−0.858584	−	2.83249i	−0.0456332	−	0.150545i
$355$	7.22469	−	1.27391i	0.383447	−	0.0676120i
$356$	−15.8321	−	0.389922i	−0.839098	−	0.0206658i
$357$	−0.385665	+	0.354247i	−0.0204116	+	0.0187487i
$358$	8.75999	−	8.54690i	0.462980	−	0.451718i
$359$	12.3865	−	21.4540i	0.653734	−	1.13230i	−0.328476	−	0.944512i	$-0.606535\pi$
$359$	12.3865	−	21.4540i	0.653734	−	1.13230i	0.982210	−	0.187787i	$-0.0601316\pi$
$360$	−3.17578	+	7.86857i	−0.167378	+	0.414710i
$361$	−9.14091	−	15.8325i	−0.481101	−	0.833291i
$362$	2.76914	+	0.778653i	0.145543	+	0.0409251i
$363$	7.60721	−	14.6561i	0.399275	−	0.769245i
$364$	7.73578	−	12.6679i	0.405465	−	0.663976i
$365$	−9.94579	−	11.8529i	−0.520586	−	0.620411i
$366$	−29.1817	+	14.7811i	−1.52535	+	0.772621i
$367$	−1.65466	−	4.54614i	−0.0863725	−	0.237306i	0.888985	−	0.457936i	$-0.151411\pi$
$367$	−1.65466	−	4.54614i	−0.0863725	−	0.237306i	−0.975358	+	0.220629i	$0.929189\pi$
$368$	−17.8141	−	7.49630i	−0.928625	−	0.390771i
$369$	−11.6361	−	0.989976i	−0.605751	−	0.0515361i
$370$	−0.264670	−	0.586328i	−0.0137596	−	0.0304817i
$371$	2.19666	−	12.4579i	0.114045	−	0.646781i
$372$	10.8130	−	19.6345i	0.560629	−	1.01800i
$373$	7.65228	+	2.78520i	0.396220	+	0.144212i	0.532443	−	0.846466i	$-0.321274\pi$
$373$	7.65228	+	2.78520i	0.396220	+	0.144212i	−0.136223	+	0.990678i	$0.543496\pi$
$374$	−0.159721	−	0.0768873i	−0.00825900	−	0.00397575i
$375$	1.05276	−	1.37539i	0.0543643	−	0.0710248i
$376$	12.7280	−	8.22899i	0.656396	−	0.424378i
$377$		−	7.10217i		−	0.365780i
$378$	20.4134	+	6.63261i	1.04995	+	0.341145i
$379$		−	10.0011i		−	0.513719i	−0.966449	−	0.256860i	$-0.917312\pi$
$379$		−	10.0011i		−	0.513719i	0.966449	−	0.256860i	$-0.0826878\pi$
$380$	−0.618729	+	1.57793i	−0.0317401	+	0.0809462i
$381$	−16.8825	−	2.20207i	−0.864914	−	0.112816i
$382$	3.99599	−	8.30104i	0.204452	−	0.424718i
$383$	−20.7270	−	7.54402i	−1.05910	−	0.385481i	−0.247011	−	0.969013i	$-0.579448\pi$
$383$	−20.7270	−	7.54402i	−1.05910	−	0.385481i	−0.812090	+	0.583532i	$0.801670\pi$
$384$	16.5030	−	10.5665i	0.842164	−	0.539221i
$385$	−0.614189	+	3.48324i	−0.0313019	+	0.177522i
$386$	−31.4204	+	14.1833i	−1.59926	+	0.721910i
$387$	−33.7043	−	15.6185i	−1.71329	−	0.793933i
$388$	17.0073	−	19.2836i	0.863412	−	0.978976i
$389$	2.42230	+	6.65520i	0.122815	+	0.337432i	0.985830	−	0.167746i	$-0.0536489\pi$
$389$	2.42230	+	6.65520i	0.122815	+	0.337432i	−0.863015	+	0.505178i	$0.831427\pi$
$390$	−3.40221	+	5.21165i	−0.172278	+	0.263902i
$391$	0.321484	+	0.383130i	0.0162582	+	0.0193757i
$392$	−1.68436	−	3.99060i	−0.0850730	−	0.201556i
$393$	13.5646	+	21.2361i	0.684244	+	1.07122i
$394$	−10.3611	+	36.8476i	−0.521987	+	1.85636i
$395$	−2.99749	−	5.19181i	−0.150820	−	0.261228i
$396$	0.472191	+	7.25025i	0.0237285	+	0.364339i
$397$	15.0649	−	26.0931i	0.756085	−	1.30958i	−0.188748	−	0.982025i	$-0.560443\pi$
$397$	15.0649	−	26.0931i	0.756085	−	1.30958i	0.944833	−	0.327552i	$-0.106224\pi$
$398$	−7.79787	−	7.99228i	−0.390872	−	0.400617i
$399$	4.09043	+	1.28433i	0.204778	+	0.0642969i
$400$	−3.82156	+	1.18139i	−0.191078	+	0.0590694i
$401$	−20.2134	+	3.56416i	−1.00941	+	0.177986i	−0.653814	−	0.756655i	$-0.726832\pi$
$401$	−20.2134	+	3.56416i	−1.00941	+	0.177986i	−0.355593	+	0.934641i	$0.615721\pi$
$402$	−3.17084	+	13.5863i	−0.158147	+	0.677622i
$403$	10.5682	−	12.5947i	0.526439	−	0.627385i
$404$	20.5949	−	6.92661i	1.02463	−	0.344612i
$405$	−8.47187	−	3.03767i	−0.420971	−	0.150943i
$406$	−9.37572	−	6.73848i	−0.465309	−	0.334425i
$407$	−0.421960	−	0.354066i	−0.0209158	−	0.0175504i
$408$	−0.504802	+	0.0481828i	−0.0249914	+	0.00238541i
$409$	−1.25581	−	7.12205i	−0.0620958	−	0.352163i	−0.999986	−	0.00523127i	$-0.998335\pi$
$409$	−1.25581	−	7.12205i	−0.0620958	−	0.352163i	0.937891	−	0.346931i	$-0.112776\pi$
$410$	−3.10185	−	4.54807i	−0.153190	−	0.224613i
$411$	2.54424	−	8.10310i	0.125498	−	0.399696i
$412$	4.69360	+	31.0747i	0.231237	+	1.53094i
$413$	−3.05648	−	1.76466i	−0.150399	−	0.0868331i
$414$	7.20197	−	19.1927i	0.353957	−	0.943272i
$415$	−7.75040	+	4.47469i	−0.380452	+	0.219654i
$416$	13.3757	−	5.26154i	0.655799	−	0.257968i
$417$	−29.9984	+	19.1616i	−1.46903	+	0.938348i
$418$	0.108678	+	1.44720i	0.00531563	+	0.0707851i
$419$	−4.16919	+	3.49837i	−0.203678	+	0.170906i	−0.738921	−	0.673792i	$-0.764664\pi$
$419$	−4.16919	+	3.49837i	−0.203678	+	0.170906i	0.535243	+	0.844698i	$0.320220\pi$
$420$	3.65201	+	9.43609i	0.178200	+	0.460434i
$421$	29.3631	−	10.6873i	1.43107	−	0.520867i	0.493832	−	0.869557i	$-0.335596\pi$
$421$	29.3631	−	10.6873i	1.43107	−	0.520867i	0.937238	+	0.348690i	$0.113373\pi$
$422$	−30.3500	−	3.03223i	−1.47742	−	0.147607i
$423$	9.25221	+	13.1465i	0.449858	+	0.639203i
$424$	8.97582	−	8.33611i	0.435905	−	0.404837i
$425$	0.101938	+	0.0179744i	0.00494472	+	0.000871888i
$426$	7.06086	−	16.5245i	0.342100	−	0.800614i
$427$	−13.3410	+	36.6542i	−0.645618	+	1.77382i
$428$	19.6201	−	10.6924i	0.948372	−	0.516837i
$429$	−0.689283	+	5.28447i	−0.0332789	+	0.255137i
$430$	−4.32369	−	16.9692i	−0.208507	−	0.818328i
$431$	6.07053			0.292407			0.146204	−	0.989255i	$-0.453295\pi$
$431$	6.07053			0.292407			0.146204	+	0.989255i	$0.453295\pi$
$432$	11.8871	+	17.0499i	0.571917	+	0.820312i
$433$	−22.4374			−1.07827			−0.539136	−	0.842218i	$-0.681249\pi$
$433$	−22.4374			−1.07827			−0.539136	+	0.842218i	$0.681249\pi$
$434$	−6.59947	−	25.9010i	−0.316785	−	1.24329i
$435$	3.84444	+	2.94264i	0.184327	+	0.141089i
$436$	1.68898	−	0.920450i	0.0808876	−	0.0440815i
$437$	1.40047	−	3.84776i	0.0669936	−	0.184063i
$438$	−37.6291	+	4.52906i	−1.79799	+	0.216407i
$439$	3.03081	+	0.534414i	0.144653	+	0.0255062i	0.245506	−	0.969395i	$-0.421046\pi$
$439$	3.03081	+	0.534414i	0.144653	+	0.0255062i	−0.100853	+	0.994901i	$0.532157\pi$
$440$	−2.50965	+	2.33079i	−0.119643	+	0.111116i
$441$	4.15915	−	1.95157i	0.198055	−	0.0929321i
$442$	−0.370107	−	0.0369769i	−0.0176042	−	0.00175881i
$443$	−12.7270	+	4.63227i	−0.604680	+	0.220086i	−0.626174	−	0.779683i	$-0.715380\pi$
$443$	−12.7270	+	4.63227i	−0.604680	+	0.220086i	0.0214938	+	0.999769i	$0.493158\pi$
$444$	−1.55702	−	0.242216i	−0.0738929	−	0.0114951i
$445$	6.06587	−	5.08987i	0.287550	−	0.241283i
$446$	2.89298	+	38.5242i	0.136987	+	1.82417i
$447$	16.4326	+	8.52928i	0.777234	+	0.403421i
$448$	5.74491	−	22.6497i	0.271422	−	1.07010i
$449$	3.78832	−	2.18719i	0.178782	−	0.103220i	−0.407938	−	0.913009i	$-0.633752\pi$
$449$	3.78832	−	2.18719i	0.178782	−	0.103220i	0.586720	+	0.809790i	$0.300419\pi$
$450$	−1.41145	−	4.00097i	−0.0665365	−	0.188608i
$451$	−4.08229	−	2.35691i	−0.192228	−	0.110983i
$452$	−5.96786	−	39.5112i	−0.280705	−	1.85845i
$453$	8.34515	+	9.08529i	0.392089	+	0.426864i
$454$	−11.4207	−	16.7455i	−0.535998	−	0.785903i
$455$	1.28874	+	7.30879i	0.0604169	+	0.342641i
$456$	2.40806	+	3.38193i	0.112768	+	0.158373i
$457$	−13.1429	−	11.0282i	−0.614800	−	0.515879i	0.281364	−	0.959601i	$-0.409213\pi$
$457$	−13.1429	−	11.0282i	−0.614800	−	0.515879i	−0.896164	+	0.443722i	$0.853658\pi$
$458$	−2.09025	−	1.50230i	−0.0976710	−	0.0701977i
$459$	−0.0721180	−	0.533000i	−0.00336618	−	0.0248783i
$460$	9.15940	−	3.08055i	0.427059	−	0.143631i
$461$	−4.07094	+	4.85156i	−0.189603	+	0.225959i	−0.852469	−	0.522779i	$-0.824895\pi$
$461$	−4.07094	+	4.85156i	−0.189603	+	0.225959i	0.662866	+	0.748738i	$0.269340\pi$
$462$	6.32215	+	5.92380i	0.294133	+	0.275600i
$463$	6.16441	−	1.08695i	0.286484	−	0.0505149i	−0.0285593	−	0.999592i	$-0.509092\pi$
$463$	6.16441	−	1.08695i	0.286484	−	0.0505149i	0.315044	+	0.949077i	$0.397981\pi$
$464$	−3.30217	−	10.6819i	−0.153300	−	0.495895i
$465$	2.43884	+	10.9390i	0.113099	+	0.507282i
$466$	26.7716	+	27.4391i	1.24017	+	1.27109i
$467$	0.501839	−	0.869211i	0.0232223	−	0.0402223i	−0.854181	−	0.519976i	$-0.825941\pi$
$467$	0.501839	−	0.869211i	0.0232223	−	0.0402223i	0.877403	+	0.479754i	$0.159274\pi$
$468$	6.13420	+	13.9567i	0.283553	+	0.645149i
$469$	8.31806	+	14.4073i	0.384092	+	0.665267i
$470$	−2.05136	+	7.29530i	−0.0946222	+	0.336507i
$471$	9.85639	−	0.442155i	0.454158	−	0.0203734i
$472$	−1.32899	−	3.14865i	−0.0611716	−	0.144928i
$473$	−9.63815	−	11.4863i	−0.443163	−	0.528141i
$474$	−14.6627	−	0.803563i	−0.673478	−	0.0369089i
$475$	−0.289846	−	0.796344i	−0.0132990	−	0.0365388i
$476$	−0.399968	+	0.453502i	−0.0183325	+	0.0207862i
$477$	9.20926	+	9.16529i	0.421663	+	0.419650i
$478$	−17.0336	+	7.68904i	−0.779100	+	0.351688i
$479$	−4.68783	+	26.5860i	−0.214193	+	1.21475i	0.668109	+	0.744063i	$0.267104\pi$
$479$	−4.68783	+	26.5860i	−0.214193	+	1.21475i	−0.882302	+	0.470684i	$0.844007\pi$
$480$	−2.69387	+	9.42036i	−0.122958	+	0.429978i
$481$	−1.08609	−	0.395304i	−0.0495214	−	0.0180243i
$482$	−0.275412	+	0.572125i	−0.0125447	+	0.0260596i
$483$	−9.38146	−	22.5724i	−0.426871	−	1.02708i
$484$	6.96056	−	17.7514i	0.316389	−	0.806881i
$485$			12.8560i			0.583759i
$486$	−17.5744	+	13.3094i	−0.797191	+	0.603728i
$487$		−	0.361033i		−	0.0163600i	−0.999967	−	0.00817999i	$-0.997396\pi$
$487$		−	0.361033i		−	0.0163600i	0.999967	−	0.00817999i	$-0.00260380\pi$
$488$	−31.7201	+	20.5079i	−1.43590	+	0.928348i
$489$	−1.58077	−	3.80343i	−0.0714847	−	0.171997i
$490$	1.95142	+	0.939382i	0.0881562	+	0.0424370i
$491$	2.51892	+	0.916811i	0.113677	+	0.0413751i	0.398232	−	0.917285i	$-0.369624\pi$
$491$	2.51892	+	0.916811i	0.113677	+	0.0413751i	−0.284555	+	0.958660i	$0.591846\pi$
$492$	−13.4820	+	0.272455i	−0.607815	+	0.0122832i
$493$	−0.0502415	+	0.284934i	−0.00226276	+	0.0128328i
$494$	1.25287	+	2.77551i	0.0563695	+	0.124876i
$495$	−2.57492	−	2.56263i	−0.115734	−	0.115182i
$496$	10.0390	−	23.8565i	0.450763	−	1.07119i
$497$	−7.32876	−	20.1356i	−0.328740	−	0.903205i
$498$	−1.19957	+	21.8886i	−0.0537540	+	0.980851i
$499$	−10.7301	−	12.7876i	−0.480344	−	0.572452i	0.470390	−	0.882459i	$-0.344113\pi$
$499$	−10.7301	−	12.7876i	−0.480344	−	0.572452i	−0.950734	+	0.310007i	$0.899669\pi$
$500$	1.04234	−	1.70690i	0.0466149	−	0.0763351i
$501$	−31.9862	+	1.43489i	−1.42904	+	0.0641063i
$502$	33.8039	+	9.50528i	1.50874	+	0.424242i
$503$	1.83883	+	3.18495i	0.0819894	+	0.142010i	0.904104	−	0.427312i	$-0.140539\pi$
$503$	1.83883	+	3.18495i	0.0819894	+	0.142010i	−0.822115	+	0.569322i	$0.807206\pi$
$504$	24.2446	+	5.14412i	1.07994	+	0.229137i
$505$	−5.43212	+	9.40871i	−0.241726	+	0.418682i
$506$	5.92256	−	5.77849i	0.263290	−	0.256885i
$507$	−2.46646	−	11.0628i	−0.109539	−	0.491318i
$508$	−19.6533	−	0.484035i	−0.871976	−	0.0214756i
$509$	2.47151	−	0.435794i	0.109548	−	0.0193162i	−0.118606	−	0.992941i	$-0.537842\pi$
$509$	2.47151	−	0.435794i	0.109548	−	0.0193162i	0.228153	+	0.973625i	$0.426731\pi$
$510$	0.173362	−	0.185020i	0.00767660	−	0.00819282i
$511$	−29.0503	+	34.6207i	−1.28511	+	1.53153i
$512$	17.6712	−	14.1326i	0.780962	−	0.624579i
$513$	−3.48388	+	2.69320i	−0.153817	+	0.118907i
$514$	10.3467	−	14.3960i	0.456371	−	0.634981i
$515$	−12.0373	−	10.1005i	−0.530427	−	0.445081i
$516$	−40.5953	−	13.8532i	−1.78711	−	0.609854i
$517$	1.12679	+	6.39035i	0.0495563	+	0.281047i
$518$	−1.55232	+	1.05871i	−0.0682051	+	0.0465169i
$519$	−11.8101	−	12.8575i	−0.518405	−	0.564382i
$520$	−3.27567	+	6.39675i	−0.143648	+	0.280516i
$521$	−3.97351	−	2.29411i	−0.174083	−	0.100507i	0.410427	−	0.911894i	$-0.365380\pi$
$521$	−3.97351	−	2.29411i	−0.174083	−	0.100507i	−0.584510	+	0.811387i	$0.698713\pi$
$522$	11.1834	−	3.94525i	0.489484	−	0.172679i
$523$	−9.01966	+	5.20750i	−0.394402	+	0.227708i	−0.684066	−	0.729420i	$-0.739790\pi$
$523$	−9.01966	+	5.20750i	−0.394402	+	0.227708i	0.289664	+	0.957128i	$0.406457\pi$
$524$	18.1486	+	22.7432i	0.792826	+	0.993541i
$525$	−4.49025	−	2.33065i	−0.195970	−	0.101718i
$526$	−14.9699	+	1.12417i	−0.652720	+	0.0490162i
$527$	−0.513084	+	0.430528i	−0.0223503	+	0.0187541i
$528$	1.42033	+	8.26850i	0.0618118	+	0.359840i
$529$	−0.325222	+	0.118371i	−0.0141401	+	0.00514658i
$530$	−0.608897	+	6.09453i	−0.0264488	+	0.264729i
$531$	3.28164	−	1.53982i	0.142411	−	0.0668227i
$532$	4.85272	+	0.979435i	0.210392	+	0.0424639i
$533$	−9.74063	−	1.71754i	−0.421914	−	0.0743948i
$534$	−2.31780	−	19.2571i	−0.100301	−	0.833338i
$535$	−3.82113	+	10.4985i	−0.165202	+	0.453888i
$536$	−1.99571	+	15.9856i	−0.0862016	+	0.690471i
$537$	11.9028	+	9.11070i	0.513642	+	0.393156i
$538$	−28.8170	+	7.34247i	−1.24239	+	0.316556i
$539$	1.85445			0.0798767
$540$	−10.0964	−	2.46221i	−0.434480	−	0.105957i
$541$	36.3146			1.56129			0.780643	−	0.624978i	$-0.214892\pi$
$541$	36.3146			1.56129			0.780643	+	0.624978i	$0.214892\pi$
$542$	−34.1581	+	8.70336i	−1.46722	+	0.373841i
$543$	−0.455667	+	3.49343i	−0.0195545	+	0.149917i
$544$	−0.573845	+	0.116468i	−0.0246034	+	0.00499351i
$545$	−0.328940	+	0.903754i	−0.0140902	+	0.0387126i
$546$	16.7168	+	7.14305i	0.715414	+	0.305694i
$547$	−26.9656	−	4.75477i	−1.15297	−	0.203299i	−0.435696	−	0.900094i	$-0.643498\pi$
$547$	−26.9656	−	4.75477i	−1.15297	−	0.203299i	−0.717271	+	0.696795i	$0.754609\pi$
$548$	1.94025	−	9.61318i	0.0828833	−	0.410655i
$549$	−23.0579	−	32.7630i	−0.984088	−	1.39829i
$550$	0.170248	−	1.70404i	0.00725941	−	0.0726604i
$551$	2.22591	−	0.810166i	0.0948271	−	0.0345142i
$552$	5.94577	−	22.9119i	0.253069	−	0.975194i
$553$	−13.4138	+	11.2555i	−0.570414	+	0.478634i
$554$	37.5469	−	2.81960i	1.59521	−	0.119793i
$555$	0.663979	−	0.424119i	0.0281844	−	0.0180029i
$556$	−32.1274	+	25.6371i	−1.36251	+	1.08725i
$557$	16.4273	−	9.48430i	0.696047	−	0.401863i	−0.109827	−	0.993951i	$-0.535030\pi$
$557$	16.4273	−	9.48430i	0.696047	−	0.401863i	0.805873	+	0.592088i	$0.201696\pi$
$558$	25.7027	+	9.64480i	1.08808	+	0.408297i
$559$	−27.2471	−	15.7311i	−1.15243	−	0.665354i
$560$	5.33655	+	10.3935i	0.225510	+	0.439204i
$561$	0.0650365	−	0.207133i	0.00274584	−	0.00874517i
$562$	−17.2556	+	11.7686i	−0.727885	+	0.496429i
$563$	5.70535	+	32.3566i	0.240452	+	1.36367i	0.830822	+	0.556538i	$0.187870\pi$
$563$	5.70535	+	32.3566i	0.240452	+	1.36367i	−0.590371	+	0.807132i	$0.701018\pi$
$564$	12.2168	+	13.9759i	0.514420	+	0.588493i
$565$	15.3053	+	12.8427i	0.643899	+	0.540296i
$566$	16.0823	−	22.3764i	0.675989	−	0.940551i
$567$	−4.44087	+	25.9099i	−0.186499	+	1.08811i
$568$	6.10689	−	19.8307i	0.256239	−	0.832079i
$569$	23.8671	−	28.4437i	1.00056	−	1.19242i	0.0192872	−	0.999814i	$-0.493860\pi$
$569$	23.8671	−	28.4437i	1.00056	−	1.19242i	0.981275	−	0.192610i	$-0.0616952\pi$
$570$	−2.02150	−	0.471789i	−0.0846713	−	0.0197611i
$571$	−10.7588	+	1.89707i	−0.450244	+	0.0793901i	−0.394172	−	0.919037i	$-0.628969\pi$
$571$	−10.7588	+	1.89707i	−0.450244	+	0.0793901i	−0.0560715	+	0.998427i	$0.517857\pi$
$572$	−0.151511	+	6.15181i	−0.00633497	+	0.257220i
$573$	10.7651	+	3.38007i	0.449719	+	0.141205i
$574$	−11.5092	+	11.2292i	−0.480384	+	0.468699i
$575$	−2.41589	+	4.18444i	−0.100750	+	0.174503i
$576$	15.7152	+	18.1392i	0.654802	+	0.755801i
$577$	−7.46190	−	12.9244i	−0.310643	−	0.538050i	0.667859	−	0.744288i	$-0.267211\pi$
$577$	−7.46190	−	12.9244i	−0.310643	−	0.538050i	−0.978502	+	0.206239i	$0.933878\pi$
$578$	−23.1295	−	6.50376i	−0.962059	−	0.270521i
$579$	−22.7279	−	35.5817i	−0.944540	−	1.47872i
$580$	4.77108	+	2.91352i	0.198108	+	0.120977i
$581$	16.8024	+	20.0243i	0.697081	+	0.830749i
$582$	26.3692	+	17.2140i	1.09304	+	0.713544i
$583$	1.79372	+	4.92820i	0.0742883	+	0.204105i
$584$	−42.6622	+	9.75822i	−1.76537	+	0.403798i
$585$	−6.91614	−	3.20492i	−0.285947	−	0.132507i
$586$	−4.60535	−	10.2023i	−0.190245	−	0.421453i
$587$	4.66381	−	26.4498i	0.192496	−	1.09170i	−0.723444	−	0.690383i	$-0.757442\pi$
$587$	4.66381	−	26.4498i	0.192496	−	1.09170i	0.915940	−	0.401316i	$-0.131447\pi$
$588$	4.53972	−	2.74478i	0.187215	−	0.113193i
$589$	5.15288	+	1.87549i	0.212321	+	0.0772784i
$590$	1.53970	+	0.741188i	0.0633886	+	0.0305142i
$591$	−46.4853	−	6.06334i	−1.91215	−	0.249412i
$592$	−1.81731	−	0.0895701i	−0.0746910	−	0.00368131i
$593$		−	36.6935i		−	1.50682i	−0.657551	−	0.753410i	$-0.728408\pi$
$593$		−	36.6935i		−	1.50682i	0.657551	−	0.753410i	$-0.271592\pi$
$594$	−8.70406	+	1.85014i	−0.357132	+	0.0759123i
$595$		−	0.302340i		−	0.0123947i
$596$	19.9030	+	7.80426i	0.815260	+	0.319675i
$597$	8.31226	−	10.8596i	0.340198	−	0.444455i
$598$	7.53077	−	15.6440i	0.307956	−	0.639731i
$599$	13.1176	+	4.77443i	0.535973	+	0.195078i	0.595803	−	0.803130i	$-0.296834\pi$
$599$	13.1176	+	4.77443i	0.535973	+	0.195078i	−0.0598306	+	0.998209i	$0.519056\pi$
$600$	−2.10538	−	4.42350i	−0.0859519	−	0.180589i
$601$	−1.26752	+	7.18847i	−0.0517032	+	0.293224i	−0.999685	−	0.0251013i	$-0.992009\pi$
$601$	−1.26752	+	7.18847i	−0.0517032	+	0.293224i	0.947982	+	0.318325i	$0.103120\pi$
$602$	−46.6187	+	21.0438i	−1.90004	+	0.857683i
$603$	−17.0254	−	1.44848i	−0.693327	−	0.0589868i
$604$	10.6833	+	9.42222i	0.434699	+	0.383385i
$605$	3.26070	+	8.95869i	0.132566	+	0.364222i
$606$	12.0248	+	23.7401i	0.488476	+	0.964376i
$607$	13.5556	+	16.1549i	0.550203	+	0.655707i	0.967443	−	0.253090i	$-0.0814468\pi$
$607$	13.5556	+	16.1549i	0.550203	+	0.655707i	−0.417239	+	0.908797i	$0.637002\pi$
$608$	3.17484	+	3.59193i	0.128757	+	0.145672i
$609$	6.51456	−	12.5510i	0.263983	−	0.508592i
$610$	5.11230	−	18.1810i	0.206991	−	0.736127i
$611$	6.80779	+	11.7914i	0.275414	+	0.477030i
$612$	−0.147368	−	0.603327i	−0.00595701	−	0.0243880i
$613$	−6.27273	+	10.8647i	−0.253353	+	0.438821i	−0.964447	−	0.264276i	$-0.914867\pi$
$613$	−6.27273	+	10.8647i	−0.253353	+	0.438821i	0.711094	+	0.703097i	$0.248200\pi$
$614$	22.5958	+	23.1591i	0.911892	+	0.934627i
$615$	4.96555	−	4.56103i	0.200230	−	0.183918i
$616$	7.97737	+	6.03679i	0.321417	+	0.243229i
$617$	1.16194	−	0.204882i	0.0467781	−	0.00824824i	−0.150210	−	0.988654i	$-0.547995\pi$
$617$	1.16194	−	0.204882i	0.0467781	−	0.00824824i	0.196988	+	0.980406i	$0.436884\pi$
$618$	−36.8352	+	11.1655i	−1.48173	+	0.449142i
$619$	−8.12900	+	9.68777i	−0.326732	+	0.389384i	−0.904257	−	0.426989i	$-0.859574\pi$
$619$	−8.12900	+	9.68777i	−0.326732	+	0.389384i	0.577525	+	0.816373i	$0.304019\pi$
$620$	4.12544	+	12.2662i	0.165682	+	0.492621i
$621$	24.5309	+	5.34606i	0.984390	+	0.214530i
$622$	−4.22054	−	3.03337i	−0.169228	−	0.121627i
$623$	−17.7176	−	14.8668i	−0.709839	−	0.595626i
$624$	8.73442	+	15.2840i	0.349657	+	0.611849i
$625$	0.173648	+	0.984808i	0.00694593	+	0.0393923i
$626$	19.9205	+	29.2083i	0.796184	+	1.16740i
$627$	−1.73485	+	0.386786i	−0.0692833	+	0.0154467i
$628$	11.2649	−	1.70147i	0.449516	−	0.0678961i
$629$	0.0407767	+	0.0235424i	0.00162587	+	0.000938698i
$630$	−10.7929	+	6.08933i	−0.429997	+	0.242605i
$631$	−29.0248	+	16.7575i	−1.15546	+	0.667104i	−0.950211	−	0.311606i	$-0.899133\pi$
$631$	−29.0248	+	16.7575i	−1.15546	+	0.667104i	−0.205247	+	0.978710i	$0.565800\pi$
$632$	−16.9349	+	0.853071i	−0.673635	+	0.0339334i
$633$	−1.67410	−	37.3186i	−0.0665395	−	1.48328i
$634$	−2.48835	−	33.1358i	−0.0988248	−	1.31599i
$635$	7.52995	−	6.31838i	0.298817	−	0.250737i
$636$	11.6853	+	9.40944i	0.463353	+	0.373109i
$637$	3.65648	−	1.33085i	0.144875	−	0.0527302i
$638$	4.76307	+	0.475872i	0.188572	+	0.0188400i
$639$	21.2721	+	5.64532i	0.841511	+	0.223325i
$640$	−1.95253	+	11.1440i	−0.0771805	+	0.440503i
$641$	−28.2651	−	4.98390i	−1.11641	−	0.196852i	−0.415143	−	0.909756i	$-0.636269\pi$
$641$	−28.2651	−	4.98390i	−1.11641	−	0.196852i	−0.701262	+	0.712904i	$0.747380\pi$
$642$	16.4172	+	21.8949i	0.647934	+	0.864124i
$643$	1.86733	−	5.13046i	0.0736405	−	0.202326i	−0.897411	−	0.441195i	$-0.854555\pi$
$643$	1.86733	−	5.13046i	0.0736405	−	0.202326i	0.971052	+	0.238870i	$0.0767769\pi$
$644$	−13.5068	−	24.7844i	−0.532243	−	0.976643i
$645$	19.8046	−	8.23110i	0.779805	−	0.324099i
$646$	−0.0306301	−	0.120214i	−0.00120513	−	0.00472977i
$647$	34.7058			1.36442			0.682212	−	0.731154i	$-0.261018\pi$
$647$	34.7058			1.36442			0.682212	+	0.731154i	$0.261018\pi$
$648$	−18.5693	+	17.4121i	−0.729471	+	0.684012i
$649$	1.46319			0.0574352
$650$	−0.887223	−	3.48209i	−0.0347997	−	0.136579i
$651$	30.2288	−	12.5636i	1.18476	−	0.492404i
$652$	−2.27589	−	4.17615i	−0.0891306	−	0.163551i
$653$	−11.8357	+	32.5182i	−0.463165	+	1.27254i	0.459927	+	0.887957i	$0.347875\pi$
$653$	−11.8357	+	32.5182i	−0.463165	+	1.27254i	−0.923092	+	0.384579i	$0.874347\pi$
$654$	1.41326	+	1.88481i	0.0552630	+	0.0737021i
$655$	−14.3274	−	2.52630i	−0.559817	−	0.0987109i
$656$	−15.4488	+	1.94570i	−0.603174	+	0.0759670i
$657$	−12.1213	−	44.8082i	−0.472897	−	1.74813i
$658$	22.0253	+	2.20052i	0.858635	+	0.0857851i
$659$	7.34978	−	2.67510i	0.286307	−	0.104207i	−0.194875	−	0.980828i	$-0.562430\pi$
$659$	7.34978	−	2.67510i	0.286307	−	0.104207i	0.481181	+	0.876621i	$0.340208\pi$
$660$	−3.26723	−	2.63089i	−0.127177	−	0.102407i
$661$	−11.2772	+	9.46270i	−0.438633	+	0.368056i	−0.835197	−	0.549950i	$-0.814647\pi$
$661$	−11.2772	+	9.46270i	−0.438633	+	0.368056i	0.396565	+	0.918007i	$0.370202\pi$
$662$	−1.45665	−	19.3973i	−0.0566143	−	0.753899i
$663$	−0.0204150	−	0.455085i	−0.000792852	−	0.0176740i
$664$	1.27348	+	25.2806i	0.0494204	+	0.981079i
$665$	−2.14366	+	1.23764i	−0.0831276	+	0.0479938i
$666$	0.0191422	−	1.92979i	0.000741744	−	0.0747780i
$667$	−11.6962	−	6.75281i	−0.452879	−	0.261470i
$668$	−36.5570	+	5.52165i	−1.41443	+	0.213639i
$669$	−46.1813	+	10.2961i	−1.78547	+	0.398071i
$670$	−4.53848	−	6.65451i	−0.175337	−	0.257086i
$671$	−2.80814	−	15.9257i	−0.108407	−	0.614806i
$672$	28.4638	+	2.97084i	1.09802	+	0.114603i
$673$	30.8595	+	25.8942i	1.18955	+	0.998149i	0.999867	+	0.0163034i	$0.00518977\pi$
$673$	30.8595	+	25.8942i	1.18955	+	0.998149i	0.189681	+	0.981846i	$0.439255\pi$
$674$	−6.65606	−	4.78382i	−0.256382	−	0.184266i
$675$	4.60040	−	2.41584i	0.177070	−	0.0929859i
$676$	−4.17216	−	12.4051i	−0.160468	−	0.477119i
$677$	26.5284	−	31.6153i	1.01957	−	1.21508i	0.0431773	−	0.999067i	$-0.486252\pi$
$677$	26.5284	−	31.6153i	1.01957	−	1.21508i	0.976392	−	0.216008i	$-0.0693036\pi$
$678$	46.8356	−	14.1968i	1.79871	−	0.545226i
$679$	36.9800	−	6.52057i	1.41916	−	0.250237i
$680$	0.176669	−	0.233460i	0.00677494	−	0.00895280i
$681$	18.2826	−	16.7932i	0.700589	−	0.643516i
$682$	7.73850	+	7.93144i	0.296323	+	0.303710i
$683$	0.495037	−	0.857430i	0.0189421	−	0.0328086i	−0.856399	−	0.516315i	$-0.827304\pi$
$683$	0.495037	−	0.857430i	0.0189421	−	0.0328086i	0.875341	+	0.483506i	$0.160637\pi$
$684$	−3.67447	+	3.51462i	−0.140497	+	0.134385i
$685$	2.45176	+	4.24657i	0.0936768	+	0.162253i
$686$	−6.11470	+	21.7458i	−0.233460	+	0.830260i
$687$	1.45238	−	2.79816i	0.0554116	−	0.106756i
$688$	−48.2947	−	10.9915i	−1.84122	−	0.419046i
$689$	7.07348	+	8.42984i	0.269478	+	0.321151i
$690$	5.34795	+	10.5582i	0.203593	+	0.401945i
$691$	1.58701	+	4.36026i	0.0603725	+	0.165872i	0.966212	−	0.257749i	$-0.0829809\pi$
$691$	1.58701	+	4.36026i	0.0603725	+	0.165872i	−0.905839	+	0.423622i	$0.860759\pi$
$692$	−15.1191	−	13.3343i	−0.574741	−	0.506896i
$693$	−6.06535	+	8.70649i	−0.230404	+	0.330732i
$694$	−31.2634	+	14.1124i	−1.18674	+	0.535699i
$695$	3.56870	−	20.2391i	0.135369	−	0.767714i
$696$	12.3644	−	5.88490i	0.468672	−	0.223066i
$697$	0.378637	+	0.137813i	0.0143419	+	0.00522002i
$698$	10.8980	−	22.6390i	0.412497	−	0.856898i
$699$	−28.5376	+	37.2832i	−1.07939	+	1.41018i
$700$	−5.43856	−	2.13254i	−0.205558	−	0.0806023i
$701$			41.1213i			1.55313i	0.630037	+	0.776565i	$0.283040\pi$
$701$			41.1213i			1.55313i	−0.630037	+	0.776565i	$0.716960\pi$
$702$	−15.8343	+	9.89448i	−0.597628	+	0.373443i
$703$		−	0.385488i		−	0.0145390i
$704$	2.63242	+	9.32296i	0.0992132	+	0.351372i
$705$	−9.20343	−	1.20045i	−0.346621	−	0.0452117i
$706$	34.2835	+	16.5035i	1.29028	+	0.621119i
$707$	29.8192	+	10.8533i	1.12147	+	0.408180i
$708$	3.58192	−	2.16568i	0.134617	−	0.0813911i
$709$	3.11537	−	17.6682i	0.117000	−	0.663541i	−0.868740	−	0.495268i	$-0.835070\pi$
$709$	3.11537	−	17.6682i	0.117000	−	0.663541i	0.985740	−	0.168273i	$-0.0538191\pi$
$710$	4.26852	+	9.45610i	0.160195	+	0.354881i
$711$	−1.61036	−	17.9127i	−0.0603932	−	0.671779i
$712$	−4.99388	−	21.8329i	−0.187154	−	0.818221i
$713$	−10.6932	−	29.3794i	−0.400464	−	1.10027i
$714$	−0.620136	−	0.404831i	−0.0232080	−	0.0151504i
$715$	−1.97775	−	2.35699i	−0.0739637	−	0.0881466i
$716$	14.7717	+	9.02054i	0.552046	+	0.337113i
$717$	−12.3212	−	19.2895i	−0.460145	−	0.720380i
$718$	33.7263	+	9.48347i	1.25865	+	0.353920i
$719$	14.8764	+	25.7668i	0.554798	+	0.960938i	0.997919	+	0.0644762i	$0.0205377\pi$
$719$	14.8764	+	25.7668i	0.554798	+	0.960938i	−0.443122	+	0.896462i	$0.646129\pi$
$720$	−11.8922	−	1.60463i	−0.443197	−	0.0598010i
$721$	−22.9486	+	39.7481i	−0.854650	+	1.48030i
$722$	18.5055	−	18.0554i	0.688704	−	0.671951i
$723$	−0.741955	−	0.232962i	−0.0275936	−	0.00866395i
$724$	−0.100160	+	4.06680i	−0.00372241	+	0.151141i
$725$	−2.75270	+	0.485375i	−0.102233	+	0.0180264i
$726$	22.7414	+	5.30752i	0.844013	+	0.196980i
$727$	22.3697	−	26.6591i	0.829645	−	0.988732i	−0.170349	−	0.985384i	$-0.554490\pi$
$727$	22.3697	−	26.6591i	0.829645	−	0.988732i	0.999994	−	0.00334866i	$-0.00106591\pi$
$728$	20.0616	+	6.17797i	0.743531	+	0.228971i
$729$	−19.2284	−	18.9543i	−0.712165	−	0.702013i
$730$	12.7707	−	17.7688i	0.472666	−	0.657653i
$731$	0.981848	+	0.823869i	0.0363150	+	0.0304719i
$732$	−30.4461	−	34.8302i	−1.12532	−	1.28736i
$733$	0.712668	+	4.04174i	0.0263230	+	0.149285i	0.995136	−	0.0985061i	$-0.0314064\pi$
$733$	0.712668	+	4.04174i	0.0263230	+	0.149285i	−0.968813	+	0.247791i	$0.920295\pi$
$734$	5.65238	−	3.85501i	0.208633	−	0.142291i
$735$	−0.794593	+	2.53068i	−0.0293090	+	0.0933456i
$736$	4.05280	−	27.0305i	0.149388	−	0.996359i
$737$	−5.97301	−	3.44852i	−0.220019	−	0.127028i
$738$	−2.70640	−	16.2921i	−0.0996240	−	0.599721i
$739$	−0.0158009	+	0.00912265i	−0.000581245	+	0.000335582i	−0.500291	−	0.865858i	$-0.666773\pi$
$739$	−0.0158009	+	0.00912265i	−0.000581245	+	0.000335582i	0.499709	+	0.866193i	$0.333440\pi$
$740$	0.711102	−	0.567445i	0.0261406	−	0.0208597i
$741$	−3.14309	+	2.00766i	−0.115464	+	0.0737532i
$742$	17.8396	−	1.33967i	0.654914	−	0.0491810i
$743$	4.86926	−	4.08579i	0.178636	−	0.149893i	−0.549086	−	0.835766i	$-0.685024\pi$
$743$	4.86926	−	4.08579i	0.178636	−	0.149893i	0.727721	+	0.685873i	$0.240579\pi$
$744$	30.6834	+	7.96251i	1.12491	+	0.291920i
$745$	−10.0446	+	3.65593i	−0.368005	+	0.133943i
$746$	−1.14490	+	11.4594i	−0.0419177	+	0.419560i
$747$	−26.7403	+	2.40396i	−0.978377	+	0.0879565i
$748$	0.0495970	−	0.245734i	0.00181345	−	0.00898493i
$749$	32.1367	+	5.66657i	1.17425	+	0.207052i
$750$	2.25247	+	0.962475i	0.0822487	+	0.0351446i
$751$	−7.83687	+	21.5316i	−0.285972	+	0.785701i	0.710648	+	0.703548i	$0.248402\pi$
$751$	−7.83687	+	21.5316i	−0.285972	+	0.785701i	−0.996620	+	0.0821530i	$0.973820\pi$
$752$	15.7216	+	14.5694i	0.573308	+	0.531291i
$753$	−5.56248	+	42.6455i	−0.202708	+	1.55409i
$754$	9.73301	−	2.47993i	0.354455	−	0.0903139i
$755$	−7.12236			−0.259209
$756$	−1.96158	+	30.2910i	−0.0713420	+	1.10167i
$757$	−4.14651			−0.150707			−0.0753537	−	0.997157i	$-0.524009\pi$
$757$	−4.14651			−0.150707			−0.0753537	+	0.997157i	$0.524009\pi$
$758$	13.7057	−	3.49216i	0.497814	−	0.126841i
$759$	8.04736	+	6.15967i	0.292101	+	0.223582i
$760$	−2.37849	−	0.296942i	−0.0862769	−	0.0107712i
$761$	0.465224	−	1.27819i	0.0168644	−	0.0463344i	−0.930975	−	0.365083i	$-0.881040\pi$
$761$	0.465224	−	1.27819i	0.0168644	−	0.0463344i	0.947839	+	0.318749i	$0.103263\pi$
$762$	−2.87723	−	23.9051i	−0.104231	−	0.865991i
$763$	2.76647	+	0.487804i	0.100153	+	0.0176597i
$764$	12.7713	+	2.57766i	0.462049	+	0.0932564i
$765$	0.254798	+	0.177505i	0.00921225	+	0.00641769i
$766$	3.10108	−	31.0391i	0.112046	−	1.12149i
$767$	2.88502	−	1.05006i	0.104172	−	0.0379155i
$768$	20.2432	+	18.9265i	0.730463	+	0.682952i
$769$	28.4794	−	23.8971i	1.02699	−	0.861751i	0.0365044	−	0.999333i	$-0.488378\pi$
$769$	28.4794	−	23.8971i	1.02699	−	0.861751i	0.990490	+	0.137583i	$0.0439333\pi$
$770$	−4.98799	+	0.374575i	−0.179755	+	0.0134987i
$771$	19.2715	+	10.0028i	0.694047	+	0.360243i
$772$	−30.4086	−	38.1069i	−1.09443	−	1.37150i
$773$	29.4511	−	17.0036i	1.05928	−	0.611576i	0.134048	−	0.990975i	$-0.457202\pi$
$773$	29.4511	−	17.0036i	1.05928	−	0.611576i	0.925233	+	0.379398i	$0.123869\pi$
$774$	9.63517	−	51.6430i	0.346329	−	1.85627i
$775$	−5.60376	−	3.23534i	−0.201293	−	0.116217i
$776$	32.3654	+	16.5738i	1.16185	+	0.594964i
$777$	−1.55674	−	1.69481i	−0.0558479	−	0.0608011i
$778$	−8.27466	+	5.64345i	−0.296661	+	0.202327i
$779$	−0.572845	−	3.24877i	−0.0205243	−	0.116399i
$780$	−8.33017	−	2.84268i	−0.298268	−	0.101784i
$781$	6.80523	+	5.71027i	0.243510	+	0.204329i
$782$	−0.412796	+	0.574352i	−0.0147616	+	0.0205388i
$783$	6.75268	+	12.8589i	0.241321	+	0.459539i
$784$	4.88068	−	3.70173i	0.174310	−	0.132205i
$785$	−3.66152	+	4.36363i	−0.130685	+	0.155745i
$786$	−24.3660	+	26.0045i	−0.869107	+	0.927551i
$787$	30.4433	−	5.36797i	1.08519	−	0.191347i	0.397678	−	0.917525i	$-0.369816\pi$
$787$	30.4433	−	5.36797i	1.08519	−	0.191347i	0.687507	+	0.726178i	$0.258705\pi$
$788$	−54.1149	−	1.33278i	−1.92776	−	0.0474782i
$789$	−4.00092	−	17.9454i	−0.142437	−	0.638872i
$790$	6.06834	−	5.92072i	0.215902	−	0.210650i
$791$	29.1789	−	50.5393i	1.03748	−	1.79697i
$792$	−9.77107	+	3.17875i	−0.347200	+	0.112952i
$793$	−16.9660	−	29.3860i	−0.602482	−	1.04353i
$794$	41.0191	+	11.5341i	1.45571	+	0.409331i
$795$	−7.49387	+	0.336173i	−0.265780	+	0.0119228i
$796$	8.22999	−	13.4772i	0.291704	−	0.477685i
$797$	25.8128	+	30.7625i	0.914337	+	1.08966i	0.995668	+	0.0929768i	$0.0296382\pi$
$797$	25.8128	+	30.7625i	0.914337	+	1.08966i	−0.0813317	+	0.996687i	$0.525917\pi$
$798$	−0.331785	+	6.05411i	−0.0117451	+	0.214313i
$799$	−0.189710	−	0.521223i	−0.00671144	−	0.0184395i
$800$	−2.95342	−	4.82466i	−0.104419	−	0.170577i
$801$	22.9311	−	6.20321i	0.810230	−	0.219180i
$802$	−11.9425	−	26.4564i	−0.421705	−	0.934209i
$803$	3.25359	−	18.4520i	0.114817	−	0.651158i
$804$	−19.7262	+	0.398642i	−0.695689	+	0.0140590i
$805$	13.2618	+	4.82691i	0.467418	+	0.170126i
$806$	20.9503	+	10.0851i	0.737942	+	0.355234i
$807$	−13.9780	−	33.6320i	−0.492049	−	1.18390i
$808$	16.6837	+	25.8052i	0.586932	+	0.907822i
$809$			10.2864i			0.361650i	0.983515	+	0.180825i	$0.0578768\pi$
$809$			10.2864i			0.361650i	−0.983515	+	0.180825i	$0.942123\pi$
$810$	1.20471	−	12.6708i	0.0423291	−	0.445206i
$811$			0.223089i			0.00783371i	0.999992	+	0.00391686i	$0.00124678\pi$
$811$			0.223089i			0.00783371i	−0.999992	+	0.00391686i	$0.998753\pi$
$812$	5.96079	−	15.2017i	0.209183	−	0.533475i
$813$	−16.5688	−	39.8656i	−0.581092	−	1.39815i
$814$	0.337883	−	0.701898i	0.0118428	−	0.0246015i
$815$	2.23461	+	0.813330i	0.0782748	+	0.0284897i
$816$	−0.242298	−	0.674971i	−0.00848212	−	0.0236287i
$817$	1.82218	−	10.3341i	0.0637499	−	0.361544i
$818$	9.32175	−	4.20787i	0.325927	−	0.147125i
$819$	−5.71103	+	21.5197i	−0.199560	+	0.751959i
$820$	5.14970	−	5.83896i	0.179835	−	0.203905i
$821$	−14.9884	−	41.1804i	−0.523100	−	1.43721i	−0.867051	−	0.498219i	$-0.833988\pi$
$821$	−14.9884	−	41.1804i	−0.523100	−	1.43721i	0.343951	−	0.938988i	$-0.388235\pi$
$822$	11.9931	+	0.657263i	0.418308	+	0.0229247i
$823$	−18.7005	−	22.2864i	−0.651859	−	0.776855i	0.334334	−	0.942455i	$-0.391489\pi$
$823$	−18.7005	−	22.2864i	−0.651859	−	0.776855i	−0.986193	+	0.165599i	$0.947044\pi$
$824$	−40.9467	+	17.2829i	−1.42645	+	0.602078i
$825$	2.09529	−	0.0939943i	0.0729488	−	0.00327246i
$826$	1.35108	−	4.80486i	0.0470100	−	0.167183i
$827$	27.4956	+	47.6238i	0.956116	+	1.65604i	0.731794	+	0.681526i	$0.238683\pi$
$827$	27.4956	+	47.6238i	0.956116	+	1.65604i	0.224321	+	0.974515i	$0.427984\pi$
$828$	28.8171	+	3.16806i	1.00146	+	0.110098i
$829$	4.93792	−	8.55273i	0.171501	−	0.297049i	−0.767444	−	0.641116i	$-0.778472\pi$
$829$	4.93792	−	8.55273i	0.171501	−	0.297049i	0.938945	+	0.344068i	$0.111805\pi$
$830$	−8.83853	−	9.05889i	−0.306790	−	0.314439i
$831$	10.0349	+	45.0098i	0.348108	+	1.56137i
$832$	11.8811	+	16.4932i	0.411903	+	0.571800i
$833$	−0.156110	+	0.0275264i	−0.00540888	+	0.000953732i
$834$	−36.7345	−	34.4199i	−1.27201	−	1.19186i
$835$	11.8825	−	14.1610i	0.411209	−	0.490060i
$836$	−1.94534	+	0.654270i	−0.0672810	+	0.0226284i
$837$	−7.15939	+	32.8515i	−0.247465	+	1.13551i
$838$	−6.25006	−	4.49202i	−0.215905	−	0.155174i
$839$	43.8544	+	36.7982i	1.51402	+	1.27042i	0.855434	+	0.517913i	$0.173291\pi$
$839$	43.8544	+	36.7982i	1.51402	+	1.27042i	0.658589	+	0.752503i	$0.271154\pi$
$840$	−11.6563	+	8.29971i	−0.402180	+	0.286367i
$841$	3.67909	+	20.8652i	0.126865	+	0.719489i
$842$	24.8992	+	36.5082i	0.858082	+	1.25816i
$843$	−17.3048	−	18.8396i	−0.596009	−	0.648869i
$844$	−6.44216	−	42.6513i	−0.221748	−	1.46812i
$845$	5.66723	+	3.27197i	0.194958	+	0.112559i
$846$	−14.7856	+	17.2700i	−0.508339	+	0.593754i
$847$	24.1157	−	13.9232i	0.828625	−	0.478407i
$848$	14.5582	+	9.38992i	0.499931	+	0.322451i
$849$	29.9546	+	15.5479i	1.02804	+	0.533602i
$850$	0.0109621	+	0.145975i	0.000375995	+	0.00500691i
$851$	−1.68367	+	1.41277i	−0.0577155	+	0.0484291i
$852$	25.1111	+	3.90638i	0.860293	+	0.133831i
$853$	−2.87396	+	1.04604i	−0.0984027	+	0.0358156i	−0.390752	−	0.920496i	$-0.627785\pi$
$853$	−2.87396	+	1.04604i	−0.0984027	+	0.0358156i	0.292350	+	0.956311i	$0.405563\pi$
$854$	−54.8903	−	5.48402i	−1.87831	−	0.187659i
$855$	0.215520	−	2.53320i	0.00737062	−	0.0866337i
$856$	21.5041	+	23.1543i	0.734995	+	0.791399i
$857$	42.5823	+	7.50841i	1.45458	+	0.256482i	0.844372	−	0.535757i	$-0.179974\pi$
$857$	42.5823	+	7.50841i	1.45458	+	0.256482i	0.610211	+	0.792239i	$0.291085\pi$
$858$	−7.48267	+	0.900619i	−0.255454	+	0.0307466i
$859$	−6.84991	+	18.8200i	−0.233716	+	0.642130i	−1.00000		0.000372582i	$-0.999881\pi$
$859$	−6.84991	+	18.8200i	−0.233716	+	0.642130i	0.766284	+	0.642502i	$0.222104\pi$
$860$	21.7453	−	11.8506i	0.741510	−	0.404103i
$861$	−15.6383	−	11.9700i	−0.532950	−	0.407935i
$862$	2.11971	+	8.31923i	0.0721975	+	0.283354i
$863$	−25.8023			−0.878321			−0.439161	−	0.898409i	$-0.644724\pi$
$863$	−25.8023			−0.878321			−0.439161	+	0.898409i	$0.644724\pi$
$864$	−19.2149	+	22.2438i	−0.653704	+	0.756751i
$865$	10.0796			0.342716
$866$	−7.83469	−	30.7489i	−0.266234	−	1.04489i
$867$	3.80600	−	29.1791i	0.129258	−	0.990975i
$868$	33.1910	−	18.0882i	1.12658	−	0.613953i
$869$	2.48291	−	6.82174i	0.0842269	−	0.231412i
$870$	−2.69028	+	6.29604i	−0.0912090	+	0.213456i
$871$	−14.2520	−	2.51302i	−0.482911	−	0.0851503i
$872$	1.85117	+	1.99323i	0.0626885	+	0.0674992i
$873$	−16.2158	+	34.9933i	−0.548822	+	1.18434i
$874$	5.76209	+	0.575683i	0.194906	+	0.0194728i
$875$	2.74471	−	0.998993i	0.0927881	−	0.0337721i
$876$	−19.3461	−	49.9866i	−0.653644	−	1.68889i
$877$	−6.42610	+	5.39214i	−0.216994	+	0.182080i	−0.744805	−	0.667282i	$-0.767457\pi$
$877$	−6.42610	+	5.39214i	−0.216994	+	0.182080i	0.527811	+	0.849362i	$0.323013\pi$
$878$	0.325922	+	4.34011i	0.0109993	+	0.146472i
$879$	11.5535	−	7.37981i	0.389688	−	0.248915i
$880$	−4.07049	−	2.62543i	−0.137216	−	0.0885033i
$881$	20.1048	−	11.6075i	0.677349	−	0.391068i	−0.121506	−	0.992591i	$-0.538772\pi$
$881$	20.1048	−	11.6075i	0.677349	−	0.391068i	0.798856	+	0.601523i	$0.205439\pi$
$882$	4.12678	+	5.01837i	0.138956	+	0.168977i
$883$	−12.7154	−	7.34126i	−0.427908	−	0.247053i	0.270547	−	0.962707i	$-0.412795\pi$
$883$	−12.7154	−	7.34126i	−0.427908	−	0.247053i	−0.698455	+	0.715654i	$0.746129\pi$
$884$	−0.0785596	−	0.520116i	−0.00264224	−	0.0174934i
$885$	−0.626947	+	1.99675i	−0.0210746	+	0.0671200i
$886$	−10.7922	−	15.8240i	−0.362572	−	0.531618i
$887$	1.41007	+	7.99693i	0.0473457	+	0.268511i	0.999286	−	0.0377717i	$-0.0120260\pi$
$887$	1.41007	+	7.99693i	0.0473457	+	0.268511i	−0.951941	+	0.306282i	$0.900915\pi$
$888$	−0.211740	−	2.21836i	−0.00710554	−	0.0744434i
$889$	−21.9939	−	18.4551i	−0.737653	−	0.618964i
$890$	9.09339	+	6.53556i	0.304811	+	0.219073i
$891$	−3.77645	−	10.2232i	−0.126516	−	0.342490i
$892$	−51.7844	+	17.4165i	−1.73387	+	0.583147i
$893$	−2.91901	+	3.47874i	−0.0976808	+	0.116411i
$894$	−5.95085	+	25.4979i	−0.199026	+	0.852778i
$895$	−8.52263	+	1.50277i	−0.284880	+	0.0502320i
$896$	33.0457	−	0.0358117i	1.10398	−	0.00119639i
$897$	20.2878	+	6.37003i	0.677389	+	0.212689i
$898$	4.32019	+	4.42790i	0.144166	+	0.147761i
$899$	9.04330	−	15.6635i	0.301611	−	0.522405i
$900$	4.99020	−	3.33135i	0.166340	−	0.111045i
$901$	−0.224149	−	0.388238i	−0.00746749	−	0.0129341i
$902$	1.80452	−	6.41747i	0.0600841	−	0.213678i
$903$	−33.7216	−	52.7928i	−1.12218	−	1.75683i
$904$	52.0634	−	21.9750i	1.73160	−	0.730879i
$905$	−1.30744	−	1.55815i	−0.0434608	−	0.0517946i
$906$	−9.53678	+	14.6088i	−0.316838	+	0.485346i
$907$	−10.9272	−	30.0222i	−0.362831	−	0.996869i	−0.978024	−	0.208493i	$-0.933144\pi$
$907$	−10.9272	−	30.0222i	−0.362831	−	0.996869i	0.615193	−	0.788376i	$-0.289078\pi$
$908$	18.9606	−	21.4984i	0.629229	−	0.713448i
$909$	−26.6536	+	18.7582i	−0.884043	+	0.622172i
$910$	−9.56617	+	4.31820i	−0.317116	+	0.143147i
$911$	−5.53237	+	31.3756i	−0.183296	+	1.03952i	0.744830	+	0.667254i	$0.232530\pi$
$911$	−5.53237	+	31.3756i	−0.183296	+	1.03952i	−0.928126	+	0.372267i	$0.878581\pi$
$912$	−3.79384	+	4.48097i	−0.125627	+	0.148380i
$913$	−10.1836	−	3.70652i	−0.337027	−	0.122668i
$914$	10.5241	−	21.8623i	0.348108	−	0.723140i
$915$	22.9363	+	2.99171i	0.758252	+	0.0989030i
$916$	1.32892	−	3.38911i	0.0439087	−	0.111979i
$917$			42.4939i			1.40327i
$918$	0.705256	−	0.284945i	0.0232769	−	0.00940460i
$919$			47.3952i			1.56342i	0.623639	+	0.781712i	$0.285654\pi$
$919$			47.3952i			1.56342i	−0.623639	+	0.781712i	$0.714346\pi$
$920$	7.41995	+	11.4766i	0.244629	+	0.378373i
$921$	−24.0863	+	31.4678i	−0.793672	+	1.03690i
$922$	−8.07020	−	3.88486i	−0.265778	−	0.127941i
$923$	17.5161	+	6.37534i	0.576549	+	0.209847i
$924$	−5.91057	+	10.7325i	−0.194444	+	0.353074i
$925$	−0.0789890	+	0.447969i	−0.00259714	+	0.0147291i
$926$	3.64208	+	8.06834i	0.119686	+	0.265142i
$927$	−20.0247	−	42.6762i	−0.657698	−	1.40167i
$928$	13.4857	−	8.25529i	0.442690	−	0.270993i
$929$	−0.423793	−	1.16436i	−0.0139042	−	0.0382015i	0.932546	−	0.361050i	$-0.117582\pi$
$929$	−0.423793	−	1.16436i	−0.0139042	−	0.0382015i	−0.946451	+	0.322849i	$0.895359\pi$
$930$	−14.1395	+	7.16192i	−0.463651	+	0.234849i
$931$	0.834211	+	0.994174i	0.0273402	+	0.0325828i
$932$	−28.2552	+	46.2697i	−0.925529	+	1.51562i
$933$	2.93257	−	5.64991i	0.0960080	−	0.184970i
$934$	1.36642	+	0.384224i	0.0447107	+	0.0125722i
$935$	0.0626723	+	0.108552i	0.00204960	+	0.00355002i
$936$	−16.9847	+	13.2799i	−0.555163	+	0.434066i
$937$	−14.1926	+	24.5824i	−0.463653	+	0.803071i	−0.999140	−	0.0414728i	$-0.986795\pi$
$937$	−14.1926	+	24.5824i	−0.463653	+	0.803071i	0.535486	+	0.844544i	$0.320128\pi$
$938$	−16.8397	+	16.4300i	−0.549835	+	0.536460i
$939$	−31.8894	+	29.2915i	−1.04067	+	0.955894i
$940$	−10.7140	−	0.263871i	−0.349452	−	0.00860651i
$941$	−20.3204	+	3.58303i	−0.662425	+	0.116803i	−0.494745	−	0.869038i	$-0.664739\pi$
$941$	−20.3204	+	3.58303i	−0.662425	+	0.116803i	−0.167680	+	0.985842i	$0.553627\pi$
$942$	4.04759	+	13.3531i	0.131878	+	0.435067i
$943$	−12.0900	+	14.4083i	−0.393705	+	0.469199i
$944$	3.85094	−	2.92073i	0.125337	−	0.0950616i
$945$	−9.28247	−	12.0077i	−0.301959	−	0.390609i
$946$	12.3757	−	17.2192i	0.402369	−	0.559844i
$947$	21.8627	+	18.3450i	0.710442	+	0.596132i	0.924723	−	0.380640i	$-0.124296\pi$
$947$	21.8627	+	18.3450i	0.710442	+	0.596132i	−0.214281	+	0.976772i	$0.568741\pi$
$948$	−4.01868	−	20.3747i	−0.130521	−	0.661740i
$949$	−6.82693	−	38.7175i	−0.221612	−	1.25682i
$950$	0.990124	−	0.675280i	0.0321239	−	0.0219090i
$951$	39.7219	−	8.85602i	1.28807	−	0.287176i
$952$	−0.761152	−	0.389774i	−0.0246691	−	0.0126326i
$953$	−31.4813	−	18.1757i	−1.01978	−	0.588770i	−0.105740	−	0.994394i	$-0.533721\pi$
$953$	−31.4813	−	18.1757i	−1.01978	−	0.588770i	−0.914040	+	0.405624i	$0.867054\pi$
$954$	−9.34469	+	15.8210i	−0.302545	+	0.512223i
$955$	−5.64165	+	3.25721i	−0.182559	+	0.105401i
$956$	−16.4851	−	20.6585i	−0.533165	−	0.668144i
$957$	0.262730	+	5.85669i	0.00849284	+	0.189320i
$958$	−38.0711	+	2.85896i	−1.23002	+	0.0923689i
$959$	10.9716	−	9.20631i	0.354293	−	0.297287i
$960$	−13.8506	−	0.402351i	−0.447025	−	0.0129858i
$961$	10.2141	−	3.71761i	0.329486	−	0.119923i
$962$	0.162496	−	1.62644i	0.00523907	−	0.0524385i
$963$	−23.6431	+	23.7565i	−0.761888	+	0.765543i
$964$	−0.880225	−	0.177658i	−0.0283501	−	0.00572197i
$965$	24.0060	+	4.23290i	0.772780	+	0.136262i
$966$	27.6581	−	20.7384i	0.889884	−	0.667249i
$967$	14.7690	−	40.5776i	0.474940	−	1.30489i	−0.438799	−	0.898585i	$-0.644596\pi$
$967$	14.7690	−	40.5776i	0.474940	−	1.30489i	0.913739	−	0.406301i	$-0.133182\pi$
$968$	26.7575	+	3.34053i	0.860018	+	0.107369i
$969$	0.140301	−	0.0583113i	0.00450711	−	0.00187323i
$970$	−17.6182	+	4.48904i	−0.565686	+	0.144135i
$971$	1.87715			0.0602407			0.0301203	−	0.999546i	$-0.490411\pi$
$971$	1.87715			0.0602407			0.0301203	+	0.999546i	$0.490411\pi$
$972$	−24.3762	−	19.4371i	−0.781868	−	0.623444i
$973$	−60.0276			−1.92440
$974$	0.494770	−	0.126065i	0.0158535	−	0.00403940i
$975$	4.06391	−	1.68903i	0.130149	−	0.0540921i
$976$	−39.1806	−	36.3092i	−1.25414	−	1.16223i
$977$	13.6863	−	37.6028i	0.437864	−	1.20302i	−0.503015	−	0.864278i	$-0.667776\pi$
$977$	13.6863	−	37.6028i	0.437864	−	1.20302i	0.940879	−	0.338743i	$-0.110002\pi$
$978$	4.66036	−	3.49441i	0.149022	−	0.111739i
$979$	9.44304	+	1.66506i	0.301801	+	0.0532156i
$980$	−0.605959	+	3.00229i	−0.0193567	+	0.0959048i
$981$	−2.03530	+	2.04507i	−0.0649822	+	0.0652940i
$982$	−0.376868	+	3.77213i	−0.0120264	+	0.120373i
$983$	40.4761	−	14.7321i	1.29099	−	0.469881i	0.396937	−	0.917846i	$-0.370073\pi$
$983$	40.4761	−	14.7321i	1.29099	−	0.469881i	0.894051	+	0.447964i	$0.147851\pi$
$984$	−5.08102	−	18.3810i	−0.161977	−	0.585964i
$985$	20.7335	−	17.3975i	0.660624	−	0.554329i
$986$	−0.408025	+	0.0306407i	−0.0129942	+	0.000975800i
$987$	1.21491	+	27.0824i	0.0386710	+	0.862043i
$988$	−3.36616	+	2.68613i	−0.107092	+	0.0854570i
$989$	−51.8135	+	29.9146i	−1.64757	+	0.951228i
$990$	2.61279	−	4.42356i	0.0830398	−	0.140590i
$991$	−2.30325	−	1.32978i	−0.0731653	−	0.0422420i	0.462971	−	0.886373i	$-0.346783\pi$
$991$	−2.30325	−	1.32978i	−0.0731653	−	0.0422420i	−0.536136	+	0.844131i	$0.680117\pi$
$992$	36.1990	+	5.42747i	1.14932	+	0.172322i
$993$	23.2528	−	5.18421i	0.737905	−	0.164516i
$994$	25.0353	−	17.0745i	0.794072	−	0.541569i
$995$	1.37107	+	7.77572i	0.0434658	+	0.246507i
$996$	−30.4156	+	5.99913i	−0.963755	+	0.190090i
$997$	44.2097	+	37.0964i	1.40014	+	1.17485i	0.961039	+	0.276414i	$0.0891461\pi$
$997$	44.2097	+	37.0964i	1.40014	+	1.17485i	0.439097	+	0.898440i	$0.355298\pi$
$998$	13.7778	−	19.1700i	0.436128	−	0.606815i
$999$	2.34228	−	0.316924i	0.0741064	−	0.0100270i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	540.2.be.a.11.43	yes	432
4.3	odd	2	inner	540.2.be.a.11.2	✓	432
27.5	odd	18	inner	540.2.be.a.491.2	yes	432
108.59	even	18	inner	540.2.be.a.491.43	yes	432

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
540.2.be.a.11.2	✓	432	4.3	odd	2	inner
540.2.be.a.11.43	yes	432	1.1	even	1	trivial
540.2.be.a.491.2	yes	432	27.5	odd	18	inner
540.2.be.a.491.43	yes	432	108.59	even	18	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 540 = 2^{2} \cdot 3^{3} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	540.be (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(0.349180 + 1.37043i) q^{2} +(-1.59941 + 0.664741i) q^{3} +(-1.75615 + 0.957052i) q^{4} +(0.342020 - 0.939693i) q^{5} +(-1.46946 - 1.95977i) q^{6} +(-2.87648 - 0.507202i) q^{7} +(-1.92478 - 2.07249i) q^{8} +(2.11624 - 2.12639i) q^{9} +(1.40721 + 0.140592i) q^{10} +(1.13791 - 0.414164i) q^{11} +(2.17261 - 2.69810i) q^{12} +(1.94642 - 1.63324i) q^{13} +(-0.309327 - 4.11912i) q^{14} +(0.0776213 + 1.73031i) q^{15} +(2.16810 - 3.36145i) q^{16} +(-0.0896428 + 0.0517553i) q^{17} +(3.65301 + 2.15766i) q^{18} +(0.733915 + 0.423726i) q^{19} +(0.298697 + 1.97757i) q^{20} +(4.93784 - 1.10089i) q^{21} +(0.964916 + 1.41480i) q^{22} +(-0.839030 - 4.75837i) q^{23} +(4.45619 + 2.03528i) q^{24} +(-0.766044 - 0.642788i) q^{25} +(2.91790 + 2.09714i) q^{26} +(-1.97124 + 4.80773i) q^{27} +(5.53695 - 1.86222i) q^{28} +(1.79670 - 2.14122i) q^{29} +(-2.34416 + 0.710564i) q^{30} +(6.37237 - 1.12362i) q^{31} +(5.36368 + 1.79748i) q^{32} +(-1.54467 + 1.41883i) q^{33} +(-0.102228 - 0.104777i) q^{34} +(-1.46043 + 2.52954i) q^{35} +(-1.68136 + 5.75960i) q^{36} +(-0.227440 - 0.393937i) q^{37} +(-0.324418 + 1.15373i) q^{38} +(-2.02745 + 3.90610i) q^{39} +(-2.60582 + 1.09987i) q^{40} +(-2.50219 - 2.98199i) q^{41} +(3.23289 + 6.38255i) q^{42} +(-4.23504 - 11.6357i) q^{43} +(-1.60195 + 1.81637i) q^{44} +(-1.27436 - 2.71588i) q^{45} +(6.22804 - 2.81136i) q^{46} +(-0.930514 + 5.27721i) q^{47} +(-1.23320 + 6.81757i) q^{48} +(1.43906 + 0.523776i) q^{49} +(0.613407 - 1.27426i) q^{50} +(0.108972 - 0.142367i) q^{51} +(-1.85511 + 4.73104i) q^{52} +4.33094i q^{53} +(-7.27696 - 1.02268i) q^{54} -1.21094i q^{55} +(4.48543 + 6.93774i) q^{56} +(-1.45550 - 0.189849i) q^{57} +(3.56176 + 1.71457i) q^{58} +(1.13544 + 0.413268i) q^{59} +(-1.79231 - 2.96439i) q^{60} +(2.31898 - 13.1516i) q^{61} +(3.76494 + 8.34052i) q^{62} +(-7.16584 + 5.04317i) q^{63} +(-0.590430 + 7.97818i) q^{64} +(-0.869031 - 2.38764i) q^{65} +(-2.48378 - 1.62143i) q^{66} +(-3.66108 - 4.36310i) q^{67} +(0.107893 - 0.176683i) q^{68} +(4.50504 + 7.05286i) q^{69} +(-3.97650 - 1.11815i) q^{70} +(3.66807 + 6.35329i) q^{71} +(-8.48022 - 0.293045i) q^{72} +(7.73645 - 13.3999i) q^{73} +(0.460445 - 0.449245i) q^{74} +(1.65251 + 0.518861i) q^{75} +(-1.69439 - 0.0417305i) q^{76} +(-3.48324 + 0.614189i) q^{77} +(-6.06097 - 1.41454i) q^{78} +(3.85350 - 4.59243i) q^{79} +(-2.41719 - 3.18703i) q^{80} +(-0.0430716 - 8.99990i) q^{81} +(3.21289 - 4.47032i) q^{82} +(-6.85563 - 5.75256i) q^{83} +(-7.61796 + 6.65910i) q^{84} +(0.0179744 + 0.101938i) q^{85} +(14.4671 - 9.86675i) q^{86} +(-1.45030 + 4.61903i) q^{87} +(-3.04857 - 1.56112i) q^{88} +(6.85757 + 3.95922i) q^{89} +(3.27694 - 2.69475i) q^{90} +(-6.42724 + 3.71077i) q^{91} +(6.02747 + 7.55341i) q^{92} +(-9.44512 + 6.03311i) q^{93} +(-7.55695 + 0.567492i) q^{94} +(0.649186 - 0.544731i) q^{95} +(-9.77359 + 0.690546i) q^{96} +(-12.0807 + 4.39700i) q^{97} +(-0.215306 + 2.15502i) q^{98} +(1.52741 - 3.29610i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 432 q + 18 q^{12} + 30 q^{14} + 30 q^{24} + 12 q^{29} - 24 q^{30} + 60 q^{33} - 60 q^{36} - 60 q^{38} + 60 q^{41} - 60 q^{42} - 72 q^{44} + 12 q^{45} - 150 q^{48} + 54 q^{52} - 84 q^{54} - 84 q^{56} - 12 q^{57}+ \cdots + 36 q^{97}+O(q^{100}) \) 432 * q + 18 * q^12 + 30 * q^14 + 30 * q^24 + 12 * q^29 - 24 * q^30 + 60 * q^33 - 60 * q^36 - 60 * q^38 + 60 * q^41 - 60 * q^42 - 72 * q^44 + 12 * q^45 - 150 * q^48 + 54 * q^52 - 84 * q^54 - 84 * q^56 - 12 * q^57 + 54 * q^58 - 198 * q^62 - 48 * q^66 - 138 * q^68 - 48 * q^69 - 84 * q^72 - 84 * q^74 - 48 * q^77 - 78 * q^78 - 66 * q^84 + 54 * q^86 - 36 * q^89 + 120 * q^92 - 54 * q^94 + 210 * q^96 + 36 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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