LMFDB - Embedded newform 572.2.bq.a.49.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [572,2,Mod(49,572)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(572, base_ring=CyclotomicField(30))

chi = DirichletCharacter(H, H._module([0, 12, 25]))

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

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

chi := DirichletCharacter("572.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 572 = 2^{2} \cdot 11 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	572.bq (of order $30$, degree $8$, 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:	$4.56744299562$
Analytic rank:	$0$
Dimension:	$112$
Relative dimension:	$14$ over $\Q(\zeta_{30})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{30}]$

Embedding invariants

Embedding label			49.10
Character	$\chi$	$=$	572.49
Dual form			572.2.bq.a.537.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.136254 - 1.29637i) q^{3} +(2.36621 + 0.768828i) q^{5} +(2.00645 - 0.210887i) q^{7} +(1.27243 + 0.270463i) q^{9} +O(q^{10})$	\(q+(0.136254 - 1.29637i) q^{3} +(2.36621 + 0.768828i) q^{5} +(2.00645 - 0.210887i) q^{7} +(1.27243 + 0.270463i) q^{9} +(1.79345 + 2.78990i) q^{11} +(-2.97050 + 2.04356i) q^{13} +(1.31909 - 2.96273i) q^{15} +(-2.78170 - 3.08939i) q^{17} +(1.80329 + 4.05026i) q^{19} -2.62984i q^{21} +(3.17599 + 5.50098i) q^{23} +(0.962763 + 0.699488i) q^{25} +(1.73242 - 5.33183i) q^{27} +(-8.37016 - 3.72663i) q^{29} +(-0.414109 + 0.134552i) q^{31} +(3.86111 - 1.94484i) q^{33} +(4.90982 + 1.04362i) q^{35} +(3.71248 - 8.33836i) q^{37} +(2.24447 + 4.12931i) q^{39} +(1.61319 + 0.169554i) q^{41} +(3.97220 - 6.88005i) q^{43} +(2.80289 + 1.61825i) q^{45} +(1.62734 - 2.23984i) q^{47} +(-2.86565 + 0.609113i) q^{49} +(-4.38401 + 3.18517i) q^{51} +(0.597134 + 1.83779i) q^{53} +(2.09872 + 7.98034i) q^{55} +(5.49636 - 1.78587i) q^{57} +(-3.77974 + 0.397266i) q^{59} +(-5.91547 - 6.56980i) q^{61} +(2.61010 + 0.274333i) q^{63} +(-8.59996 + 2.55169i) q^{65} +(-11.0917 + 6.40378i) q^{67} +(7.56406 - 3.36774i) q^{69} +(9.41908 - 8.48098i) q^{71} +(-0.624856 - 0.860040i) q^{73} +(1.03798 - 1.15279i) q^{75} +(4.18682 + 5.21959i) q^{77} +(-4.23256 - 13.0265i) q^{79} +(-3.11082 - 1.38503i) q^{81} +(3.38372 + 1.09944i) q^{83} +(-4.20687 - 9.44878i) q^{85} +(-5.97158 + 10.3431i) q^{87} +(-6.82145 + 3.93836i) q^{89} +(-5.52920 + 4.72675i) q^{91} +(0.118006 + 0.555173i) q^{93} +(1.15301 + 10.9702i) q^{95} +(-2.60582 + 12.2594i) q^{97} +(1.52747 + 4.03500i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 112 q + 20 q^{9}+O(q^{10}) $ 112 * q + 20 * q^9	$ 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) $ 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/572\mathbb{Z}\right)^\times$.

$n$	$287$	$353$	$365$
$\chi(n)$	$1$	$e\left(\frac{5}{6}\right)$	$e\left(\frac{2}{5}\right)$

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			0
$2$		0			0
$3$	0.136254	−	1.29637i	0.0786664	−	0.748461i	−0.882093	−	0.471076i	$-0.843866\pi$
$3$	0.136254	−	1.29637i	0.0786664	−	0.748461i	0.960759	−	0.277385i	$-0.0894677\pi$
$4$		0			0
$5$	2.36621	+	0.768828i	1.05820	+	0.343830i	0.785882	−	0.618377i	$-0.212209\pi$
$5$	2.36621	+	0.768828i	1.05820	+	0.343830i	0.272319	+	0.962207i	$0.412209\pi$
$6$		0			0
$7$	2.00645	−	0.210887i	0.758368	−	0.0797077i	0.282551	−	0.959252i	$-0.408819\pi$
$7$	2.00645	−	0.210887i	0.758368	−	0.0797077i	0.475817	+	0.879544i	$0.342153\pi$
$8$		0			0
$9$	1.27243	+	0.270463i	0.424142	+	0.0901542i
$10$		0			0
$11$	1.79345	+	2.78990i	0.540745	+	0.841186i
$11$	1.79345	+	2.78990i	0.540745	+	0.841186i
$12$		0			0
$13$	−2.97050	+	2.04356i	−0.823868	+	0.566782i
$13$	−2.97050	+	2.04356i	−0.823868	+	0.566782i
$14$		0			0
$15$	1.31909	−	2.96273i	0.340588	−	0.764974i
$16$		0			0
$17$	−2.78170	−	3.08939i	−0.674660	−	0.749286i	0.304469	−	0.952522i	$-0.401521\pi$
$17$	−2.78170	−	3.08939i	−0.674660	−	0.749286i	−0.979130	+	0.203236i	$0.934854\pi$
$18$		0			0
$19$	1.80329	+	4.05026i	0.413704	+	0.929194i	0.993436	+	0.114387i	$0.0364905\pi$
$19$	1.80329	+	4.05026i	0.413704	+	0.929194i	−0.579732	+	0.814807i	$0.696843\pi$
$20$		0			0
$21$		−	2.62984i		−	0.573879i
$22$		0			0
$23$	3.17599	+	5.50098i	0.662240	+	1.14703i	0.980026	+	0.198871i	$0.0637276\pi$
$23$	3.17599	+	5.50098i	0.662240	+	1.14703i	−0.317785	+	0.948163i	$0.602939\pi$
$24$		0			0
$25$	0.962763	+	0.699488i	0.192553	+	0.139898i
$26$		0			0
$27$	1.73242	−	5.33183i	0.333404	−	1.02611i
$28$		0			0
$29$	−8.37016	−	3.72663i	−1.55430	−	0.692019i	−0.563346	−	0.826221i	$-0.690486\pi$
$29$	−8.37016	−	3.72663i	−1.55430	−	0.692019i	−0.990954	+	0.134203i	$0.957153\pi$
$30$		0			0
$31$	−0.414109	+	0.134552i	−0.0743762	+	0.0241663i	−0.345969	−	0.938246i	$-0.612450\pi$
$31$	−0.414109	+	0.134552i	−0.0743762	+	0.0241663i	0.271593	+	0.962412i	$0.412450\pi$
$32$		0			0
$33$	3.86111	−	1.94484i	0.672134	−	0.338554i
$34$		0			0
$35$	4.90982	+	1.04362i	0.829912	+	0.176403i
$36$		0			0
$37$	3.71248	−	8.33836i	0.610328	−	1.37082i	−0.298806	−	0.954314i	$-0.596588\pi$
$37$	3.71248	−	8.33836i	0.610328	−	1.37082i	0.909134	−	0.416505i	$-0.136745\pi$
$38$		0			0
$39$	2.24447	+	4.12931i	0.359404	+	0.661219i
$40$		0			0
$41$	1.61319	+	0.169554i	0.251939	+	0.0264798i	0.229656	−	0.973272i	$-0.426240\pi$
$41$	1.61319	+	0.169554i	0.251939	+	0.0264798i	0.0222828	+	0.999752i	$0.492907\pi$
$42$		0			0
$43$	3.97220	−	6.88005i	0.605754	−	1.04920i	−0.386177	−	0.922425i	$-0.626205\pi$
$43$	3.97220	−	6.88005i	0.605754	−	1.04920i	0.991932	−	0.126773i	$-0.0404619\pi$
$44$		0			0
$45$	2.80289	+	1.61825i	0.417830	+	0.241234i
$46$		0			0
$47$	1.62734	−	2.23984i	0.237371	−	0.326714i	−0.673667	−	0.739035i	$-0.735282\pi$
$47$	1.62734	−	2.23984i	0.237371	−	0.326714i	0.911039	+	0.412321i	$0.135282\pi$
$48$		0			0
$49$	−2.86565	+	0.609113i	−0.409379	+	0.0870162i
$50$		0			0
$51$	−4.38401	+	3.18517i	−0.613885	+	0.446013i
$52$		0			0
$53$	0.597134	+	1.83779i	0.0820226	+	0.252440i	0.983655	−	0.180064i	$-0.0576304\pi$
$53$	0.597134	+	1.83779i	0.0820226	+	0.252440i	−0.901632	+	0.432503i	$0.857630\pi$
$54$		0			0
$55$	2.09872	+	7.98034i	0.282992	+	1.07607i
$56$		0			0
$57$	5.49636	−	1.78587i	0.728010	−	0.236545i
$58$		0			0
$59$	−3.77974	+	0.397266i	−0.492080	+	0.0517197i	−0.347319	−	0.937747i	$-0.612908\pi$
$59$	−3.77974	+	0.397266i	−0.492080	+	0.0517197i	−0.144761	+	0.989467i	$0.546241\pi$
$60$		0			0
$61$	−5.91547	−	6.56980i	−0.757399	−	0.841177i	0.233975	−	0.972243i	$-0.424827\pi$
$61$	−5.91547	−	6.56980i	−0.757399	−	0.841177i	−0.991374	+	0.131066i	$0.958160\pi$
$62$		0			0
$63$	2.61010	+	0.274333i	0.328842	+	0.0345627i
$64$		0			0
$65$	−8.59996	+	2.55169i	−1.06669	+	0.316499i
$66$		0			0
$67$	−11.0917	+	6.40378i	−1.35506	+	0.782346i	−0.988954	−	0.148225i	$-0.952644\pi$
$67$	−11.0917	+	6.40378i	−1.35506	+	0.782346i	−0.366110	+	0.930572i	$0.619311\pi$
$68$		0			0
$69$	7.56406	−	3.36774i	0.910606	−	0.405428i
$70$		0			0
$71$	9.41908	−	8.48098i	1.11784	−	1.00651i	0.117930	−	0.993022i	$-0.462374\pi$
$71$	9.41908	−	8.48098i	1.11784	−	1.00651i	0.999909	−	0.0134853i	$-0.00429263\pi$
$72$		0			0
$73$	−0.624856	−	0.860040i	−0.0731338	−	0.100660i	0.770883	−	0.636977i	$-0.219815\pi$
$73$	−0.624856	−	0.860040i	−0.0731338	−	0.100660i	−0.844017	+	0.536317i	$0.819815\pi$
$74$		0			0
$75$	1.03798	−	1.15279i	0.119855	−	0.133113i
$76$		0			0
$77$	4.18682	+	5.21959i	0.477133	+	0.594827i
$78$		0			0
$79$	−4.23256	−	13.0265i	−0.476200	−	1.46559i	−0.844333	−	0.535819i	$-0.820003\pi$
$79$	−4.23256	−	13.0265i	−0.476200	−	1.46559i	0.368133	−	0.929773i	$-0.379997\pi$
$80$		0			0
$81$	−3.11082	−	1.38503i	−0.345647	−	0.153892i
$82$		0			0
$83$	3.38372	+	1.09944i	0.371411	+	0.120679i	0.488774	−	0.872410i	$-0.337444\pi$
$83$	3.38372	+	1.09944i	0.371411	+	0.120679i	−0.117363	+	0.993089i	$0.537444\pi$
$84$		0			0
$85$	−4.20687	−	9.44878i	−0.456299	−	1.02486i
$86$		0			0
$87$	−5.97158	+	10.3431i	−0.640220	+	1.10889i
$88$		0			0
$89$	−6.82145	+	3.93836i	−0.723072	+	0.417466i	−0.815882	−	0.578218i	$-0.803748\pi$
$89$	−6.82145	+	3.93836i	−0.723072	+	0.417466i	0.0928104	+	0.995684i	$0.470415\pi$
$90$		0			0
$91$	−5.52920	+	4.72675i	−0.579618	+	0.495498i
$92$		0			0
$93$	0.118006	+	0.555173i	0.0122366	+	0.0575687i
$94$		0			0
$95$	1.15301	+	10.9702i	0.118297	+	1.12552i
$96$		0			0
$97$	−2.60582	+	12.2594i	−0.264580	+	1.24475i	0.622309	+	0.782772i	$0.286195\pi$
$97$	−2.60582	+	12.2594i	−0.264580	+	1.24475i	−0.886889	+	0.461982i	$0.847139\pi$
$98$		0			0
$99$	1.52747	+	4.03500i	0.153516	+	0.405533i
$100$		0			0
$101$	−10.3998	+	11.5501i	−1.03482	+	1.14928i	−0.0461831	+	0.998933i	$0.514706\pi$
$101$	−10.3998	+	11.5501i	−1.03482	+	1.14928i	−0.988633	+	0.150347i	$0.951961\pi$
$102$		0			0
$103$	−3.08429	+	2.24087i	−0.303904	+	0.220799i	−0.729276	−	0.684219i	$-0.760143\pi$
$103$	−3.08429	+	2.24087i	−0.303904	+	0.220799i	0.425372	+	0.905018i	$0.360143\pi$
$104$		0			0
$105$	2.02190	−	6.22276i	0.197317	−	0.607279i
$106$		0			0
$107$	−0.356699	+	3.39376i	−0.0344834	+	0.328088i	0.963658	+	0.267140i	$0.0860788\pi$
$107$	−0.356699	+	3.39376i	−0.0344834	+	0.328088i	−0.998141	+	0.0609471i	$0.980588\pi$
$108$		0			0
$109$			5.55450i			0.532025i	0.963970	+	0.266012i	$0.0857062\pi$
$109$			5.55450i			0.532025i	−0.963970	+	0.266012i	$0.914294\pi$
$110$		0			0
$111$	−10.3038	−	5.94889i	−0.977992	−	0.564644i
$112$		0			0
$113$	17.1365	−	7.62965i	1.61206	−	0.717737i	0.614595	−	0.788843i	$-0.289319\pi$
$113$	17.1365	−	7.62965i	1.61206	−	0.717737i	0.997469	+	0.0711057i	$0.0226528\pi$
$114$		0			0
$115$	3.28576	+	15.4583i	0.306398	+	1.44149i
$116$		0			0
$117$	−4.33245	+	1.79687i	−0.400535	+	0.166121i
$118$		0			0
$119$	−6.23285	−	5.61209i	−0.571365	−	0.514459i
$120$		0			0
$121$	−4.56708	+	10.0071i	−0.415189	+	0.909735i
$122$		0			0
$123$	0.439609	−	2.06820i	0.0396382	−	0.186483i
$124$		0			0
$125$	−5.57168	−	7.66875i	−0.498346	−	0.685914i
$126$		0			0
$127$	−18.4574	+	3.92323i	−1.63783	+	0.348131i	−0.932617	−	0.360869i	$-0.882480\pi$
$127$	−18.4574	+	3.92323i	−1.63783	+	0.348131i	−0.705209	+	0.708999i	$0.749147\pi$
$128$		0			0
$129$	−8.37787	−	6.08688i	−0.737631	−	0.535920i
$130$		0			0
$131$	6.78054			0.592419			0.296209	−	0.955123i	$-0.404277\pi$
$131$	6.78054			0.592419			0.296209	+	0.955123i	$0.404277\pi$
$132$		0			0
$133$	4.47237	+	7.74637i	0.387804	+	0.671696i
$134$		0			0
$135$	8.19852	−	11.2843i	0.705616	−	0.971197i
$136$		0			0
$137$	10.8658	−	9.78359i	0.928326	−	0.835869i	−0.0583947	−	0.998294i	$-0.518598\pi$
$137$	10.8658	−	9.78359i	0.928326	−	0.835869i	0.986721	+	0.162425i	$0.0519315\pi$
$138$		0			0
$139$	1.35390	+	12.8815i	0.114836	+	1.09259i	0.888462	+	0.458949i	$0.151774\pi$
$139$	1.35390	+	12.8815i	0.114836	+	1.09259i	−0.773626	+	0.633642i	$0.781559\pi$
$140$		0			0
$141$	−2.68193	−	2.41482i	−0.225859	−	0.203365i
$142$		0			0
$143$	−11.0288	−	4.62236i	−0.922272	−	0.386542i
$144$		0			0
$145$	−16.9404	−	15.2532i	−1.40682	−	1.26671i
$146$		0			0
$147$	0.399180	+	3.79795i	0.0329238	+	0.313249i
$148$		0			0
$149$	−7.66353	+	6.90027i	−0.627821	+	0.565292i	−0.920414	−	0.390945i	$-0.872148\pi$
$149$	−7.66353	+	6.90027i	−0.627821	+	0.565292i	0.292594	+	0.956237i	$0.405482\pi$
$150$		0			0
$151$	0.00566417	−	0.00779606i	0.000460944	−	0.000634435i	−0.808786	−	0.588102i	$-0.799875\pi$
$151$	0.00566417	−	0.00779606i	0.000460944	−	0.000634435i	0.809247	+	0.587468i	$0.199875\pi$
$152$		0			0
$153$	−2.70394	−	4.68336i	−0.218601	−	0.378627i
$154$		0			0
$155$	−1.08332			−0.0870140
$156$		0			0
$157$	−9.54076	−	6.93177i	−0.761436	−	0.553215i	0.137915	−	0.990444i	$-0.455960\pi$
$157$	−9.54076	−	6.93177i	−0.761436	−	0.553215i	−0.899350	+	0.437229i	$0.855960\pi$
$158$		0			0
$159$	2.46382	−	0.523701i	0.195394	−	0.0415322i
$160$		0			0
$161$	7.53257	+	10.3677i	0.593649	+	0.817088i
$162$		0			0
$163$	0.354024	−	1.66555i	0.0277293	−	0.130456i	−0.962106	−	0.272677i	$-0.912091\pi$
$163$	0.354024	−	1.66555i	0.0277293	−	0.130456i	0.989835	+	0.142221i	$0.0454243\pi$
$164$		0			0
$165$	10.6315	−	1.63337i	0.827657	−	0.127158i
$166$		0			0
$167$	−7.13121	−	6.42097i	−0.551830	−	0.496870i	0.345387	−	0.938460i	$-0.387748\pi$
$167$	−7.13121	−	6.42097i	−0.551830	−	0.496870i	−0.897217	+	0.441591i	$0.854414\pi$
$168$		0			0
$169$	4.64771	−	12.1408i	0.357516	−	0.933907i
$170$		0			0
$171$	1.19911	+	5.64139i	0.0916985	+	0.431408i
$172$		0			0
$173$	21.8764	−	9.73998i	1.66323	−	0.740517i	0.663260	−	0.748389i	$-0.269172\pi$
$173$	21.8764	−	9.73998i	1.66323	−	0.740517i	0.999969	+	0.00787183i	$0.00250571\pi$
$174$		0			0
$175$	2.07925	+	1.20046i	0.157177	+	0.0907460i
$176$		0			0
$177$			4.95407i			0.372371i
$178$		0			0
$179$	−1.13247	+	10.7747i	−0.0846447	+	0.805341i	0.867035	+	0.498248i	$0.166023\pi$
$179$	−1.13247	+	10.7747i	−0.0846447	+	0.805341i	−0.951680	+	0.307093i	$0.900644\pi$
$180$		0			0
$181$	−3.59341	+	11.0594i	−0.267096	+	0.822037i	0.724107	+	0.689687i	$0.242252\pi$
$181$	−3.59341	+	11.0594i	−0.267096	+	0.822037i	−0.991203	+	0.132349i	$0.957748\pi$
$182$		0			0
$183$	−9.32291	+	6.77349i	−0.689170	+	0.500711i
$184$		0			0
$185$	15.1953	−	16.8761i	1.11718	−	1.24075i
$186$		0			0
$187$	3.63025	−	13.3013i	0.265470	−	0.972688i
$188$		0			0
$189$	2.35160	−	11.0634i	0.171054	−	0.804745i
$190$		0			0
$191$	−0.832569	−	7.92136i	−0.0602425	−	0.573170i	−0.982457	−	0.186490i	$-0.940289\pi$
$191$	−0.832569	−	7.92136i	−0.0602425	−	0.573170i	0.922214	−	0.386679i	$-0.126378\pi$
$192$		0			0
$193$	−4.90352	−	23.0693i	−0.352963	−	1.66056i	−0.693595	−	0.720365i	$-0.743974\pi$
$193$	−4.90352	−	23.0693i	−0.352963	−	1.66056i	0.340632	−	0.940197i	$-0.389359\pi$
$194$		0			0
$195$	2.13616	+	11.4964i	0.152974	+	0.823277i
$196$		0			0
$197$	−15.5462	+	8.97561i	−1.10762	+	0.639486i	−0.938212	−	0.346060i	$-0.887519\pi$
$197$	−15.5462	+	8.97561i	−1.10762	+	0.639486i	−0.169409	+	0.985546i	$0.554186\pi$
$198$		0			0
$199$	−5.95015	+	10.3060i	−0.421795	+	0.730570i	−0.996115	−	0.0880605i	$-0.971933\pi$
$199$	−5.95015	+	10.3060i	−0.421795	+	0.730570i	0.574320	+	0.818631i	$0.305266\pi$
$200$		0			0
$201$	6.79040	+	15.2515i	0.478958	+	1.07576i
$202$		0			0
$203$	−17.5802	−	5.71216i	−1.23389	−	0.400915i
$204$		0			0
$205$	3.68680	+	1.64147i	0.257497	+	0.114645i
$206$		0			0
$207$	2.55341	+	7.85858i	0.177474	+	0.546209i
$208$		0			0
$209$	−8.06572	+	12.2949i	−0.557917	+	0.850459i
$210$		0			0
$211$	−6.60360	+	7.33405i	−0.454611	+	0.504896i	−0.926258	−	0.376891i	$-0.876993\pi$
$211$	−6.60360	+	7.33405i	−0.454611	+	0.504896i	0.471647	+	0.881788i	$0.343660\pi$
$212$		0			0
$213$	−9.71112	−	13.3662i	−0.665395	−	0.915837i
$214$		0			0
$215$	14.6886	−	13.2257i	1.00176	−	0.901985i
$216$		0			0
$217$	−0.802515	+	0.357303i	−0.0544783	+	0.0242553i
$218$		0			0
$219$	−1.20007	+	0.692862i	−0.0810933	+	0.0468192i
$220$		0			0
$221$	14.5764	+	3.49244i	0.980513	+	0.234927i
$222$		0			0
$223$	27.7748	+	2.91924i	1.85994	+	0.195487i	0.967013	−	0.254725i	$-0.0819850\pi$
$223$	27.7748	+	2.91924i	1.85994	+	0.195487i	0.892922	+	0.450212i	$0.148652\pi$
$224$		0			0
$225$	1.03586	+	1.15044i	0.0690573	+	0.0766959i
$226$		0			0
$227$	5.17697	−	0.544121i	0.343607	−	0.0361146i	0.0688467	−	0.997627i	$-0.478068\pi$
$227$	5.17697	−	0.544121i	0.343607	−	0.0361146i	0.274761	+	0.961513i	$0.411401\pi$
$228$		0			0
$229$	−10.7866	+	3.50478i	−0.712799	+	0.231602i	−0.642898	−	0.765952i	$-0.722268\pi$
$229$	−10.7866	+	3.50478i	−0.712799	+	0.231602i	−0.0699006	+	0.997554i	$0.522268\pi$
$230$		0			0
$231$	7.33700	−	4.71649i	0.482739	−	0.310322i
$232$		0			0
$233$	−0.616091	−	1.89613i	−0.0403614	−	0.124220i	0.928846	−	0.370467i	$-0.120802\pi$
$233$	−0.616091	−	1.89613i	−0.0403614	−	0.124220i	−0.969207	+	0.246247i	$0.920802\pi$
$234$		0			0
$235$	5.57267	−	4.04878i	0.363521	−	0.264113i
$236$		0			0
$237$	−17.4639	+	3.71206i	−1.13440	+	0.241124i
$238$		0			0
$239$	7.56705	−	10.4152i	0.489472	−	0.673700i	−0.490819	−	0.871262i	$-0.663302\pi$
$239$	7.56705	−	10.4152i	0.489472	−	0.673700i	0.980290	+	0.197562i	$0.0633023\pi$
$240$		0			0
$241$	−4.30001	−	2.48261i	−0.276988	−	0.159919i	0.355071	−	0.934839i	$-0.384457\pi$
$241$	−4.30001	−	2.48261i	−0.276988	−	0.159919i	−0.632059	+	0.774920i	$0.717790\pi$
$242$		0			0
$243$	6.18995	−	10.7213i	0.397086	−	0.687773i
$244$		0			0
$245$	−7.24903	−	0.761904i	−0.463124	−	0.0486763i
$246$		0			0
$247$	−13.6336	−	8.34615i	−0.867488	−	0.531053i
$248$		0			0
$249$	1.88632	−	4.23675i	0.119541	−	0.268493i
$250$		0			0
$251$	26.8780	+	5.71308i	1.69652	+	0.360607i	0.951788	−	0.306756i	$-0.0992435\pi$
$251$	26.8780	+	5.71308i	1.69652	+	0.360607i	0.744733	+	0.667363i	$0.232577\pi$
$252$		0			0
$253$	−9.65121	+	18.7264i	−0.606766	+	1.17732i
$254$		0			0
$255$	−12.8223	+	4.16623i	−0.802966	+	0.260899i
$256$		0			0
$257$	23.5410	+	10.4811i	1.46845	+	0.653796i	0.976242	−	0.216683i	$-0.0695237\pi$
$257$	23.5410	+	10.4811i	1.46845	+	0.653796i	0.492207	+	0.870478i	$0.336190\pi$
$258$		0			0
$259$	5.69047	−	17.5135i	0.353588	−	1.08823i
$260$		0			0
$261$	−9.64250	−	7.00569i	−0.596856	−	0.433641i
$262$		0			0
$263$	8.64659	+	14.9763i	0.533172	+	0.923480i	0.999249	+	0.0387366i	$0.0123333\pi$
$263$	8.64659	+	14.9763i	0.533172	+	0.923480i	−0.466078	+	0.884744i	$0.654333\pi$
$264$		0			0
$265$			4.80769i			0.295334i
$266$		0			0
$267$	4.17614	+	9.37975i	0.255575	+	0.574032i
$268$		0			0
$269$	0.0846648	+	0.0940298i	0.00516210	+	0.00573310i	0.745720	−	0.666259i	$-0.232106\pi$
$269$	0.0846648	+	0.0940298i	0.00516210	+	0.00573310i	−0.740558	+	0.671992i	$0.765439\pi$
$270$		0			0
$271$	−0.139986	+	0.314414i	−0.00850354	+	0.0190993i	−0.917747	−	0.397165i	$-0.869994\pi$
$271$	−0.139986	+	0.314414i	−0.00850354	+	0.0190993i	0.909244	+	0.416264i	$0.136661\pi$
$272$		0			0
$273$	5.37425	+	7.81195i	0.325265	+	0.472800i
$274$		0			0
$275$	−0.224836	+	3.94051i	−0.0135581	+	0.237622i
$276$		0			0
$277$	10.9109	+	2.31918i	0.655572	+	0.139346i	0.523676	−	0.851918i	$-0.324560\pi$
$277$	10.9109	+	2.31918i	0.655572	+	0.139346i	0.131896	+	0.991264i	$0.457894\pi$
$278$		0			0
$279$	−0.563315	+	0.0592068i	−0.0337248	+	0.00354462i
$280$		0			0
$281$	14.4841	+	4.70617i	0.864048	+	0.280746i	0.707318	−	0.706895i	$-0.249905\pi$
$281$	14.4841	+	4.70617i	0.864048	+	0.280746i	0.156730	+	0.987642i	$0.449905\pi$
$282$		0			0
$283$	−1.41743	+	13.4859i	−0.0842572	+	0.801654i	0.868043	+	0.496490i	$0.165378\pi$
$283$	−1.41743	+	13.4859i	−0.0842572	+	0.801654i	−0.952300	+	0.305164i	$0.901289\pi$
$284$		0			0
$285$	14.3786			0.851712
$286$		0			0
$287$	3.27256			0.193173
$288$		0			0
$289$	−0.0294920	+	0.280597i	−0.00173482	+	0.0165057i
$290$		0			0
$291$	15.5377	+	5.04850i	0.910836	+	0.295948i
$292$		0			0
$293$	−1.25316	+	0.131713i	−0.0732106	+	0.00769475i	−0.141063	−	0.990001i	$-0.545052\pi$
$293$	−1.25316	+	0.131713i	−0.0732106	+	0.00769475i	0.0678523	+	0.997695i	$0.478385\pi$
$294$		0			0
$295$	−9.24907	−	1.96595i	−0.538502	−	0.114462i
$296$		0			0
$297$	17.9823	−	4.72910i	1.04344	−	0.274410i
$298$		0			0
$299$	−20.6759	−	9.85031i	−1.19572	−	0.569658i
$300$		0			0
$301$	6.51912	−	14.6422i	0.375756	−	0.843961i
$302$		0			0
$303$	13.5562	+	15.0557i	0.778786	+	0.864929i
$304$		0			0
$305$	−8.94620	−	20.0935i	−0.512258	−	1.15055i
$306$		0			0
$307$			7.13226i			0.407060i	0.979069	+	0.203530i	$0.0652414\pi$
$307$			7.13226i			0.407060i	−0.979069	+	0.203530i	$0.934759\pi$
$308$		0			0
$309$	2.48475	+	4.30371i	0.141352	+	0.244830i
$310$		0			0
$311$	24.3436	+	17.6866i	1.38040	+	1.00292i	0.996843	+	0.0793991i	$0.0253002\pi$
$311$	24.3436	+	17.6866i	1.38040	+	1.00292i	0.383554	+	0.923518i	$0.374700\pi$
$312$		0			0
$313$	−3.16094	+	9.72836i	−0.178667	+	0.549879i	−0.999782	−	0.0208830i	$-0.993352\pi$
$313$	−3.16094	+	9.72836i	−0.178667	+	0.549879i	0.821115	+	0.570762i	$0.193352\pi$
$314$		0			0
$315$	5.96513	+	2.65585i	0.336097	+	0.149640i
$316$		0			0
$317$	4.71975	−	1.53354i	0.265088	−	0.0861323i	−0.173457	−	0.984841i	$-0.555494\pi$
$317$	4.71975	−	1.53354i	0.265088	−	0.0861323i	0.438545	+	0.898709i	$0.355494\pi$
$318$		0			0
$319$	−4.61451	−	30.0354i	−0.258363	−	1.68166i
$320$		0			0
$321$	4.35098	+	0.924829i	0.242848	+	0.0516189i
$322$		0			0
$323$	7.49662	−	16.8377i	0.417123	−	0.936873i
$324$		0			0
$325$	−4.28933	−	0.110362i	−0.237929	−	0.00612176i
$326$		0			0
$327$	7.20070	+	0.756824i	0.398200	+	0.0418525i
$328$		0			0
$329$	2.79282	−	4.83731i	0.153973	−	0.266690i
$330$		0			0
$331$	−24.0725	−	13.8983i	−1.32314	−	0.763917i	−0.338915	−	0.940817i	$-0.610060\pi$
$331$	−24.0725	−	13.8983i	−1.32314	−	0.763917i	−0.984229	+	0.176900i	$0.943393\pi$
$332$		0			0
$333$	6.97907	−	9.60587i	0.382451	−	0.526398i
$334$		0			0
$335$	−31.1686	+	6.62509i	−1.70292	+	0.361968i
$336$		0			0
$337$	3.36744	−	2.44659i	0.183436	−	0.133274i	−0.492278	−	0.870438i	$-0.663835\pi$
$337$	3.36744	−	2.44659i	0.183436	−	0.133274i	0.675714	+	0.737164i	$0.263835\pi$
$338$		0			0
$339$	−7.55595	−	23.2548i	−0.410383	−	1.26303i
$340$		0			0
$341$	−1.11807	−	0.914010i	−0.0605469	−	0.0494964i
$342$		0			0
$343$	−19.0527	+	6.19059i	−1.02875	+	0.334260i
$344$		0			0
$345$	20.4874	−	2.15331i	1.10300	−	0.115930i
$346$		0			0
$347$	1.72633	+	1.91729i	0.0926743	+	0.102925i	0.787698	−	0.616062i	$-0.211273\pi$
$347$	1.72633	+	1.91729i	0.0926743	+	0.102925i	−0.695024	+	0.718987i	$0.744606\pi$
$348$		0			0
$349$	0.869192	+	0.0913557i	0.0465268	+	0.00489016i	0.127763	−	0.991805i	$-0.459220\pi$
$349$	0.869192	+	0.0913557i	0.0465268	+	0.00489016i	−0.0812365	+	0.996695i	$0.525887\pi$
$350$		0			0
$351$	5.74979	+	19.3785i	0.306901	+	1.03435i
$352$		0			0
$353$	3.42072	−	1.97495i	0.182067	−	0.105116i	−0.406197	−	0.913786i	$-0.633145\pi$
$353$	3.42072	−	1.97495i	0.182067	−	0.105116i	0.588263	+	0.808669i	$0.299812\pi$
$354$		0			0
$355$	28.8079	−	12.8261i	1.52897	−	0.680740i
$356$		0			0
$357$	−8.12461	+	7.31543i	−0.430000	+	0.387174i
$358$		0			0
$359$	12.1209	+	16.6829i	0.639715	+	0.880492i	0.998600	−	0.0528898i	$-0.0168432\pi$
$359$	12.1209	+	16.6829i	0.639715	+	0.880492i	−0.358886	+	0.933382i	$0.616843\pi$
$360$		0			0
$361$	−0.439287	+	0.487877i	−0.0231203	+	0.0256777i
$362$		0			0
$363$	12.3506	+	7.28415i	0.648240	+	0.382319i
$364$		0			0
$365$	−0.817316	−	2.51544i	−0.0427803	−	0.131664i
$366$		0			0
$367$	−10.6051	−	4.72169i	−0.553581	−	0.246470i	0.110828	−	0.993840i	$-0.464650\pi$
$367$	−10.6051	−	4.72169i	−0.553581	−	0.246470i	−0.664409	+	0.747369i	$0.731317\pi$
$368$		0			0
$369$	2.00681	+	0.652054i	0.104471	+	0.0339446i
$370$		0			0
$371$	1.58569	+	3.56151i	0.0823247	+	0.184904i
$372$		0			0
$373$	−7.63866	+	13.2305i	−0.395515	+	0.685051i	−0.993167	−	0.116704i	$-0.962767\pi$
$373$	−7.63866	+	13.2305i	−0.395515	+	0.685051i	0.597652	+	0.801756i	$0.296100\pi$
$374$		0			0
$375$	−10.7007	+	6.17807i	−0.552583	+	0.319034i
$376$		0			0
$377$	32.4791	−	6.03498i	1.67276	−	0.310817i
$378$		0			0
$379$	−5.73159	−	26.9650i	−0.294412	−	1.38510i	−0.837965	−	0.545724i	$-0.816255\pi$
$379$	−5.73159	−	26.9650i	−0.294412	−	1.38510i	0.543553	−	0.839375i	$-0.317079\pi$
$380$		0			0
$381$	2.57108	+	24.4622i	0.131720	+	1.25323i
$382$		0			0
$383$	−0.664886	+	3.12804i	−0.0339741	+	0.159836i	−0.991864	−	0.127299i	$-0.959369\pi$
$383$	−0.664886	+	3.12804i	−0.0339741	+	0.159836i	0.957890	+	0.287134i	$0.0927026\pi$
$384$		0			0
$385$	5.89393	+	15.5696i	0.300383	+	0.793499i
$386$		0			0
$387$	6.91513	−	7.68003i	0.351516	−	0.390398i
$388$		0			0
$389$	−15.0632	+	10.9440i	−0.763733	+	0.554884i	−0.900053	−	0.435781i	$-0.856472\pi$
$389$	−15.0632	+	10.9440i	−0.763733	+	0.554884i	0.136320	+	0.990665i	$0.456472\pi$
$390$		0			0
$391$	8.16001	−	25.1139i	0.412670	−	1.27007i
$392$		0			0
$393$	0.923878	−	8.79011i	0.0466035	−	0.443402i
$394$		0			0
$395$		−	34.0775i		−	1.71462i
$396$		0			0
$397$	−8.65306	−	4.99584i	−0.434284	−	0.250734i	0.266886	−	0.963728i	$-0.414005\pi$
$397$	−8.65306	−	4.99584i	−0.434284	−	0.250734i	−0.701170	+	0.712994i	$0.747339\pi$
$398$		0			0
$399$	10.6516	−	4.74238i	0.533245	−	0.237416i
$400$		0			0
$401$	−3.49744	−	16.4541i	−0.174654	−	0.821681i	−0.975011	−	0.222157i	$-0.928690\pi$
$401$	−3.49744	−	16.4541i	−0.174654	−	0.821681i	0.800357	−	0.599523i	$-0.204643\pi$
$402$		0			0
$403$	0.955144	−	1.24594i	0.0475791	−	0.0620649i
$404$		0			0
$405$	−6.29601	−	5.66895i	−0.312851	−	0.281692i
$406$		0			0
$407$	29.9213	−	4.59699i	1.48315	−	0.227864i
$408$		0			0
$409$	−5.11408	+	24.0599i	−0.252875	+	1.18968i	0.650052	+	0.759890i	$0.274747\pi$
$409$	−5.11408	+	24.0599i	−0.252875	+	1.18968i	−0.902927	+	0.429794i	$0.858586\pi$
$410$		0			0
$411$	−11.2027	−	15.4192i	−0.552587	−	0.760571i
$412$		0			0
$413$	−7.50008	+	1.59419i	−0.369055	+	0.0784451i
$414$		0			0
$415$	7.16130	+	5.20299i	0.351535	+	0.255405i
$416$		0			0
$417$	16.8836			0.826796
$418$		0			0
$419$	0.499047	+	0.864375i	0.0243800	+	0.0422275i	0.877958	−	0.478738i	$-0.158905\pi$
$419$	0.499047	+	0.864375i	0.0243800	+	0.0422275i	−0.853578	+	0.520965i	$0.825572\pi$
$420$		0			0
$421$	−20.4605	+	28.1615i	−0.997185	+	1.37251i	−0.0701488	+	0.997537i	$0.522347\pi$
$421$	−20.4605	+	28.1615i	−0.997185	+	1.37251i	−0.927036	+	0.374971i	$0.877653\pi$
$422$		0			0
$423$	2.67646	−	2.40989i	0.130134	−	0.117173i
$424$		0			0
$425$	−0.517124	−	4.92011i	−0.0250842	−	0.238660i
$426$		0			0
$427$	−13.2546	−	11.9345i	−0.641435	−	0.577551i
$428$		0			0
$429$	−7.49502	+	13.6676i	−0.361863	+	0.659877i
$430$		0			0
$431$	−9.04679	−	8.14577i	−0.435769	−	0.392368i	0.421840	−	0.906670i	$-0.361384\pi$
$431$	−9.04679	−	8.14577i	−0.435769	−	0.392368i	−0.857609	+	0.514302i	$0.828051\pi$
$432$		0			0
$433$	−1.88794	−	17.9626i	−0.0907287	−	0.863226i	−0.941346	−	0.337442i	$-0.890438\pi$
$433$	−1.88794	−	17.9626i	−0.0907287	−	0.863226i	0.850618	−	0.525785i	$-0.176228\pi$
$434$		0			0
$435$	−22.0820	+	19.8828i	−1.05875	+	0.953305i
$436$		0			0
$437$	−16.5532	+	22.7835i	−0.791846	+	1.08988i
$438$		0			0
$439$	−15.9398	−	27.6086i	−0.760767	−	1.31769i	−0.942455	−	0.334332i	$-0.891489\pi$
$439$	−15.9398	−	27.6086i	−0.760767	−	1.31769i	0.181688	−	0.983356i	$-0.441844\pi$
$440$		0			0
$441$	−3.81107			−0.181480
$442$		0			0
$443$	−9.20041	−	6.68449i	−0.437125	−	0.317590i	0.347367	−	0.937729i	$-0.387076\pi$
$443$	−9.20041	−	6.68449i	−0.437125	−	0.317590i	−0.784491	+	0.620140i	$0.787076\pi$
$444$		0			0
$445$	−19.1689	+	4.07447i	−0.908693	+	0.193149i
$446$		0			0
$447$	7.90113	+	10.8750i	0.373711	+	0.514369i
$448$		0			0
$449$	3.35608	−	15.7891i	0.158383	−	0.745133i	−0.825224	−	0.564806i	$-0.808951\pi$
$449$	3.35608	−	15.7891i	0.158383	−	0.745133i	0.983607	−	0.180327i	$-0.0577157\pi$
$450$		0			0
$451$	2.42015	+	4.80474i	0.113960	+	0.226246i
$452$		0			0
$453$	−0.00933483	−	0.00840512i	−0.000438589	−	0.000394907i
$454$		0			0
$455$	−16.7173	+	6.93347i	−0.783719	+	0.325046i
$456$		0			0
$457$	−0.388862	−	1.82945i	−0.0181902	−	0.0855782i	0.968116	−	0.250502i	$-0.0805956\pi$
$457$	−0.388862	−	1.82945i	−0.0181902	−	0.0855782i	−0.986306	+	0.164924i	$0.947262\pi$
$458$		0			0
$459$	−21.2911	+	9.47943i	−0.993786	+	0.442462i
$460$		0			0
$461$	−17.8866	−	10.3268i	−0.833062	−	0.480969i	0.0218379	−	0.999762i	$-0.493048\pi$
$461$	−17.8866	−	10.3268i	−0.833062	−	0.480969i	−0.854900	+	0.518793i	$0.826382\pi$
$462$		0			0
$463$		−	0.773917i		−	0.0359670i	−0.999838	−	0.0179835i	$-0.994275\pi$
$463$		−	0.773917i		−	0.0359670i	0.999838	−	0.0179835i	$-0.00572463\pi$
$464$		0			0
$465$	−0.147606	+	1.40438i	−0.00684508	+	0.0651266i
$466$		0			0
$467$	−3.62165	+	11.1463i	−0.167590	+	0.515789i	−0.999218	−	0.0395445i	$-0.987409\pi$
$467$	−3.62165	+	11.1463i	−0.167590	+	0.515789i	0.831628	+	0.555333i	$0.187409\pi$
$468$		0			0
$469$	−20.9044	+	15.1880i	−0.965278	+	0.701315i
$470$		0			0
$471$	−10.2861	+	11.4239i	−0.473959	+	0.526385i
$472$		0			0
$473$	26.3186	−	1.25698i	1.21013	−	0.0577960i
$474$		0			0
$475$	−1.09697	+	5.16082i	−0.0503323	+	0.236795i
$476$		0			0
$477$	0.262756	+	2.49995i	0.0120308	+	0.114465i
$478$		0			0
$479$	−3.70713	−	17.4407i	−0.169383	−	0.796884i	−0.978009	−	0.208561i	$-0.933122\pi$
$479$	−3.70713	−	17.4407i	−0.169383	−	0.796884i	0.808626	−	0.588323i	$-0.200211\pi$
$480$		0			0
$481$	6.01206	+	32.3558i	0.274126	+	1.47530i
$482$		0			0
$483$	14.4667	−	8.35237i	0.658259	−	0.380046i
$484$		0			0
$485$	−15.5913	+	27.0049i	−0.707963	+	1.22623i
$486$		0			0
$487$	−14.8185	−	33.2829i	−0.671491	−	1.50819i	−0.851404	−	0.524511i	$-0.824248\pi$
$487$	−14.8185	−	33.2829i	−0.671491	−	1.50819i	0.179913	−	0.983683i	$-0.442418\pi$
$488$		0			0
$489$	−2.11094	−	0.685886i	−0.0954600	−	0.0310168i
$490$		0			0
$491$	2.89461	+	1.28877i	0.130632	+	0.0581612i	0.471012	−	0.882127i	$-0.343889\pi$
$491$	2.89461	+	1.28877i	0.130632	+	0.0581612i	−0.340380	+	0.940288i	$0.610556\pi$
$492$		0			0
$493$	11.7702	+	36.2250i	0.530104	+	1.63149i
$494$		0			0
$495$	0.512086	+	10.7220i	0.0230166	+	0.481919i
$496$		0			0
$497$	17.1104	−	19.0030i	0.767507	−	0.852403i
$498$		0			0
$499$	7.95364	+	10.9472i	0.356054	+	0.490066i	0.949044	−	0.315144i	$-0.102053\pi$
$499$	7.95364	+	10.9472i	0.356054	+	0.490066i	−0.592990	+	0.805210i	$0.702053\pi$
$500$		0			0
$501$	−9.29563	+	8.36982i	−0.415298	+	0.373936i
$502$		0			0
$503$	−11.6580	+	5.19049i	−0.519805	+	0.231432i	−0.649832	−	0.760078i	$-0.725161\pi$
$503$	−11.6580	+	5.19049i	−0.519805	+	0.231432i	0.130026	+	0.991511i	$0.458494\pi$
$504$		0			0
$505$	−33.4881	+	19.3344i	−1.49020	+	0.860368i
$506$		0			0
$507$	−15.1057	−	7.67939i	−0.670868	−	0.341054i
$508$		0			0
$509$	−38.2383	−	4.01900i	−1.69488	−	0.178139i	−0.792734	−	0.609567i	$-0.791343\pi$
$509$	−38.2383	−	4.01900i	−1.69488	−	0.178139i	−0.902147	+	0.431428i	$0.858010\pi$
$510$		0			0
$511$	−1.43511	−	1.59386i	−0.0634857	−	0.0705081i
$512$		0			0
$513$	24.7194	−	2.59811i	1.09139	−	0.114709i
$514$		0			0
$515$	−9.02091	+	2.93107i	−0.397509	+	0.129158i
$516$		0			0
$517$	9.16746	+	0.523074i	0.403185	+	0.0230048i
$518$		0			0
$519$	−9.64590	−	29.6870i	−0.423408	−	1.30312i
$520$		0			0
$521$	10.5652	−	7.67606i	0.462869	−	0.336294i	−0.331786	−	0.943355i	$-0.607651\pi$
$521$	10.5652	−	7.67606i	0.462869	−	0.336294i	0.794656	+	0.607060i	$0.207651\pi$
$522$		0			0
$523$	44.2876	−	9.41362i	1.93656	−	0.411629i	0.938823	−	0.344399i	$-0.111917\pi$
$523$	44.2876	−	9.41362i	1.93656	−	0.411629i	0.997738	−	0.0672299i	$-0.0214161\pi$
$524$		0			0
$525$	1.83954	−	2.53192i	0.0802843	−	0.110502i
$526$		0			0
$527$	1.56761	+	0.905060i	0.0682861	+	0.0394250i
$528$		0			0
$529$	−8.67387	+	15.0236i	−0.377125	+	0.653199i
$530$		0			0
$531$	−4.91688	−	0.516785i	−0.213375	−	0.0224266i
$532$		0			0
$533$	−5.13848	+	2.79301i	−0.222572	+	0.120979i
$534$		0			0
$535$	−3.45324	+	7.75611i	−0.149297	+	0.335326i
$536$		0			0
$537$	13.8137	+	2.93620i	0.596107	+	0.126706i
$538$		0			0
$539$	−6.83876	−	6.90247i	−0.294566	−	0.297310i
$540$		0			0
$541$	20.2223	−	6.57061i	0.869423	−	0.282493i	0.159864	−	0.987139i	$-0.448894\pi$
$541$	20.2223	−	6.57061i	0.869423	−	0.282493i	0.709559	+	0.704646i	$0.248894\pi$
$542$		0			0
$543$	13.8474	+	6.16528i	0.594251	+	0.264578i
$544$		0			0
$545$	−4.27045	+	13.1431i	−0.182926	+	0.562989i
$546$		0			0
$547$	−2.15378	−	1.56481i	−0.0920889	−	0.0669065i	0.540788	−	0.841159i	$-0.318126\pi$
$547$	−2.15378	−	1.56481i	−0.0920889	−	0.0669065i	−0.632877	+	0.774252i	$0.718126\pi$
$548$		0			0
$549$	−5.75012	−	9.95950i	−0.245409	−	0.425061i
$550$		0			0
$551$		−	40.6216i		−	1.73054i
$552$		0			0
$553$	−11.2395	−	25.2444i	−0.477954	−	1.07350i
$554$		0			0
$555$	−19.8072	−	21.9982i	−0.840770	−	0.933770i
$556$		0			0
$557$	−12.3067	+	27.6414i	−0.521453	+	1.17120i	0.440441	+	0.897782i	$0.354822\pi$
$557$	−12.3067	+	27.6414i	−0.521453	+	1.17120i	−0.961894	+	0.273422i	$0.911845\pi$
$558$		0			0
$559$	2.26041	+	28.5546i	0.0956050	+	1.20773i
$560$		0			0
$561$	−16.7488	−	6.51851i	−0.707135	−	0.275212i
$562$		0			0
$563$	28.8771	+	6.13803i	1.21703	+	0.258687i	0.771294	−	0.636479i	$-0.219610\pi$
$563$	28.8771	+	6.13803i	1.21703	+	0.258687i	0.445733	+	0.895166i	$0.352943\pi$
$564$		0			0
$565$	46.4144	−	4.87835i	1.95267	−	0.205234i
$566$		0			0
$567$	−6.53380	−	2.12296i	−0.274394	−	0.0891560i
$568$		0			0
$569$	2.56173	−	24.3732i	0.107393	−	1.02178i	−0.799571	−	0.600572i	$-0.794940\pi$
$569$	2.56173	−	24.3732i	0.107393	−	1.02178i	0.906964	−	0.421208i	$-0.138394\pi$
$570$		0			0
$571$	−11.8075			−0.494130			−0.247065	−	0.968999i	$-0.579466\pi$
$571$	−11.8075			−0.494130			−0.247065	+	0.968999i	$0.579466\pi$
$572$		0			0
$573$	−10.3825			−0.433734
$574$		0			0
$575$	−0.790143	+	7.51771i	−0.0329512	+	0.313510i
$576$		0			0
$577$	43.0482	+	13.9872i	1.79212	+	0.582295i	0.999620	−	0.0275783i	$-0.00877955\pi$
$577$	43.0482	+	13.9872i	1.79212	+	0.582295i	0.792499	+	0.609873i	$0.208780\pi$
$578$		0			0
$579$	−30.5745	+	3.21351i	−1.27063	+	0.133549i
$580$		0			0
$581$	7.02113	+	1.49239i	0.291285	+	0.0619146i
$582$		0			0
$583$	−4.05632	+	4.96192i	−0.167996	+	0.205502i
$584$		0			0
$585$	−11.6330	+	0.920875i	−0.480964	+	0.0380735i
$586$		0			0
$587$	−11.6933	+	26.2635i	−0.482633	+	1.08401i	0.494072	+	0.869421i	$0.335508\pi$
$587$	−11.6933	+	26.2635i	−0.482633	+	1.08401i	−0.976704	+	0.214589i	$0.931159\pi$
$588$		0			0
$589$	−1.29173	−	1.43461i	−0.0532249	−	0.0591122i
$590$		0			0
$591$	9.51750	+	21.3766i	0.391497	+	0.879318i
$592$		0			0
$593$			20.3662i			0.836341i	0.908369	+	0.418170i	$0.137329\pi$
$593$			20.3662i			0.836341i	−0.908369	+	0.418170i	$0.862671\pi$
$594$		0			0
$595$	−10.4335	−	18.0714i	−0.427732	−	0.740854i
$596$		0			0
$597$	12.5496	+	9.11784i	0.513622	+	0.373168i
$598$		0			0
$599$	1.17122	−	3.60463i	0.0478546	−	0.147281i	−0.924274	−	0.381730i	$-0.875328\pi$
$599$	1.17122	−	3.60463i	0.0478546	−	0.147281i	0.972129	+	0.234449i	$0.0753285\pi$
$600$		0			0
$601$	−14.5396	−	6.47344i	−0.593082	−	0.264057i	0.0881707	−	0.996105i	$-0.471898\pi$
$601$	−14.5396	−	6.47344i	−0.593082	−	0.264057i	−0.681253	+	0.732048i	$0.738565\pi$
$602$		0			0
$603$	−15.8453	+	5.14846i	−0.645271	+	0.209661i
$604$		0			0
$605$	−18.5004	+	20.1676i	−0.752148	+	0.819928i
$606$		0			0
$607$	−15.8500	−	3.36903i	−0.643333	−	0.136745i	−0.125318	−	0.992117i	$-0.539995\pi$
$607$	−15.8500	−	3.36903i	−0.643333	−	0.136745i	−0.518014	+	0.855372i	$0.673329\pi$
$608$		0			0
$609$	−9.80047	+	22.0122i	−0.397135	+	0.891980i
$610$		0			0
$611$	−0.256753	+	9.97899i	−0.0103871	+	0.403707i
$612$		0			0
$613$	36.3711	+	3.82275i	1.46901	+	0.154400i	0.804979	−	0.593303i	$-0.202176\pi$
$613$	36.3711	+	3.82275i	1.46901	+	0.154400i	0.664034	+	0.747702i	$0.268843\pi$
$614$		0			0
$615$	2.63030	−	4.55581i	0.106064	−	0.183708i
$616$		0			0
$617$	14.2238	+	8.21210i	0.572628	+	0.330607i	0.758198	−	0.652024i	$-0.226080\pi$
$617$	14.2238	+	8.21210i	0.572628	+	0.330607i	−0.185570	+	0.982631i	$0.559413\pi$
$618$		0			0
$619$	−3.09543	+	4.26050i	−0.124416	+	0.171244i	−0.866681	−	0.498862i	$-0.833751\pi$
$619$	−3.09543	+	4.26050i	−0.124416	+	0.171244i	0.742265	+	0.670106i	$0.233751\pi$
$620$		0			0
$621$	34.8325	−	7.40387i	1.39778	−	0.297107i
$622$		0			0
$623$	−12.8564	+	9.34070i	−0.515079	+	0.374227i
$624$		0			0
$625$	−9.12651	−	28.0885i	−0.365060	−	1.12354i
$626$		0			0
$627$	14.8398	+	12.1314i	0.592646	+	0.484482i
$628$		0			0
$629$	−36.0874	+	11.7255i	−1.43890	+	0.467527i
$630$		0			0
$631$	10.9210	−	1.14784i	0.434757	−	0.0456948i	0.115378	−	0.993322i	$-0.463192\pi$
$631$	10.9210	−	1.14784i	0.434757	−	0.0456948i	0.319379	+	0.947627i	$0.396526\pi$
$632$		0			0
$633$	8.60788	+	9.56002i	0.342133	+	0.379977i
$634$		0			0
$635$	−46.6903	−	4.90734i	−1.85285	−	0.194742i
$636$		0			0
$637$	7.26765	−	7.66551i	0.287955	−	0.303718i
$638$		0			0
$639$	14.2789	−	8.24392i	0.564864	−	0.326124i
$640$		0			0
$641$	6.67577	−	2.97224i	0.263677	−	0.117397i	−0.270640	−	0.962681i	$-0.587235\pi$
$641$	6.67577	−	2.97224i	0.263677	−	0.117397i	0.534317	+	0.845284i	$0.320569\pi$
$642$		0			0
$643$	9.55226	−	8.60090i	0.376704	−	0.339186i	−0.458930	−	0.888473i	$-0.651767\pi$
$643$	9.55226	−	8.60090i	0.376704	−	0.339186i	0.835634	+	0.549286i	$0.185100\pi$
$644$		0			0
$645$	−15.1440	−	20.8440i	−0.596296	−	0.820731i
$646$		0			0
$647$	−17.7777	+	19.7441i	−0.698912	+	0.776220i	−0.983202	−	0.182518i	$-0.941575\pi$
$647$	−17.7777	+	19.7441i	−0.698912	+	0.776220i	0.284291	+	0.958738i	$0.408242\pi$
$648$		0			0
$649$	−7.88710	−	9.83261i	−0.309596	−	0.385964i
$650$		0			0
$651$	0.353851	+	1.08904i	0.0138685	+	0.0426829i
$652$		0			0
$653$	−31.3402	−	13.9536i	−1.22644	−	0.546046i	−0.311734	−	0.950169i	$-0.600910\pi$
$653$	−31.3402	−	13.9536i	−1.22644	−	0.546046i	−0.914704	+	0.404124i	$0.867577\pi$
$654$		0			0
$655$	16.0442	+	5.21307i	0.626898	+	0.203692i
$656$		0			0
$657$	−0.562474	−	1.26334i	−0.0219442	−	0.0492875i
$658$		0			0
$659$	−19.8151	+	34.3207i	−0.771886	+	1.33695i	0.164642	+	0.986353i	$0.447353\pi$
$659$	−19.8151	+	34.3207i	−0.771886	+	1.33695i	−0.936528	+	0.350592i	$0.885980\pi$
$660$		0			0
$661$	−6.91011	+	3.98955i	−0.268772	+	0.155176i	−0.628329	−	0.777947i	$-0.716261\pi$
$661$	−6.91011	+	3.98955i	−0.268772	+	0.155176i	0.359557	+	0.933123i	$0.382928\pi$
$662$		0			0
$663$	6.51360	−	18.4205i	0.252967	−	0.715395i
$664$		0			0
$665$	4.62694	+	21.7680i	0.179425	+	0.844128i
$666$		0			0
$667$	−6.08342	−	57.8799i	−0.235551	−	2.24112i
$668$		0			0
$669$	7.56886	−	35.6087i	0.292629	−	1.37671i
$670$		0			0
$671$	7.71998	−	28.2862i	0.298027	−	1.09198i
$672$		0			0
$673$	−10.2307	+	11.3623i	−0.394364	+	0.437986i	−0.907327	−	0.420425i	$-0.861881\pi$
$673$	−10.2307	+	11.3623i	−0.394364	+	0.437986i	0.512963	+	0.858410i	$0.328548\pi$
$674$		0			0
$675$	5.39746	−	3.92148i	0.207748	−	0.150938i
$676$		0			0
$677$	6.04619	−	18.6083i	0.232374	−	0.715173i	−0.765085	−	0.643929i	$-0.777303\pi$
$677$	6.04619	−	18.6083i	0.232374	−	0.715173i	0.997459	−	0.0712441i	$-0.0226969\pi$
$678$		0			0
$679$	−2.64310	+	25.1474i	−0.101433	+	0.965070i
$680$		0			0
$681$		−	6.78542i		−	0.260018i
$682$		0			0
$683$	33.2314	+	19.1862i	1.27156	+	0.734138i	0.975282	−	0.220963i	$-0.0709199\pi$
$683$	33.2314	+	19.1862i	1.27156	+	0.734138i	0.296282	+	0.955101i	$0.404253\pi$
$684$		0			0
$685$	33.2326	−	14.7961i	1.26975	−	0.565330i
$686$		0			0
$687$	3.07378	+	14.4610i	0.117272	+	0.551721i
$688$		0			0
$689$	−5.52942	−	4.23887i	−0.210654	−	0.161488i
$690$		0			0
$691$	21.0004	+	18.9088i	0.798892	+	0.719326i	0.963696	−	0.267000i	$-0.0860325\pi$
$691$	21.0004	+	18.9088i	0.798892	+	0.719326i	−0.164804	+	0.986326i	$0.552699\pi$
$692$		0			0
$693$	3.91572	+	7.77392i	0.148746	+	0.295307i
$694$		0			0
$695$	−6.70002	+	31.5211i	−0.254146	+	1.19566i
$696$		0			0
$697$	−3.96360	−	5.45543i	−0.150132	−	0.206639i
$698$		0			0
$699$	−2.54204	+	0.540327i	−0.0961487	+	0.0204370i
$700$		0			0
$701$	12.6299	+	9.17616i	0.477025	+	0.346579i	0.800173	−	0.599770i	$-0.204741\pi$
$701$	12.6299	+	9.17616i	0.477025	+	0.346579i	−0.323148	+	0.946349i	$0.604741\pi$
$702$		0			0
$703$	40.4673			1.52625
$704$		0			0
$705$	−4.48943	−	7.77591i	−0.169082	−	0.292858i
$706$		0			0
$707$	−18.4309	+	25.3680i	−0.693165	+	0.954060i
$708$		0			0
$709$	27.5159	−	24.7754i	1.03338	−	0.930459i	0.0357562	−	0.999361i	$-0.488616\pi$
$709$	27.5159	−	24.7754i	1.03338	−	0.930459i	0.997623	+	0.0689013i	$0.0219494\pi$
$710$		0			0
$711$	−1.86244	−	17.7200i	−0.0698471	−	0.664551i
$712$		0			0
$713$	−2.05538	−	1.85067i	−0.0769745	−	0.0693081i
$714$		0			0
$715$	−22.5426	−	19.4167i	−0.843044	−	0.726144i
$716$		0			0
$717$	−12.4709	−	11.2288i	−0.465733	−	0.419348i
$718$		0			0
$719$	−8.40301e−5	0	0.000799493i	−3.13379e−6	0	2.98161e-5i	0.994520	−	0.104543i	$-0.0333381\pi$
$719$	−8.40301e−5	0	0.000799493i	−3.13379e−6	0	2.98161e-5i	−0.994523	+	0.104514i	$0.966671\pi$
$720$		0			0
$721$	−5.71591	+	5.14663i	−0.212872	+	0.191670i
$722$		0			0
$723$	−3.80428	+	5.23615i	−0.141483	+	0.194734i
$724$		0			0
$725$	−5.45174	−	9.44269i	−0.202473	−	0.350693i
$726$		0			0
$727$	−9.79402			−0.363240			−0.181620	−	0.983369i	$-0.558134\pi$
$727$	−9.79402			−0.363240			−0.181620	+	0.983369i	$0.558134\pi$
$728$		0			0
$729$	−21.3201	−	15.4899i	−0.789631	−	0.573701i
$730$		0			0
$731$	−32.3046	+	6.86655i	−1.19483	+	0.253968i
$732$		0			0
$733$	15.6936	+	21.6004i	0.579658	+	0.797830i	0.993658	−	0.112447i	$-0.0358687\pi$
$733$	15.6936	+	21.6004i	0.579658	+	0.797830i	−0.414000	+	0.910277i	$0.635869\pi$
$734$		0			0
$735$	−1.97542	+	9.29363i	−0.0728646	+	0.342801i
$736$		0			0
$737$	−37.7583	−	19.4598i	−1.39084	−	0.716811i
$738$		0			0
$739$	13.1466	+	11.8373i	0.483606	+	0.435441i	0.874522	−	0.484985i	$-0.161175\pi$
$739$	13.1466	+	11.8373i	0.483606	+	0.435441i	−0.390916	+	0.920426i	$0.627842\pi$
$740$		0			0
$741$	−12.6774	+	16.5371i	−0.465715	+	0.607505i
$742$		0			0
$743$	−1.90783	−	8.97565i	−0.0699916	−	0.329285i	0.929196	−	0.369588i	$-0.120501\pi$
$743$	−1.90783	−	8.97565i	−0.0699916	−	0.329285i	−0.999188	+	0.0403029i	$0.987168\pi$
$744$		0			0
$745$	−23.4386	+	10.4355i	−0.858725	+	0.382329i
$746$		0			0
$747$	4.00817	+	2.31412i	0.146651	+	0.0846693i
$748$		0			0
$749$			6.88465i			0.251560i
$750$		0			0
$751$	1.90120	−	18.0887i	0.0693758	−	0.660067i	−0.903476	−	0.428639i	$-0.858993\pi$
$751$	1.90120	−	18.0887i	0.0693758	−	0.660067i	0.972852	−	0.231428i	$-0.0743399\pi$
$752$		0			0
$753$	11.0685	−	34.0654i	0.403359	−	1.24141i
$754$		0			0
$755$	0.0193964	−	0.0140923i	0.000705909	−	0.000512873i
$756$		0			0
$757$	−5.20855	+	5.78468i	−0.189308	+	0.210248i	−0.830326	−	0.557278i	$-0.811846\pi$
$757$	−5.20855	+	5.78468i	−0.189308	+	0.210248i	0.641018	+	0.767526i	$0.278512\pi$
$758$		0			0
$759$	22.9614	+	15.0631i	0.833446	+	0.546756i
$760$		0			0
$761$	4.56810	−	21.4912i	0.165594	−	0.779056i	−0.814444	−	0.580243i	$-0.802958\pi$
$761$	4.56810	−	21.4912i	0.165594	−	0.779056i	0.980037	−	0.198814i	$-0.0637089\pi$
$762$		0			0
$763$	1.17137	+	11.1448i	0.0424065	+	0.403470i
$764$		0			0
$765$	−2.79739	−	13.1607i	−0.101140	−	0.475825i
$766$		0			0
$767$	10.4159	−	8.90420i	0.376095	−	0.321512i
$768$		0			0
$769$	−19.8949	+	11.4863i	−0.717429	+	0.414208i	−0.813806	−	0.581137i	$-0.802608\pi$
$769$	−19.8949	+	11.4863i	−0.717429	+	0.414208i	0.0963766	+	0.995345i	$0.469275\pi$
$770$		0			0
$771$	16.7950	−	29.0898i	0.604858	−	1.04764i
$772$		0			0
$773$	3.83626	+	8.61638i	0.137981	+	0.309910i	0.969298	−	0.245888i	$-0.0790796\pi$
$773$	3.83626	+	8.61638i	0.137981	+	0.309910i	−0.831318	+	0.555798i	$0.812413\pi$
$774$		0			0
$775$	−0.492806	−	0.160122i	−0.0177021	−	0.00575177i
$776$		0			0
$777$	−21.9286	−	9.76324i	−0.786684	−	0.350254i
$778$		0			0
$779$	2.22233	+	6.83962i	0.0796231	+	0.245055i
$780$		0			0
$781$	40.5537	+	11.0681i	1.45113	+	0.396048i
$782$		0			0
$783$	−34.3704	+	38.1722i	−1.22830	+	1.36416i
$784$		0			0
$785$	−17.2461	−	23.7372i	−0.615540	−	0.847217i
$786$		0			0
$787$	−7.92035	+	7.13152i	−0.282330	+	0.254211i	−0.798112	−	0.602508i	$-0.794168\pi$
$787$	−7.92035	+	7.13152i	−0.282330	+	0.254211i	0.515782	+	0.856720i	$0.327501\pi$
$788$		0			0
$789$	20.5930	−	9.16861i	0.733132	−	0.326411i
$790$		0			0
$791$	32.7745	−	18.9224i	1.16533	−	0.672803i
$792$		0			0
$793$	30.9977	+	7.42693i	1.10076	+	0.263738i
$794$		0			0
$795$	6.23255	+	0.655067i	0.221046	+	0.0232328i
$796$		0			0
$797$	−25.8487	−	28.7079i	−0.915608	−	1.01689i	−0.999791	−	0.0204351i	$-0.993495\pi$
$797$	−25.8487	−	28.7079i	−0.915608	−	1.01689i	0.0841835	−	0.996450i	$-0.473172\pi$
$798$		0			0
$799$	−11.4465	+	1.20307i	−0.404947	+	0.0425617i
$800$		0			0
$801$	−9.74497	+	3.16633i	−0.344322	+	0.111877i
$802$		0			0
$803$	1.27878	−	3.28572i	0.0451271	−	0.115951i
$804$		0			0
$805$	9.85266	+	30.3234i	0.347261	+	1.06876i
$806$		0			0
$807$	0.133434	−	0.0969452i	0.00469708	−	0.00341263i
$808$		0			0
$809$	44.5024	−	9.45928i	1.56462	−	0.332570i	0.657505	−	0.753451i	$-0.271612\pi$
$809$	44.5024	−	9.45928i	1.56462	−	0.332570i	0.907116	+	0.420880i	$0.138279\pi$
$810$		0			0
$811$	27.1023	−	37.3032i	0.951692	−	1.30989i	0.000920275	−	1.00000i	$-0.499707\pi$
$811$	27.1023	−	37.3032i	0.951692	−	1.30989i	0.950772	−	0.309892i	$-0.100293\pi$
$812$		0			0
$813$	0.388523	+	0.224314i	0.0136261	+	0.00786704i
$814$		0			0
$815$	2.11822	−	3.66886i	0.0741980	−	0.128515i
$816$		0			0
$817$	35.0290	+	3.68170i	1.22551	+	0.128806i
$818$		0			0
$819$	−8.31392	+	4.51900i	−0.290512	+	0.157907i
$820$		0			0
$821$	7.41542	−	16.6553i	0.258800	−	0.581274i	−0.736680	−	0.676241i	$-0.763608\pi$
$821$	7.41542	−	16.6553i	0.258800	−	0.581274i	0.995480	+	0.0949667i	$0.0302745\pi$
$822$		0			0
$823$	23.5538	+	5.00652i	0.821034	+	0.174516i	0.599232	−	0.800576i	$-0.295473\pi$
$823$	23.5538	+	5.00652i	0.821034	+	0.174516i	0.221802	+	0.975092i	$0.428806\pi$
$824$		0			0
$825$	5.07773	+	0.828382i	0.176784	+	0.0288406i
$826$		0			0
$827$	38.1882	−	12.4081i	1.32793	−	0.431472i	0.442722	−	0.896659i	$-0.354013\pi$
$827$	38.1882	−	12.4081i	1.32793	−	0.431472i	0.885213	+	0.465187i	$0.154013\pi$
$828$		0			0
$829$	−45.4402	−	20.2313i	−1.57820	−	0.702662i	−0.584159	−	0.811639i	$-0.698576\pi$
$829$	−45.4402	−	20.2313i	−1.57820	−	0.702662i	−0.994044	+	0.108977i	$0.965242\pi$
$830$		0			0
$831$	4.49318	−	13.8286i	0.155867	−	0.479708i
$832$		0			0
$833$	9.85316	+	7.15874i	0.341392	+	0.248036i
$834$		0			0
$835$	−11.9373	−	20.6760i	−0.413108	−	0.715524i
$836$		0			0
$837$			2.44106i			0.0843754i
$838$		0			0
$839$	7.67262	+	17.2330i	0.264888	+	0.594949i	0.996200	−	0.0870945i	$-0.0277582\pi$
$839$	7.67262	+	17.2330i	0.264888	+	0.594949i	−0.731312	+	0.682043i	$0.761092\pi$
$840$		0			0
$841$	36.7670	+	40.8339i	1.26783	+	1.40806i
$842$		0			0
$843$	8.07446	−	18.1355i	0.278099	−	0.624621i
$844$		0			0
$845$	20.3316	−	25.1544i	0.699429	−	0.865336i
$846$		0			0
$847$	−7.05328	+	21.0419i	−0.242353	+	0.723008i
$848$		0			0
$849$	17.2896	+	3.67502i	0.593378	+	0.126126i
$850$		0			0
$851$	57.6600	−	6.06031i	1.97656	−	0.207745i
$852$		0			0
$853$	−16.1047	−	5.23272i	−0.551413	−	0.179165i	0.0200408	−	0.999799i	$-0.493620\pi$
$853$	−16.1047	−	5.23272i	−0.551413	−	0.179165i	−0.571454	+	0.820634i	$0.693620\pi$
$854$		0			0
$855$	−1.49990	+	14.2706i	−0.0512956	+	0.488045i
$856$		0			0
$857$	−0.348964			−0.0119204			−0.00596018	−	0.999982i	$-0.501897\pi$
$857$	−0.348964			−0.0119204			−0.00596018	+	0.999982i	$0.501897\pi$
$858$		0			0
$859$	−11.7638			−0.401374			−0.200687	−	0.979655i	$-0.564317\pi$
$859$	−11.7638			−0.401374			−0.200687	+	0.979655i	$0.564317\pi$
$860$		0			0
$861$	0.445900	−	4.24245i	0.0151962	−	0.144582i
$862$		0			0
$863$	23.6576	+	7.68683i	0.805315	+	0.261663i	0.682612	−	0.730781i	$-0.260844\pi$
$863$	23.6576	+	7.68683i	0.805315	+	0.261663i	0.122703	+	0.992443i	$0.460844\pi$
$864$		0			0
$865$	59.2524	−	6.22768i	2.01464	−	0.211747i
$866$		0			0
$867$	0.359740	+	0.0764651i	0.0122174	+	0.00259689i
$868$		0			0
$869$	28.7517	−	35.1707i	0.975334	−	1.19308i
$870$		0			0
$871$	19.8613	−	41.6889i	0.672973	−	1.41258i
$872$		0			0
$873$	−6.63142	+	14.8944i	−0.224440	+	0.504099i
$874$		0			0
$875$	−12.7965	−	14.2120i	−0.432602	−	0.480453i
$876$		0			0
$877$	−1.65074	−	3.70762i	−0.0557416	−	0.125198i	0.883527	−	0.468379i	$-0.155162\pi$
$877$	−1.65074	−	3.70762i	−0.0557416	−	0.125198i	−0.939269	+	0.343182i	$0.888495\pi$
$878$		0			0
$879$			1.64251i			0.0554006i
$880$		0			0
$881$	23.2941	+	40.3466i	0.784799	+	1.35931i	0.929119	+	0.369781i	$0.120567\pi$
$881$	23.2941	+	40.3466i	0.784799	+	1.35931i	−0.144319	+	0.989531i	$0.546099\pi$
$882$		0			0
$883$	−17.4149	−	12.6527i	−0.586058	−	0.425796i	0.254845	−	0.966982i	$-0.417975\pi$
$883$	−17.4149	−	12.6527i	−0.586058	−	0.425796i	−0.840903	+	0.541186i	$0.817975\pi$
$884$		0			0
$885$	−3.80883	+	11.7224i	−0.128032	+	0.394043i
$886$		0			0
$887$	34.2320	+	15.2411i	1.14940	+	0.511746i	0.890870	−	0.454258i	$-0.150096\pi$
$887$	34.2320	+	15.2411i	1.14940	+	0.511746i	0.258529	+	0.966003i	$0.416762\pi$
$888$		0			0
$889$	−36.2065	+	11.7642i	−1.21433	+	0.394558i
$890$		0			0
$891$	−1.71501	−	11.1629i	−0.0574551	−	0.373970i
$892$		0			0
$893$	12.0065	+	2.55206i	0.401782	+	0.0854014i
$894$		0			0
$895$	−10.9636	+	24.6246i	−0.366472	+	0.823109i
$896$		0			0
$897$	−15.5868	+	25.4615i	−0.520430	+	0.850134i
$898$		0			0
$899$	3.96759	+	0.417010i	0.132326	+	0.0139081i
$900$		0			0
$901$	4.01660	−	6.95695i	0.133812	−	0.231770i
$902$		0			0
$903$	−18.0935	−	10.4463i	−0.602112	−	0.347630i
$904$		0			0
$905$	−17.0055	+	23.4061i	−0.565282	+	0.778044i
$906$		0			0
$907$	8.41092	−	1.78780i	0.279280	−	0.0593628i	−0.0661420	−	0.997810i	$-0.521069\pi$
$907$	8.41092	−	1.78780i	0.279280	−	0.0593628i	0.345422	+	0.938447i	$0.387736\pi$
$908$		0			0
$909$	−16.3568	+	11.8839i	−0.542522	+	0.394165i
$910$		0			0
$911$	10.8809	+	33.4880i	0.360501	+	1.10951i	0.952751	+	0.303753i	$0.0982397\pi$
$911$	10.8809	+	33.4880i	0.360501	+	1.10951i	−0.592250	+	0.805754i	$0.701760\pi$
$912$		0			0
$913$	3.00121	+	11.4120i	0.0993254	+	0.377682i
$914$		0			0
$915$	−27.2676	+	8.85978i	−0.901439	+	0.292895i
$916$		0			0
$917$	13.6048	−	1.42993i	0.449272	−	0.0472203i
$918$		0			0
$919$	25.7788	+	28.6303i	0.850364	+	0.944425i	0.999011	−	0.0444650i	$-0.0141583\pi$
$919$	25.7788	+	28.6303i	0.850364	+	0.944425i	−0.148646	+	0.988890i	$0.547492\pi$
$920$		0			0
$921$	9.24607	+	0.971801i	0.304668	+	0.0320219i
$922$		0			0
$923$	−10.6479	+	44.4412i	−0.350481	+	1.46280i
$924$		0			0
$925$	9.40682	−	5.43103i	0.309294	−	0.178571i
$926$		0			0
$927$	−4.53060	+	2.01715i	−0.148804	+	0.0662520i
$928$		0			0
$929$	16.0901	−	14.4876i	0.527900	−	0.475323i	−0.361552	−	0.932352i	$-0.617753\pi$
$929$	16.0901	−	14.4876i	0.527900	−	0.475323i	0.889452	+	0.457029i	$0.151086\pi$
$930$		0			0
$931$	−7.63468	−	10.5082i	−0.250217	−	0.344394i
$932$		0			0
$933$	26.2454	−	29.1485i	0.859235	−	0.954278i
$934$		0			0
$935$	18.8163	−	28.6826i	0.615360	−	0.938023i
$936$		0			0
$937$	5.93838	+	18.2764i	0.193998	+	0.597066i	0.999987	+	0.00513430i	$0.00163430\pi$
$937$	5.93838	+	18.2764i	0.193998	+	0.597066i	−0.805988	+	0.591931i	$0.798366\pi$
$938$		0			0
$939$	12.1809	+	5.42328i	0.397508	+	0.176982i
$940$		0			0
$941$	−29.2013	−	9.48807i	−0.951934	−	0.309302i	−0.208433	−	0.978037i	$-0.566836\pi$
$941$	−29.2013	−	9.48807i	−0.951934	−	0.309302i	−0.743501	+	0.668734i	$0.766836\pi$
$942$		0			0
$943$	4.19079	+	9.41266i	0.136471	+	0.306518i
$944$		0			0
$945$	14.0702	−	24.3704i	0.457705	−	0.792768i
$946$		0			0
$947$	37.1551	−	21.4515i	1.20738	−	0.697080i	0.245192	−	0.969474i	$-0.421149\pi$
$947$	37.1551	−	21.4515i	1.20738	−	0.697080i	0.962186	+	0.272395i	$0.0878156\pi$
$948$		0			0
$949$	3.61368	+	1.27782i	0.117305	+	0.0414796i
$950$		0			0
$951$	−1.34495	−	6.32751i	−0.0436131	−	0.205184i
$952$		0			0
$953$	−0.805055	−	7.65959i	−0.0260783	−	0.248118i	−0.999793	−	0.0203472i	$-0.993523\pi$
$953$	−0.805055	−	7.65959i	−0.0260783	−	0.248118i	0.973715	−	0.227771i	$-0.0731438\pi$
$954$		0			0
$955$	4.12013	−	19.3837i	0.133324	−	0.627242i
$956$		0			0
$957$	−39.5659	+	1.88967i	−1.27898	+	0.0610845i
$958$		0			0
$959$	19.7385	−	21.9218i	0.637388	−	0.707891i
$960$		0			0
$961$	−24.9261	+	18.1099i	−0.804069	+	0.584190i
$962$		0			0
$963$	−1.37176	+	4.22184i	−0.0442043	+	0.136047i
$964$		0			0
$965$	6.13353	−	58.3567i	0.197445	−	1.87857i
$966$		0			0
$967$		−	5.36132i		−	0.172409i	−0.996277	−	0.0862043i	$-0.972526\pi$
$967$		−	5.36132i		−	0.172409i	0.996277	−	0.0862043i	$-0.0274738\pi$
$968$		0			0
$969$	−20.8064	−	12.0126i	−0.668399	−	0.385901i
$970$		0			0
$971$	−52.2887	+	23.2804i	−1.67803	+	0.747105i	−0.678099	+	0.734971i	$0.737196\pi$
$971$	−52.2887	+	23.2804i	−1.67803	+	0.747105i	−0.999926	+	0.0121345i	$0.996137\pi$
$972$		0			0
$973$	5.43306	+	25.5605i	0.174176	+	0.819433i
$974$		0			0
$975$	−0.727509	+	5.54553i	−0.0232989	+	0.177599i
$976$		0			0
$977$	−7.62088	−	6.86187i	−0.243814	−	0.219531i	0.538159	−	0.842843i	$-0.319120\pi$
$977$	−7.62088	−	6.86187i	−0.243814	−	0.219531i	−0.781973	+	0.623312i	$0.785787\pi$
$978$		0			0
$979$	−23.2216	−	11.9679i	−0.742164	−	0.382496i
$980$		0			0
$981$	−1.50228	+	7.06769i	−0.0479643	+	0.225654i
$982$		0			0
$983$	−14.7706	−	20.3299i	−0.471108	−	0.648425i	0.505658	−	0.862734i	$-0.331250\pi$
$983$	−14.7706	−	20.3299i	−0.471108	−	0.648425i	−0.976766	+	0.214310i	$0.931250\pi$
$984$		0			0
$985$	−43.6863	+	9.28581i	−1.39196	+	0.295870i
$986$		0			0
$987$	−5.89042	−	4.27964i	−0.187494	−	0.136223i
$988$		0			0
$989$	50.4627			1.60462
$990$		0			0
$991$	−2.41016	−	4.17452i	−0.0765613	−	0.132608i	0.825203	−	0.564836i	$-0.191061\pi$
$991$	−2.41016	−	4.17452i	−0.0765613	−	0.132608i	−0.901764	+	0.432228i	$0.857727\pi$
$992$		0			0
$993$	−21.2973	+	29.3132i	−0.675849	+	0.930227i
$994$		0			0
$995$	−22.0028	+	19.8114i	−0.697536	+	0.628064i
$996$		0			0
$997$	−2.07268	−	19.7203i	−0.0656426	−	0.624547i	−0.977045	−	0.213032i	$-0.931666\pi$
$997$	−2.07268	−	19.7203i	−0.0656426	−	0.624547i	0.911403	−	0.411516i	$-0.135000\pi$
$998$		0			0
$999$	−38.0272	−	34.2398i	−1.20313	−	1.08330i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	572.2.bq.a.49.10	✓	112
11.9	even	5	inner	572.2.bq.a.361.5	yes	112
13.4	even	6	inner	572.2.bq.a.225.5	yes	112
143.108	even	30	inner	572.2.bq.a.537.10	yes	112

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
572.2.bq.a.49.10	✓	112	1.1	even	1	trivial
572.2.bq.a.225.5	yes	112	13.4	even	6	inner
572.2.bq.a.361.5	yes	112	11.9	even	5	inner
572.2.bq.a.537.10	yes	112	143.108	even	30	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:	\( N \)	\(=\)	\( 572 = 2^{2} \cdot 11 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	572.bq (of order \(30\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(0.136254 - 1.29637i) q^{3} +(2.36621 + 0.768828i) q^{5} +(2.00645 - 0.210887i) q^{7} +(1.27243 + 0.270463i) q^{9} +O(q^{10})\)	\(q+(0.136254 - 1.29637i) q^{3} +(2.36621 + 0.768828i) q^{5} +(2.00645 - 0.210887i) q^{7} +(1.27243 + 0.270463i) q^{9} +(1.79345 + 2.78990i) q^{11} +(-2.97050 + 2.04356i) q^{13} +(1.31909 - 2.96273i) q^{15} +(-2.78170 - 3.08939i) q^{17} +(1.80329 + 4.05026i) q^{19} -2.62984i q^{21} +(3.17599 + 5.50098i) q^{23} +(0.962763 + 0.699488i) q^{25} +(1.73242 - 5.33183i) q^{27} +(-8.37016 - 3.72663i) q^{29} +(-0.414109 + 0.134552i) q^{31} +(3.86111 - 1.94484i) q^{33} +(4.90982 + 1.04362i) q^{35} +(3.71248 - 8.33836i) q^{37} +(2.24447 + 4.12931i) q^{39} +(1.61319 + 0.169554i) q^{41} +(3.97220 - 6.88005i) q^{43} +(2.80289 + 1.61825i) q^{45} +(1.62734 - 2.23984i) q^{47} +(-2.86565 + 0.609113i) q^{49} +(-4.38401 + 3.18517i) q^{51} +(0.597134 + 1.83779i) q^{53} +(2.09872 + 7.98034i) q^{55} +(5.49636 - 1.78587i) q^{57} +(-3.77974 + 0.397266i) q^{59} +(-5.91547 - 6.56980i) q^{61} +(2.61010 + 0.274333i) q^{63} +(-8.59996 + 2.55169i) q^{65} +(-11.0917 + 6.40378i) q^{67} +(7.56406 - 3.36774i) q^{69} +(9.41908 - 8.48098i) q^{71} +(-0.624856 - 0.860040i) q^{73} +(1.03798 - 1.15279i) q^{75} +(4.18682 + 5.21959i) q^{77} +(-4.23256 - 13.0265i) q^{79} +(-3.11082 - 1.38503i) q^{81} +(3.38372 + 1.09944i) q^{83} +(-4.20687 - 9.44878i) q^{85} +(-5.97158 + 10.3431i) q^{87} +(-6.82145 + 3.93836i) q^{89} +(-5.52920 + 4.72675i) q^{91} +(0.118006 + 0.555173i) q^{93} +(1.15301 + 10.9702i) q^{95} +(-2.60582 + 12.2594i) q^{97} +(1.52747 + 4.03500i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 112 q + 20 q^{9}+O(q^{10}) \) 112 * q + 20 * q^9	\( 112 q + 20 q^{9} - 6 q^{11} + 11 q^{13} + 30 q^{15} + 16 q^{17} - 12 q^{19} + 6 q^{23} + 40 q^{25} - 12 q^{27} - 5 q^{29} + 9 q^{33} - 33 q^{35} - 45 q^{39} - 18 q^{41} + 30 q^{45} - 16 q^{49} + 48 q^{51} - 2 q^{53} - 20 q^{55} - 39 q^{59} + 4 q^{61} - 102 q^{63} - 6 q^{65} + 48 q^{67} + 34 q^{69} + 84 q^{71} - 56 q^{75} - 22 q^{77} - 24 q^{79} + 16 q^{81} + 60 q^{85} - 34 q^{87} - 66 q^{89} - 41 q^{91} + 123 q^{93} + 12 q^{95} - 15 q^{97}+O(q^{100}) \) 112 * q + 20 * q^9 - 6 * q^11 + 11 * q^13 + 30 * q^15 + 16 * q^17 - 12 * q^19 + 6 * q^23 + 40 * q^25 - 12 * q^27 - 5 * q^29 + 9 * q^33 - 33 * q^35 - 45 * q^39 - 18 * q^41 + 30 * q^45 - 16 * q^49 + 48 * q^51 - 2 * q^53 - 20 * q^55 - 39 * q^59 + 4 * q^61 - 102 * q^63 - 6 * q^65 + 48 * q^67 + 34 * q^69 + 84 * q^71 - 56 * q^75 - 22 * q^77 - 24 * q^79 + 16 * q^81 + 60 * q^85 - 34 * q^87 - 66 * q^89 - 41 * q^91 + 123 * q^93 + 12 * q^95 - 15 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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